title: Explicit Spectral formulae for scaling quantum graphs

abstract:
  We present an exact analytical solution of the spectral problem of quasi
one-dimensional scaling quantum graphs. Strongly stochastic in the classical
limit, these systems are frequently employed as models of quantum chaos. We
show that despite their classical stochasticity all scaling quantum graphs are
explicitly solvable in the form $E_n=f(n)$, where $n$ is the sequence number of
the energy level of the quantum graph and $f$ is a known function, which
depends only on the physical and geometrical properties of the quantum graph.
Our method of solution motivates a new classification scheme for quantum
graphs: we show that each quantum graph can be uniquely assigned an integer $m$
reflecting its level of complexity. We show that a taut string with piecewise
constant mass density provides an experimentally realizable analogue system of
scaling quantum graphs.


title:
Quantum adiabatic algorithm for Hilbert's tenth problem: I. The
  algorithm

abstract:
  We review the proposal of a quantum algorithm for Hilbert's tenth problem and
provide further arguments towards the proof that: (i) the algorithm terminates
after a finite time for any input of Diophantine equation; (ii) the final
ground state which contains the answer for the Diophantine equation can be
identified as the component state having better-than-even probability to be
found by measurement at the end time--even though probability for the final
ground state in a quantum adiabatic process need not monotonically increase
towards one in general. Presented finally are the reasons why our algorithm is
outside the jurisdiction of no-go arguments previously employed to show that
Hilbert's tenth problem is recursively non-computable.


title: Two and Three Qubits Geometry and Hopf Fibrations

abstract:
  This paper reviews recent attempts to describe the two- and three-qubit
Hilbert space geometries with the help of Hopf fibrations. In both cases, it is
shown that the associated Hopf map is strongly sensitive to states entanglement
content. In the two-qubit case, a generalization of the one-qubit celebrated
Bloch sphere representation is described.


title: Quantum correlations and secret bits

abstract:
  It is shown that (i) all entangled states can be mapped by single-copy
measurements into probability distributions containing secret correlations, and
(ii) if a probability distribution obtained from a quantum state contains
secret correlations, then this state has to be entangled. These results prove
the existence of a two-way connection between secret and quantum correlations
in the process of preparation. They also imply that either it is possible to
map any bound entangled state into a distillable probability distribution or
bipartite bound information exists.


title: A deterministic Bell model

abstract:
  Following ideas given by John Bell in a paper entitled \textit{Beables for
quantum field theory}, we show that it is possible to obtain a realistic and
deterministic interpretation of any quantum field-theoretic model involving
Fermi fields.


title: Beables for Quantum Electrodynamics

abstract:
  We show that it is possible to obtain a realistic and deterministic model,
based on a previous work of John Bell, which reproduces the experimental
predictions of the orthodox interpretation of quantum electrodynamics.


title: Interfacing quantum optical and solid state qubits

abstract:
  We present a generic model of coupling quantum optical and solid state
qubits, and the corresponding transfer protocols. The example discussed is a
trapped ion coupled to a charge qubit (e.g. Cooper pair box). To enhance the
coupling, and achieve compatibility between the different experimental setups
we introduce a superconducting cavity as the connecting element.


title: Violating Bell's inequalities in the vacuum

abstract:
  We employ an approach wherein vacuum entanglement is directly probed in a
controlled manner. The approach consists of having a pair of initially
nonentangled detectors locally interact with the field for a finite duration,
such that the two detectors remain causally disconnected, and then analyzing
the resulting detector mixed state. It is demonstrated that the correlations
between arbitrarily far-apart regions of the vacuum of a relativistic free
scalar field cannot be reproduced by a local hidden-variable model, and that as
a function of the distance L between the regions, the entanglement decreases at
a slower rate than exp(-(L/cT)^3).


title: Dispersion Relations and Relativistic Causality

abstract:
  In this paper we show that if the refractive index, or rather (n(w) -1)
satisfies the dispersion relations then, it is implied by Titchmarsh's theorem
that n(w) -> 1 as w -> infinity. Any other limiting value for n(w) would
violate relativistic causality, by which we mean not only that cause must
precede effect but also that signals cannot travel faster-than-c (the velocity
of light) in a vacuum. This paper does not claim to be a mathematically
rigorous proof, but the authors hope to have succeeded in supplying a very
convincing argument against faster-than-c light signals.
  Keywords: Dispersion relations, Kramers Kronig relations, Causality,
faster-than-c signals.


title: Quantum state targeting

abstract:
  We introduce a new primitive for quantum communication that we term "state
targeting" wherein the goal is to pass a test for a target state even though
the system upon which the test is performed is submitted prior to learning the
target state's identity. Success in state targeting can be described as having
some control over the outcome of the test. We show that increasing one's
control above a minimum amount implies an unavoidable increase in the
probability of failing the test. This is analogous to the unavoidable
disturbance to a quantum state that results from gaining information about its
identity, and can be shown to be a purely quantum effect. We provide some
applications of the results to the security analysis of cryptographic tasks
implemented between remote antagonistic parties. Although we focus on weak coin
flipping, the results are significant for other two-party protocols, such as
strong coin flipping, partially binding and concealing bit commitment, and bit
escrow. Furthermore, the results have significance not only for the traditional
notion of security in cryptography, that of restricting a cheater's ability to
bias the outcome of the protocol, but also on a novel notion of security that
arises only in the quantum context, that of cheat-sensitivity. Finally, our
analysis of state targeting leads to some interesting secondary results, for
instance, a generalization of Uhlmann's theorem and an operational
interpretation of the fidelity between two mixed states.


title: The volume of separable states is super-doubly-exponentially small

abstract:
  In this note we give sharp estimates on the volume of the set of separable
states on N qubits. In particular, the magnitude of the "effective radius" of
that set in the sense of volume is determined up to a factor which is a (small)
power of N, and thus precisely on the scale of powers of its dimension.
Additionally, one of the appendices contains sharp estimates (by known methods)
for the expected values of norms of the GUE random matrices. We employ standard
tools of classical convexity, high-dimensional probability and geometry of
Banach spaces.


title: Quantum Implication Algebras

abstract:
  Quantum implication algebras without complementation are formulated with the
same axioms for all five quantum implications. Previous formulations of
orthoimplication, orthomodular implication, and quasi-implication algebras are
analysed and put in perspective to each other and our results.


title:
Equivalences, Identities, Symmetric Differences, and Congruences in
  Orthomodular Lattices

abstract:
  It is shown that operations of equivalence cannot serve for building algebras
which would induce orthomodular lattices as the operations of implication can.
Several properties of equivalence operations have been investigated.
Distributivity of equivalence terms and several other 3 variable expressions
involving equivalence terms have been proved to hold in any orthomodular
lattice. Symmetric differences have been shown to reduce to complements of
equivalence terms. Some congruence relations related to equivalence operations
and symmetric differences have been considered.


title: Entanglement measure for the universal classes of fractons

abstract:
  We introduce the notion of entanglement measure for the universal classes of
fractons as an entanglement between ocuppation-numbers of fractons in the
lowest Landau levels and the rest of the many-body system of particles. This
definition came as an entropy of the probability distribution {\it \`a la}
Shannon. Fractons are charge-flux systems classified in universal classes of
particles or quasiparticles labelled by a fractal or Hausdorff dimension
defined within the interval $1 < h < 2$ and associated with the fractal quantum
curves of such objects. They carry rational or irrational values of spin and
the spin-statistics connection takes place in this fractal approach to the
fractional spin particles. We take into account the fractal von Neumann entropy
associated with the fractal distribution function which each universal class of
fractons satisfies. We consider the fractional quantum Hall effect-FQHE given
that fractons can model Hall states. According to our formulation entanglement
between occupaton-numbers in this context increases with the universality
classes of the quantum Hall transitions considered as fractal sets of dual
topological quantum numbers filling factors. We verify that the Hall states
have stronger entanglement between ocuppation-numbers and so we can consider
this resource for fracton quantum computing.


title:
Statistical properties of twin beams generated in spontaneous parametric
  downconversion

abstract:
  Measurement of photon-number statistics of fields composed of photon pairs
generated in spontaneous parametric downcoversion pumped by strong ultrashort
pulses is described. Final detection quantum efficiencies, noises as well as
possible loss of one or both photons from a pair are taken into account.
Measured data provided by an intensified single-photon CCD camera are analyzed
along the developed model. The joint signal-idler photon-number distribution is
obtained using the expectation maximization algorithm. Covariance of the signal
and idler photon-numbers equals 80 %. Statistics of the generated photon pairs
are identified to be Poissonian in our case. Distribution of the integrated
intensities of the signal and idler fields shows strong correlations between
the fields. Negative values of this distribution occurring in some regions
clearly demonstrate a nonclassical character of the light composed of photon
pairs.


title:
A high-efficiency quantum non-demolition single photon number resolving
  detector

abstract:
  We discuss a novel approach to the problem of creating a photon number
resolving detector using the giant Kerr nonlinearities available in
electromagnetically induced transparency. Our scheme can implement a photon
number quantum non-demolition measurement with high efficiency ($\sim$99%)
using less than 1600 atoms embedded in a dielectric waveguide.


title: Can Quantum Cryptography Imply Quantum Mechanics?

abstract:
  It has been suggested that the ability of quantum mechanics to allow secure
distribution of secret key together with its inability to allow bit commitment
or communicate superluminally might be sufficient to imply the rest of quantum
mechanics. I argue using a toy theory as a counterexample that this is not the
case. I further discuss whether an additional axiom (key storage) brings back
the quantum nature of the theory.


title: High-multipolar effects on the Casimir force: the non-retarded limit

abstract:
  We calculate exactly the Casimir force or dispersive force, in the
non-retarded limit, between a spherical nanoparticle and a substrate beyond the
London's or dipolar approximation. We find that the force is a non-monotonic
function of the distance between the sphere and the substrate, such that, it is
enhanced by several orders of magnitude as the sphere approaches the substrate.
Our results do not agree with previous predictions like the Proximity theorem
approach.


title: Stability of holonomic quantum computations

abstract:
  We study the stability of holonomic quantum computations with respect to
errors in assignment of control parameters. The general expression for fidelity
is obtaned. In the small errors limit the simple formulae for the fidelity
decrease rate is derived.


title: Uncertainty Relations for Joint Measurements of Noncommuting Observables

abstract:
  Universally valid uncertainty relations are proven in a model independent
formulation for inherent and unavoidable extra noises in arbitrary joint
measurements on single systems, from which Heisenber's original uncertainty
relation is proven valid for any joint measurements with statistically
independent noises.


title: Uncertainty principle for quantum instruments and computing

abstract:
  Recently, universally valid uncertainty relations have been established to
set a precision limit for any instruments given a disturbance constraint in a
form more general than the one originally proposed by Heisenberg. One of them
leads to a quantitative generalization of the Wigner-Araki-Yanase theorem on
the precision limit of measurements under conservation laws. Applying this, a
rigorous lower bound is obtained for the gate error probability of physical
implementations of Hadamard gates on a standard qubit of a spin 1/2 system by
interactions with control fields or ancilla systems obeying the angular
momentum conservation law.


title: Perfect correlations between noncommuting observables

abstract:
  The problem as to when two noncommuting observables are considered to have
the same value arises commonly, but shows a nontrivial difficulty. Here, an
answer is given by establishing the notion of perfect correlations between
noncommuting observables, and applied to obtain a criterion for precise
measurements of a given observable in a given state.


title: Probabilities as Measures of Information

abstract:
  We analyze the notion that physical theories are quantitative and testable by
observations in experiments. This leads us to propose a new, Bayesian,
interpretation of probabilities in physics that unifies their current use in
classical physical theories, experimental physics and quantum mechanics.
Probabilities are the result of quantifying the domain of possibilities that
results when we interpret observations within the framework of a physical
theory. They could also be said to be measures of information used to make
predictions based upon a physical theory.


title: Energy Dissipation in Quantum Computers

abstract:
  A method is described for calculating the heat generated in a quantum
computer due to loss of quantum phase information. Amazingly enough, this heat
generation can take place at zero temperature. and may explain why it is
impossible to extract energy from vacuum fluctuations. Implications for optical
computers and quantum cosmology are also briefly discussed.


title: Symmetric Informationally Complete Quantum Measurements

abstract:
  We consider the existence in arbitrary finite dimensions d of a POVM
comprised of d^2 rank-one operators all of whose operator inner products are
equal. Such a set is called a ``symmetric, informationally complete'' POVM
(SIC-POVM) and is equivalent to a set of d^2 equiangular lines in C^d.
SIC-POVMs are relevant for quantum state tomography, quantum cryptography, and
foundational issues in quantum mechanics. We construct SIC-POVMs in dimensions
two, three, and four. We further conjecture that a particular kind of
group-covariant SIC-POVM exists in arbitrary dimensions, providing numerical
results up to dimension 45 to bolster this claim.


title: Quantum Public-Key Cryptosystem Based on Classical NP-Complete Problem

abstract:
  We present a quantum public-key cryptosystem based on a classical NP-complete
problem related with finding a code word of a given weight in a linear binary
code.


title: Certain quantum key distribution achieved by using Bell states

abstract:
  A new protocol for quantum key distribution based on entanglement swapping is
presented. In this protocol, both certain key and random key can be generated
without any loss of security. It is this property differs our protocol from the
previous ones. The rate of generated key bits per particle is improved which
can approach six bits (4 random bits and 2 certain bits) per four particles.


title: Quantum message authentication based on classical NP-complete problem

abstract:
  This note presents a method to authenticate a quantum message based on
classical SN-S authentication code and the computations between different
quantum registers. If the pre-coding generator matrix in SN-S code is public,
the quantum scheme is a public-key data integrity scheme; if it is secret, the
quantum scheme is a hybrid data origin authentication scheme.


title: Comparative study of quantum anharmonic potentials

abstract:
  We perform a study of various anharmonic potentials using a recently
developed method. We calculate both the wave functions and the energy
eigenvalues for the ground and first excited states of the quartic, sextic and
octic potentials with high precision, comparing the results with other
techniques available in the literature.


title:
Two-Point Attack on the Two Nonorthogonal State QKD Protocol over a
  Fiber-Optic Channel

abstract:
  We suggest here a two-point eavesdropping strategy to two nonorthogonal
states protocol of quantum key distribution over a fiber-optic channel. Suppose
that the single-photon sources and detectors of Alice, Bob and Eves are ideal
ones, the two-point attack can break the two nonorthogonal states protocol if
the distance between Alice and Bob is sufficiently long. For single-photon type
B92 protocol, the upper bound of distance is about 30 kilometers. It is
interesting that Bennett's original multi-photon protocol is secure against
both two-point attack and beam splitting attack, even if the protocol is
realized with weak pulse source.


title:
The Uncertainty Relation in "Which-Way" Experiments: How to Observe
  Directly the Momentum Transfer using Weak Values

abstract:
  A which-way measurement destroys the twin-slit interference pattern. Bohr
argued that distinguishing between two slits a distance s apart gives the
particle a random momentum transfer \wp of order h/s. This was accepted for
more than 60 years, until Scully, Englert and Walther (SEW) proposed a
which-way scheme that, they claimed, entailed no momentum transfer. Storey,
Tan, Collett and Walls (STCW) in turn proved a theorem that, they claimed,
showed that Bohr was right. This work reviews and extends a recent proposal
[Wiseman, Phys. Lett. A 311, 285 (2003)] to resolve the issue using a
weak-valued probability distribution for momentum transfer, P_wv(\wp). We show
that P_wv(\wp) must be wider than h/6s. However, its moments can still be zero
because P_wv(\wp) is not necessarily positive definite. Nevertheless, it is
measurable in a way understandable to a classical physicist. We introduce a new
measure of spread for P_wv(\wp): half of the unit-confidence interval, and
conjecture that it is never less than h/4s. For an idealized example with
infinitely narrow slits, the moments of P_wv(\wp) and of the momentum
distributions are undefined unless a process of apodization is used. We show
that by considering successively smoother initial wave functions, successively
more moments of both P_wv(\wp) and the momentum distributions become defined.
For this example the moments of P_wv(\wp) are zero, and these are equal to the
changes in the moments of the momentum distribution. We prove that this
relation holds for schemes in which the moments of P_wv(\wp) are non-zero, but
only for the first two moments. We also compare these moments to those of two
other momentum-transfer distributions and \hat{p}_f-\hat{p}_i. We find
agreement between all of these, but again only for the first two moments.


title:
Invitation to the "Spooky" Quantum Phase-Locking Effect and its Link to
  1/F Fluctuations

abstract:
  An overview of the concept of phase-locking at the non linear, geometric and
quantum level is attempted, in relation to finite resolution measurements in a
communication receiver and its 1/f noise. Sine functions, automorphic functions
and cyclotomic arithmetic are respectively used as the relevant trigonometric
tools. The common point of the three topics is found to be the Mangoldt
function of prime number theory as the generator of low frequency noise in the
coupling coefficient, the scattering coefficient and in quantum critical
statistical states. Huyghens coupled pendulums, the Adler equation, the Arnold
map, continued fraction expansions, discrete Mobius transformations, Ford
circles, coherent and squeezed phase states, Ramanujan sums, the Riemann zeta
function and Bost and Connes KMS states are some but a few concepts which are
used synchronously in the paper.


title: Projective Measurement Scheme for Solid-State Qubits

abstract:
  We present an effective measurement scheme for the solid-state qubits that
does {\bf not} introduce extra decoherence to the qubits until the measurement
is switched on by a resonant pulse. The resonant pulse then maximally entangles
the qubit with the detector. The scheme has the feature of being projective,
noiseless, and switchable. This method is illustrated on the superconducting
persistent-current qubit, but can be applied to the measurement of a wide
variety of solid-state qubits, the {\bf direct} detection of the
electromagnetic signals of which gives poor resolution of the qubit states.


title:
Single-atom trajectories in higher-order transverse modes of a
  high-finesse optical cavity

abstract:
  Transits of single atoms through higher-order Hermite-Gaussian transverse
modes of a high-finesse optical cavity are observed. Compared to the
fundamental Gaussian mode, the use of higher-order modes increases the
information on the atomic position. The experiment is a first experimental step
towards the realisation of an atomic kaleidoscope.


title: Quantum theory of multimode fields: Applications to optical resonators

abstract:
  A recently developed technique for the system--and--bath quantization of open
optical cavities is applied to three resonator geometries: A one dimensional
dielectric, a Fabry--Perot resonator, and a dielectric disk. The
system--and--bath Hamiltonian for these geometries is derived starting from
Maxwell's equations and employed to compute the electromagnetic fields, the
resonances, and the cavity gain factors. Exact agreement is found with standard
quantization methods based on a modes--of--the--universe description. Our
analysis provides a microscopic justification for the system--and--bath
quantization even in the regime of spectrally overlapping modes.


title: Problems and Aspects of Energy-Driven Wavefunction Collapse Models

abstract:
  Four problematic circumstances are considered, involving models which
describe dynamical wavefunction collapse toward energy eigenstates, for which
it is shown that wavefunction collapse of macroscopic objects does not work
properly. In one case, a common particle position measuring situation, the
apparatus evolves to a superposition of macroscopically distinguishable states
(does not collapse to one of them as it should) because each such
particle/apparatus/environment state has precisely the same energy spectrum.
Second, assuming an experiment takes place involving collapse to one of two
possible outcomes which is permanently recorded, it is shown in general that
this can only happen in the unlikely case that the two apparatus states
corresponding to the two outcomes have disjoint energy spectra. Next, the
progressive narrowing of the energy spectrum due to the collapse mechanism is
considered. This has the effect of broadening the time evolution of objects as
the universe evolves. Two examples, one involving a precessing spin, the other
involving creation of an excited state followed by its decay, are presented in
the form of paradoxes. In both examples, the microscopic behavior predicted by
standard quantum theory is significantly altered under energy-driven collapse,
but this alteration is not observed by an apparatus when it is included in the
quantum description. The resolution involves recognition that the statevector
describing the apparatus does not collapse, but evolves to a superposition of
macroscopically different states.


title: Entanglement and purity of two-mode Gaussian states in noisy channels

abstract:
  We study the evolution of purity, entanglement and total correlations of
general two--mode Gaussian states of continuous variable systems in arbitrary
uncorrelated Gaussian environments. The time evolution of purity, Von Neumann
entropy, logarithmic negativity and mutual information is analyzed for a wide
range of initial conditions. In general, we find that a local squeezing of the
bath leads to a faster degradation of purity and entanglement, while it can
help to preserve the mutual information between the modes.


title: Superselection rules and quantum protocols

abstract:
  We show that superselection rules do not enhance the information-theoretic
security of quantum cryptographic protocols. Our analysis employs two quite
different methods. The first method uses the concept of a reference system --
in a world subject to a superselection rule, unrestricted operations can be
simulated by parties who share access to a reference system with suitable
properties. By this method, we prove that if an n-party protocol is secure in a
world subject to a superselection rule, then the security is maintained even if
the superselection rule is relaxed. However, the proof applies only to a
limited class of superselection rules, those in which the superselection
sectors are labeled by unitary irreducible representations of a compact
symmetry group. The second method uses the concept of the format of a message
sent between parties -- by verifying the format, the recipient of a message can
check whether the message could have been sent by a party who performed
charge-conserving operations. By this method, we prove that protocols subject
to general superselection rules (including those pertaining to nonabelian
anyons in two dimensions) are no more secure than protocols in the unrestricted
world. However, the proof applies only to two-party protocols. Our results show
in particular that, if no assumptions are made about the computational power of
the cheater, then secure quantum bit commitment and strong quantum coin
flipping with arbitrarily small bias are impossible in a world subject to
superselection rules.


title: Efficient simulation of one-dimensional quantum many-body systems

abstract:
  We present a numerical method to simulate the time evolution, according to a
Hamiltonian made of local interactions, of quantum spin chains and systems
alike. The efficiency of the scheme depends on the amount of the entanglement
involved in the simulated evolution. Numerical analysis indicate that this
method can be used, for instance, to efficiently compute time-dependent
properties of low-energy dynamics of sufficiently regular but otherwise
arbitrary one-dimensional quantum many-body systems.


title: Impossibility of distant indirect measurement of the quantum Zeno effect

abstract:
  We critically study the possibility of quantum Zeno effect for indirect
measurements. If the detector is prepared to detect the emitted signal from the
core system, and the detector does not reflect the signal back to the core
system, then we can prove the decay probability of the system is not changed by
the continuous measurement of the signal and the quantum Zeno effect never
takes place. This argument also applies to the quantum Zeno effect for
accelerated two-level systems, unstable particle decay, etc.


title: Experimental Realization of the Quantum Box Problem

abstract:
  The three-box problem is a gedankenexperiment designed to elucidate some
interesting features of quantum measurement and locality. A particle is
prepared in a particular superposition of three boxes, and later found in a
different (but nonorthogonal) superposition. It was predicted that appropriate
"weak" measurements of particle position in the interval between preparation
and post-selection would find the particle in two different places, each with
certainty. We verify these predictions in an optical experiment and address the
issues of locality and of negative probability.


title: Duality and Quantum Mechanics

abstract:
  This Festschrift in honour of J. A. de Azcarraga gives an introduction to the
concept of duality, i.e., to the relativity of the notion of a quantum, in the
context of the quantum mechanics of a finite number of degrees of freedom.
Although the concept of duality arises in string and M--theory, Vafa has argued
that it should also have a counterpart in quantum mechanics, before moving on
to second quantisation, fields, strings and branes. We illustrate our analysis
with the case when classical phase space is complex projective space, but our
conclusions can be generalised to other complex, symplectic phase spaces, both
compact and noncompact.


title:
Sufficient conditions of entanglement for tripartite and higher
  dimensional multipartite qubit density matrixes

abstract:
  In this paper we give the new sufficient conditions of entanglement for
multipartite qubit density matrixes. We discuss in detail the case for
tripartite qubit density matrixes. As a criterion in concrete application, its
steps are quite simple and easy to operate. Some examples and discussions are
given.
  PACC numbers: 03.67.Mn, 03.65.Ud, 03.67.Hk.


title:
One-spin quantum logic gates from exchange interactions and a global
  magnetic field

abstract:
  It has been widely assumed that one-qubit gates in spin-based quantum
computers suffer from severe technical difficulties. We show that one-qubit
gates can in fact be generated using only modest and presently feasible
technological requirements. Our solution uses only global magnetic fields and
controllable Heisenberg exchange interactions, thus circumventing the need for
single-spin addressing.


title: Loss of coherence in double-slit diffraction experiments

abstract:
  The effects of incoherence and decoherence in the double--slit experiment are
studied using both optical and quantum--phenomenological models. The results
are compared with experimental data obtained with cold neutrons.


title: A quantum trajectory description of decoherence

abstract:
  A complete theoretical treatment in many problems relevant to physics,
chemistry, and biology requires considering the action of the environment over
the system of interest. Usually the environment involves a relatively large
number of degrees of freedom, this making the problem numerically intractable
from a purely quantum-mechanical point of view. To overcome this drawback, a
new class of quantum trajectories is proposed. These trajectories, based on the
same grounds as Bohmian ones, are solely associated to the system reduced
density matrix, since the evolution of the environment degrees of freedom is
not considered explicitly. Within this approach, environment effects come into
play through a time-dependent damping factor that appears in the system
equations of motion. Apart from their evident computational advantage, this
type of trajectories also results very insightful to understand the system
decoherence. In particular, here we show the usefulness of these trajectories
analyzing decoherence effects in interference phenomena, taking as a working
model the well-known double-slit experiment.


title: The Minimum Distance Problem for Two-Way Entanglement Purification

abstract:
  Entanglement purification takes a number of noisy EPR pairs and processes
them to produce a smaller number of more reliable pairs. If this is done with
only a forward classical side channel, the procedure is equivalent to using a
quantum error-correcting code (QECC). We instead investigate entanglement
purification protocols with two-way classical side channels (2-EPPs) for finite
block sizes. In particular, we consider the analog of the minimum distance
problem for QECCs, and show that 2-EPPs can exceed the quantum Hamming bound
and the quantum Singleton bound. We also show that 2-EPPs can achieve the rate
k/n = 1 - (t/n) \log_2 3 - h(t/n) - O(1/n) (asymptotically reaching the quantum
Hamming bound), where the EPP produces at least k good pairs out of n total
pairs with up to t arbitrary errors, and h(x) = -x \log_2 x - (1-x) \log_2
(1-x) is the usual binary entropy. In contrast, the best known lower bound on
the rate of QECCs is the quantum Gilbert-Varshamov bound k/n \geq 1 - (2t/n)
\log_2 3 - h(2t/n). Indeed, in some regimes, the known upper bound on the
asymptotic rate of good QECCs is strictly below our lower bound on the
achievable rate of 2-EPPs.


title: The Meaning of Bell's Theorem

abstract:
  The import of Bell's Theorem is elucidated. The theorem's proof is
illustrated both heuristically and in mathematical detail in a pedagogical
fashion. In the same fashion, it is shown that the proof is correct
mathematically, but it doesn't require, as is usually thought, one to abandon
locality or realism.


title: Reaching optimally oriented molecular states by laser kicks

abstract:
  We present a strategy for post-pulse orientation aiming both at efficiency
and maximal duration within a rotational period. We first identify the
optimally oriented states which fulfill both requirements. We show that a
sequence of half-cycle pulses of moderate intensity can be devised for reaching
these target states.


title: Quantification of quantum correlation of ensemble of states

abstract:
  We present first measure of quantum correlation of an ensemble of multiparty
states. It is based on the idea of minimal entropy production in a locally
distinguishable basis measurement. It is shown to be a relative entropy
distance from a set of ensembles. For bipartite ensembles, which span the whole
bipartite Hilbert space, the measure is bounded below by average relative
entropy of entanglement. We naturally obtain a monotonicity axiom for any
measure of quantum correlation of ensembles. We evaluate this measure for
certain cases. Subsequently we use this measure to propose a complementarity
relation between our measure and the accessible information obtainable about
the ensemble under local operations. The measure along with the monotonicity
axiom are well-defined even for the case of a single system, where the
complementarity relation is seen to be yet another face of the "Heisenberg
uncertainty relation".


title: A note on information theoretic characterizations of physical theories

abstract:
  Clifton, Bub, and Halvorson [Foundations of Physics 33, 1561 (2003)] have
recently argued that quantum theory is characterized by its satisfaction of
three information-theoretic axioms. However, it is not difficult to construct
apparent counterexamples to the CBH characterization theorem. In this paper, we
discuss the limits of the characterization theorem, and we provide some
technical tools for checking whether a theory (specified in terms of the convex
structure of its state space) falls within these limits.


title:
Multi-Component Bell Inequality and its Violation for Continuous
  Variable Systems

abstract:
  Multi-component correlation functions are developed by utilizing d-outcome
measurements. Based on the multi-component correlation functions, we propose a
Bell inequality for bipartite d-dimensional systems. Violation of the Bell
inequality for continuous variable (CV) systems is investigated. The violation
of the original Einstein-Podolsky-Rosen state can exceed the Cirel'son bound,
the maximal violation is 2.96981. For finite value of squeezing parameter,
violation strength of CV states increases with dimension d. Numerical results
show that the violation strength of CV states with finite squeezing parameter
is stronger than that of original EPR state.


title: Dynamical symmetries and well-localized hydrogenic wave packets

abstract:
  A new method for constructing of composite coherent states of the hydrogen
atom, based on the dynamical group approach and various schemes of reduction to
subgroups, is presented. A wide class of well-localized (Gaussian) hydrogenic
wave packets for circular and elliptic orbits is found using the saddle-point
method.


title:
Using Conditional Phase Change Operations to Probe the Nature of Quantum
  Mechanical Systems

abstract:
  Recent developments in quantum computing suggest that it could be possible to
make conditional changes to the state of a quantum mechanical system without
resorting to classical observation. It is accomplished through collective
response of atoms comprising a lattice for the system and involves relative
phase adjustments only. We exploit this possibility and describe experimental
designs that could help elucidate quantum mechanical properties of these
systems and distinguish between interpretations.


title: Selecting ensembles for rare earth quantum computation

abstract:
  We discuss the issues surrounding the implementation of quantum computation
in rare-earth-ion doped solids. We describe a practical scheme for two qubit
gate operations which utilise experimentally available interactions between the
qubits. Possibilities for a scalable quantum computer are discussed.


title:
Pseudo-Hermitian Hamiltonians, indefinite inner product spaces and their
  symmetries

abstract:
  We extend the definition of generalized parity $P$, charge-conjugation $C$
and time-reversal $T$ operators to nondiagonalizable pseudo-Hermitian
Hamiltonians, and we use these generalized operators to describe the full set
of symmetries of a pseudo-Hermitian Hamiltonian according to a fourfold
classification. In particular we show that $TP$ and $CTP$ are the generators of
the antiunitary symmetries; moreover, a necessary and sufficient condition is
provided for a pseudo-Hermitian Hamiltonian $H$ to admit a $P$-reflecting
symmetry which generates the $P$-pseudounitary and the $P$-pseudoantiunitary
symmetries. Finally, a physical example is considered and some hints on the
$P$-unitary evolution of a physical system are also given.


title: On the Quantum Query Complexity of Detecting Triangles in Graphs

abstract:
  We show that in the quantum query model the complexity of detecting a
triangle in an undirected graph on $n$ nodes can be done using $O(n^{1+{3\over
7}}\log^{2}n)$ quantum queries. The same complexity bound applies for
outputting the triangle if there is any. This improves upon the earlier bound
of $O(n^{1+{1\over 2}})$.


title: Image formation by manipulation of the entangled angular spectrum

abstract:
  We demonstrate theoretical and experimentally how it is possible to
manipulate an entangled angular spectrum of twin beams, in order to reconstruct
correlated images with coincidence detection. The entangled angular spectrum
comes from the pump and the image is obtained only if signal and idler are
properly treated.


title:
Construction of entangled states with positive partial transposes based
  on indecomposable positive linear maps

abstract:
  We show that every entanglement with positive partial transpose may be
constructed from an indecomposable positive linear map between matrix algebras.


title:
Superluminal solutions to the Klein-Gordon equation and a causality
  problem

abstract:
  We present a new axially symmetric monochromatic free-space solution to the
Klein-Gordon equation propagating with a superluminal group velocity and show
that it gives rise to an imaginary part of the causal propagator outside the
light cone. We address the question about causality of the spacelike paths and
argue that the signal with a well-defined wavefront formed by the superluminal
modes would propagate in vacuum with the light speed.


title: Optical bistability in sideband output modes induced by squeezed vacuum

abstract:
  We consider $N$ two-level atoms in a ring cavity interacting with a broadband
squeezed vacuum centered at frequency $\omega_{s}$ and an input monochromatic
driving field at frequency $\omega $. We show that, besides the central mode
(at $\o$), many other {\em sideband modes} are produced at the output, with
frequencies shifted from $\omega $ by multiples of $ 2(\omega -\omega_{s})$.
Here we analyze the optical bistability of the two nearest sideband modes, one
red-shifted and the other blue-shifted.


title: Testing quantum correlations with nuclear probes

abstract:
  We investigated the feasibility of quantum-correlation measurements in
nuclear physics experiments. In a first approach, we measured spin correlations
of singlet-spin (1S0) proton pairs, which were generated in 1H(d,2He) and
12C(d,2He) nuclear charge-exchange reactions. The experiment was optimized for
a clean preparation of the 2He singlet state and offered a 2pi detection
geometry for both protons in the exit channel. Our results confirm the
effectiveness of the setup for theses studies, despite limitations of a small
data sample recorded during the feasibility studies.


title: Extracting joint weak values with local, single-particle measurements

abstract:
  Weak measurement is a new technique which allows one to describe the
evolution of postselected quantum systems. It appears to be useful for
resolving a variety of thorny quantum paradoxes, particularly when used to
study properties of pairs of particles. Unfortunately, such nonlocal or joint
observables often prove difficult to measure weakly in practice (for instance,
in optics -- a common testing ground for this technique -- strong photon-photon
interactions would be needed). Here we derive a general, experimentally
feasible, method for extracting these values from correlations between
single-particle observables.


title:
The Contextual Quantization and the Principle of Complementarity of
  Probabilities

abstract:
  The Principle of Complementarity of Probabilities based on of noncommutative
probability is introduced.


title: The Question Whether an Energy Gap Does Exist in Helium II or Not

abstract:
  The present paper makes an assumption on the existence of an energy gap in
Helium II. An experiment is proposed to verify this assumption.


title:
On separability of quantum states and the violation of Bell-type
  inequalities

abstract:
  In contrast to the wide-spread opinion that any separable quantum state
satisfies every classical probabilistic constraint, we present a simple example
where a separable quantum state does not satisfy the original Bell inequality
although the latter inequality, in its perfect correlation form, is valid for
all joint classical measurements. In a very general setting, we discuss
inequalities for joint experiments upon a bipartite quantum system in a
separable state. We derive quantum analogues of the original Bell inequality
and specify the conditions sufficient for a separable state to satisfy the
original Bell inequality. We introduce the extended CHSH inequality and prove
that, for any separable quantum state, this inequality holds for a variety of
linear combinations.


title: Dynamical decoherence in a cavity with a large number of two-level atoms

abstract:
  We consider a large number of two-level atoms interacting with the mode of a
cavity in the rotating-wave approximation (Tavis-Cummings model). We apply the
Holstein-Primakoff transformation to study the model in the limit of the number
of two-level atoms, all in their ground state, becoming very large. The unitary
evolution that we obtain in this approximation is applied to a macroscopic
superposition state showing that, when the coherent states forming the
superposition are enough distant, then the state collapses on a single coherent
state describing a classical radiation mode. This appear as a true dynamical
effect that could be observed in experiments with cavities.


title: Entanglement distillation for three-particle W class states

abstract:
  In this paper, we propose two general entanglement distillation protocols,
which can concentrate the non-maximally entangled pure W class state. The
general protocols are mainly based on the unitary transformation on the
auxiliary particle and one of the three entangled particles, and in the second
protocol, the entanglement distillation includes two meanings, namely,
extracting the concentrated tripartite entangled W state and obtaining the
maximally entangled bipartite state from the garbage state, which gives no
contribution to the distillation of non-maximally entangled pure W class state.
We can make use of the garbage in the distillation process, and make the
entanglement waste in quantum communication as small as possible. A feasible
physical scheme is suggested based on the cavity QED.


title:
Grandma's local realistic theory for the Greenberger-Horne-Zeilinger
  experiment

abstract:
  A realistic theory is constructed for the GHZ experiment. It is shown that
the theory is local and it reproduces all the probabilistic predictions of
quantum theory. This local realistic theory shows that GHZ had formulated
Einstein's locality or no-action-at-a-distance principle incorrectly in their
local realistic theory for the experiment.


title:
An optimal entropic uncertainty relation in a two-dimensional Hilbert
  space

abstract:
  We derive an optimal entropic uncertainty relation for an arbitrary pair of
observables in a two-dimensional Hilbert space. Such a result, for the simple
case we are considering, definitively improves all the entropic uncertainty
relations which have appeared in the literature.


title:
Reply to Comment on "Quantum inversion of cold atoms in a microcavity:
  spatial dependence"

abstract:
  The question raised by [Bastin and Martin 2003 J. Phys. B: At. Mol. Opt.
Phys. 36, 4201] is examined and used to explain in more detail a key point of
our calculations. They have sought to rebut criticisms raised by us of certain
techniques used in the calculation of the off-resonance case. It is also
explained why this result is not a problem for the off-resonance case, but, on
the contrary, opens the door to a general situation. Their comment is based on
a blatant misunderstanding of our proposal and as such is simply wrong.


title: Inequivalent classes of closed three-level systems

abstract:
  We show here that the $\Lambda$ and V configurations of three-level atomic
systems, while they have recently been shown to be equivalent for many
important physical quantities when driven with classical fields [M. B. Plenio,
Phys. Rev. A \textbf{62}, 015802 (2000)], are no longer equivalent when coupled
via a quantum field. We analyze the physical origin of such behavior and show
how the equivalence between these two configurations emerges in the
semiclassical limit.


title: Reversibility of continuous-variable quantum cloning

abstract:
  We analyze a reversibility of optimal Gaussian $1\to 2$ quantum cloning of a
coherent state using only local operations on the clones and classical
communication between them and propose a feasible experimental test of this
feature. Performing Bell-type homodyne measurement on one clone and anti-clone,
an arbitrary unknown input state (not only a coherent state) can be restored in
the other clone by applying appropriate local unitary displacement operation.
We generalize this concept to a partial LOCC reversal of the cloning and we
show that this procedure converts the symmetric cloner to an asymmetric cloner.
Further, we discuss a distributed LOCC reversal in optimal $1\to M$ Gaussian
cloning of coherent states which transforms it to optimal $1\to M'$ cloning for
$M'<M$. Assuming the quantum cloning as a possible eavesdropping attack on
quantum communication link, the reversibility can be utilized to improve the
security of the link even after the attack.


title: Nonlocal resources in the presence of Superselection Rules

abstract:
  Superselection rules severely alter the possible operations that can be
implemented on a distributed quantum system. Whereas the restriction to local
operations imposed by a bipartite setting gives rise to the notion of
entanglement as a nonlocal resource, the superselection rule associated with
particle number conservation leads to a new resource, the \emph{superselection
induced variance} of local particle number. We show that, in the case of pure
quantum states, one can quantify the nonlocal properties by only two additive
measures, and that all states with the same measures can be asymptotically
interconverted into each other by local operations and classical communication.
Furthermore we discuss how superselection rules affect the concepts of
majorization, teleportation and mixed state entanglement.


title: Fractal Noise in Quantum Ballistic and Diffusive Lattice Systems

abstract:
  We demonstrate fractal noise in the quantum evolution of wave packets moving
either ballistically or diffusively in periodic and quasiperiodic tight-binding
lattices, respectively. For the ballistic case with various initial
superpositions we obtain a space-time self-affine fractal $\Psi(x,t)$ which
verify the predictions by Berry for "a particle in a box", in addition to
quantum revivals. For the diffusive case self-similar fractal evolution is also
obtained. These universal fractal features of quantum theory might be useful in
the field of quantum information, for creating efficient quantum algorithms,
and can possibly be detectable in scattering from nanostructures.


title: Quantum algorithms for phase space tomography

abstract:
  We present efficient circuits that can be used for the phase space tomography
of quantum states. The circuits evaluate individual values or selected averages
of the Wigner, Kirkwood and Husimi distributions. These quantum gate arrays can
be programmed by initializing appropriate computational states. The Husimi
circuit relies on a subroutine that is also interesting in its own right: the
efficient preparation of a coherent state, which is the ground state of the
Harper Hamiltonian.


title: Quantum Mechanics without the quantum

abstract:
  Incompatibility between conjugate variables and complementary pictures comes
in two kinds, exclusive of one another. The first kind is unconditional, and
the second conditional on quantum's indivisibility. We employ this distinction
to study the wave-particle dualism and the energy-time uncertainty relation.
Afterwards we look upon the present state of the quantum mechanical formalism.
We demonstrate that the two incompatibilities are employed in the same
treatment forming a "hybrid" description of the phenomena and leading to a
contradiction.


title: Finite Size Universe or Perfect Squash Problem v2

abstract:
  We give a physical notion to all self-adjoint extensions of the operator
$id/dx$ in the finite interval. It appears that these extensions realize
different non-unitary equivalent representations of CCR and are related to the
momentum operator viewed from different inertial systems. This leads to the
generalization of Galilei equivalence principle and gives a new insight into
quantum correspondence rule. It is possible to get transformation laws of wave
function under Galilei transformation for any scalar potential. This
generalizes mass superselection rule. There is also given a new and general
interpretation of a momentum representation of wave function. It appears that
consistent treatment of this problem leads to the time-dependent interactions
and to the abrupt switching-off of the interaction.


title:
Critical fluctuations and entanglement in the nondegenerate parametric
  oscillator

abstract:
  We present a fully quantum mechanical treatment of the nondegenerate optical
parametric oscillator both below and near threshold. This is a non-equilibrium
quantum system with a critical point phase-transition, that is also known to
exhibit strong yet easily observed squeezing and quantum entanglement. Our
treatment makes use of the positive P-representation and goes beyond the usual
linearized theory. We compare our analytical results with numerical simulations
and find excellent agreement. We also carry out a detailed comparison of our
results with those obtained from stochastic electrodynamics, a theory obtained
by truncating the equation of motion for the Wigner function, with a view to
locating regions of agreement and disagreement between the two. We calculate
commonly used measures of quantum behavior including entanglement, squeezing
and EPR correlations as well as higher order tripartite correlations, and show
how these are modified as the critical point is approached. In general, the
critical fluctuations represent an ultimate limit to the possible entanglement
that can be achieved in a nondegenerate parametric oscillator.


title: Dreams versus Reality: Plenary Debate Session on Quantum Computing

abstract:
  This is a transcript of a debate on quantum computing that took place at
6:00pm, Wednesday, 4th June 2003, La Fonda Hotel, Santa Fe, USA. Transcript
editor: Derek Abbott. Pro Team: Carlton M. Caves, Daniel Lidar, Howard Brandt,
Alex Hamilton. Con Team: David Ferry, Julio Gea-Banacloche, Sergey Bezrukov,
Laszlo Kish.


title:
Understanding Time and Causality is the Key to Understanding Quantum
  Mechanics

abstract:
  A new interpretation of quantum mechanics, similar to the Copenhagen
interpretation, is developed from time-symmetry arguments and commonly held
principles concerning time and causality. These principles, which are grounded
in ideas outside of quantum mechanics, suggest that the strange features and
paradoxes of quantum mechanics come from backward causation, in which future
events can change the past. Using these principles this paper gives a better
understanding of (and reasons for) stationary states, tunneling, wave-particle
duality, the measurement problem with the collapse of the state vector, Hardy's
paradox, non-locality, and the EPR paradox. These are only a few of the
interpretational successes, and the model will be contrasted to other popular
and/or recent interpretations. Unfortunately, this model is metaphysical,
without any predictive power.


title: Special relativity and reduced spin density matrices

abstract:
  We derive the general formula for Lorentz-transformed spin density matrix. It
is shown that an appropriate Lorentz transformation can prduce totally
unpolarized state out of pure one. Further properties, as depurification by an
arbitrary Lorentz boost and its relation to the localization properties are
also discussed.


title: Quantum algorithms in group theory

abstract:
  We present a survey of quantum algorithms, primarily for an intended audience
of pure mathematicians. We place an emphasis on algorithms involving group
theory.


title: Quantum Algorithms for the Triangle Problem

abstract:
  We present two new quantum algorithms that either find a triangle (a copy of
$K_{3}$) in an undirected graph $G$ on $n$ nodes, or reject if $G$ is triangle
free. The first algorithm uses combinatorial ideas with Grover Search and makes
$\tilde{O}(n^{10/7})$ queries. The second algorithm uses $\tilde{O}(n^{13/10})$
queries, and it is based on a design concept of Ambainis~\cite{amb04} that
incorporates the benefits of quantum walks into Grover search~\cite{gro96}. The
first algorithm uses only $O(\log n)$ qubits in its quantum subroutines,
whereas the second one uses O(n) qubits. The Triangle Problem was first treated
in~\cite{bdhhmsw01}, where an algorithm with $O(n+\sqrt{nm})$ query complexity
was presented, where $m$ is the number of edges of $G$.


title: Conceptual analysis of quantum history theory

abstract:
  We give formal content to some concepts, naturally stemming from consistent
history approach (CHA), which are not formalized in the standard formulation of
the theory. The outcoming (extended) conceptual basis is used to perform a
formal, conceptually transparent analysis of some debated questions in CHA. As
results, the problems raised by contrary inferences of Kent are ruled out,
whereas some prescriptions of the theory cannot be mantained.


title: An Upper Bound on the Threshold Quantum Decoherence Rate

abstract:
  Let $\eta_0$ be the supremum of those $\eta$ for which every poly-size
quantum circuit can be simulated by another poly-size quantum circuit with
gates of fan-in $\leq 2$ that tolerates random noise independently occurring on
all wires at the constant rate $\eta$. Recent fundamental results showing the
principal fact $\eta_0>0$ give estimates like $\eta_0\geq 10^{-6}-10^{-4}$,
whereas the only upper bound known before is $\eta_0\leq 0.74$.
  In this note we improve the latter bound to $\eta_0\leq 1/2$, under the
assumption $QP\not\subseteq QNC^1$. More generally, we show that if the
decoherence rate $\eta$ is greater than 1/2, then we can not even store a
single qubit for more than logarithmic time. Our bound also generalizes to the
simulating circuits allowing gates of any (constant) fan-in $k$, in which case
we have $\eta_0\leq 1-1/k$.


title:
Multipartite entanglement, quantum-error-correcting codes, and
  entangling power of quantum evolutions

abstract:
  We investigate the average bipartite entanglement, over all possible
divisions of a multipartite system, as a useful measure of multipartite
entanglement. We expose a connection between such measures and
quantum-error-correcting codes by deriving a formula relating the weight
distribution of the code to the average entanglement of encoded states.
Multipartite entangling power of quantum evolutions is also investigated.


title: Revised Iterative Solution for Groundstate of Schroedinger Equation

abstract:
  A revised iterative method based on Green function defined by quadratures
along a single trajectory is proposed to solve the low-lying quantum wave
function for Schroedinger equation. Specially a new expression of the perturbed
energy is obtained, which is much simpler than the traditional one. The method
is applied to solve the unharmonic oscillator potential. The revised iteration
procedure gives exactly the same result as those based on the single trajectory
quadrature method. A comparison of the revised iteration method to the old one
is made using the example of Stark effect. The obtained results are consistent
to each other after making power expansion.


title: Entanglement and squeezing in a two-mode system: theory and experiment

abstract:
  We report on the generation of non separable beams produced via the
interaction of a linearly polarized beam with a cloud of cold cesium atoms
placed in an optical cavity. We convert the squeezing of the two linear
polarization modes into quadrature entanglement and show how to find out the
best entanglement generated in a two-mode system using the inseparability
criterion for continuous variable [Duan et al., Phys. Rev. Lett. 84, 2722
(2000)]. We verify this method experimentally with a direct measurement of the
inseparability using two homodyne detections. We then map this entanglement
into a polarization basis and achieve polarization entanglement.


title: Bell Inequalities for Position Measurements

abstract:
  Bell inequalities for position measurements are derived using the bits of the
binary expansion of position-measurement results. Violations of these
inequalities are obtained from the output state of the Non-degenerate Optical
Parametric Amplifier.


title: Schr\"odinger Quantization Problem and Neutron Stars

abstract:
  We are discussing the possibility to find a proper unique conditions for an
experimental study of the Schr\"odinger quantization problem in the neutron
stars physics. A simple toy model for physically different quantizations is
formulated and a possible physical consequences are derived.


title: Cloning of orthogonal mixed states entails irreversibility

abstract:
  Orthogonal pure states can be cloned as well as deleted. However if there is
an initial disorder in the system, that is for orthogonal mixed states, one
cannot perform deletion. And cloning, in such cases, necessarily produces an
irreversibility, in the form of leakage of information into the environment.


title: Spheroidal analysis of the generalized MIC-Kepler system

abstract:
  This paper deals with the dynamical system that generalizes the MIC-Kepler
system. It is shown that the Schr\"{o}dinger equation for this generalized
MIC-Kepler system can be separated in prolate spheroidal coordinates. The
coefficients of the interbasis expansions between three bases (spherical,
parabolic and spheroidal) are studied in detail. It is found that the
coefficients for this expansion of the parabolic basis in terms of the
spherical basis, and vice-versa, can be expresses through the Clebsch-Gordan
coefficients for the group SU(2) analytically continued to real values of their
arguments. The coefficients for the expansions of the prolate spheroidal basis
in terms of the spherical and parabolic bases are proved to satisfy three-term
recursion relations.


title: Quantum Cryptography: Security Criteria Reexamined

abstract:
  We find that the generally accepted security criteria are flawed for a whole
class of protocols for quantum cryptography. This is so because a standard
assumption of the security analysis, namely that the so-called square-root
measurement is optimal for eavesdropping purposes, is not true in general.
There are rather large parameter regimes in which the optimal measurement
extracts substantially more information than the square-root measurement.


title: Depurification by Lorentz boosts

abstract:
  We consider a particle of half-integer spin which is nonrelativistic in the
rest frame. Assuming the particle is completely polarized along third axis we
calculate the Bloch vector as seen by a moving observer. The result for its
length is expressed in terms of dispersion of some vector operator linear in
momentum. The relation with the localization properties is discussed.


title:
Canonical Form and Separability of PPT States in 2x2x2xN Composite
  Quantum Systems

abstract:
  We give a canonical form of PPT states in ${\cal C}^2 \otimes {\cal
C}^2\otimes {\cal C}^2 \otimes {\cal C}^N$ with rank=$N$. From this canonical
form a necessary separable condition for these states is presented.


title: Representations of Coherent States in Non-orthogonal Bases

abstract:
  Starting with the canonical coherent states, we demonstrate that all the
so-called nonlinear coherent states, used in the physical literature, as well
as large classes of other generalized coherent states, can be obtained by
changes of bases in the underlying Hilbert space. This observation leads to an
interesting duality between pairs of generalized coherent states, bringing into
play a Gelfand triple of (rigged) Hilbert spaces. Moreover, it is shown that in
each dual pair of families of nonlinear coherent states, at least one family is
related to a (generally) non-unitary projective representation of the
Weyl-Heisenberg group, which can then be thought of as characterizing the dual
pair.

categories: quant-ph math-ph math.MP physics.atom-ph


title: Polarization phase gate with a tripod atomic system

abstract:
  We analyze the nonlinear optical response of a four-level atomic system
driven into a tripod configuration. The large cross-Kerr nonlinearities that
occurr in such a system are shown to produce nonlinear phase shift of order
$\pi$. Such a substantial shift may be observed in a cold atomic gas in a
magneto-optical trap where it coupl be fasibly exploited towards the
realization of a polarization quantum phase gate. The experimental feasibility
of such a gate is here examined in detail.


title: Applications of Partial Supersymmetry

abstract:
  I examine quantum mechanical Hamiltonians with partial supersymmetry, and
explore two main applications. First, I analyze a theory with a logarithmic
spectrum, and show how to use partial supersymmetry to reveal the underlying
structure of this theory. This method reveals an intriguing equivalence between
two formulations of this theory, one of which is one-dimensional, and the other
of which is infinite-dimensional. Second, I demonstrate the use of partial
supersymmetry as a tool to obtain the asymptotic energy levels in
non-relativistic quantum mechanics in an exceptionally easy way. In the end, I
discuss possible extensions of this work, including the possible connections
between partial supersymmetry and renormalization group arguments.


title: Determination of continuous variable entanglement by purity measurements

abstract:
  We classify the entanglement of two--mode Gaussian states according to their
degree of total and partial mixedness. We derive exact bounds that determine
maximally and minimally entangled states for fixed global and marginal
purities. This characterization allows for an experimentally reliable estimate
of continuous variable entanglement based on measurements of purity.

categories: quant-ph cond-mat hep-th math-ph math.MP


title: Complete positivity and dissipative factorized dynamics: some comments

abstract:
  After reviewing the main properties of time-evolutions of open quantum
systems, some considerations about the positivity of factorized Markovian
dynamics for bipartite systems are made. In particular, it is shown that the
positivity of the whole time-evolution in general does not ask for the complete
positivity of the single system time-evolutions, if they are allowed to differ.
However, they must be completely positive if one is a small perturbation of the
other, which is the typical situation for open systems in a heat bath.


title:
A quantitative model for the effective decoherence of a quantum computer
  with imperfect unitary operations

abstract:
  The problem of the quantitative degradation of the performance of a quantum
computer due to noisy unitary gates (imperfect external control) is studied. It
is shown that quite general conclusions on the evolution of the fidelity can be
reached by using the conjecture that the set of states visited by a quantum
algorithm can be replaced by the uniform (Haar) ensemble. These general results
are tested numerically against quantum computer simulations of two particular
periodically driven quantum systems.


title: Quantum Feedback Control of Atomic Motion in an Optical Cavity

abstract:
  We study quantum feedback cooling of atomic motion in an optical cavity as a
prototypical nonlinear quantum control problem. We design a feedback algorithm
that can cool the atom to the ground state of the optical potential with high
efficiency despite the nonlinear nature of this problem. An important
ingredient is a simplified state-estimation algorithm, necessary for a
real-time implementation of the feedback loop. We also describe the critical
role of parity dynamics in the cooling process and present a simple theory that
predicts the achievable steady-state atomic energies.


title: Transmission Spectrum of an Optical Cavity Containing N Atoms

abstract:
  The transmission spectrum of a high-finesse optical cavity containing an
arbitrary number of trapped atoms is presented. We take spatial and motional
effects into account and show that in the limit of strong coupling, the
important spectral features can be determined for an arbitrary number of atoms,
N. We also show that these results have important ramifications in limiting our
ability to determine the number of atoms in the cavity.


title:
Classifying chemical elements and particles: from the atomic to the
  sub-atomic world

abstract:
  This paper presents two facets. First, we show that the periodic table of
chemical elements can be described, understood and modified (as far as its
format is concerned) on the basis of group theory and more specifically by
using the group SO(4,2)xSU(2). Second, we show that "periodic tables" also
exist in the sub-atomic and sub-nuclear worlds and that group theory is of
paramount importance for these tables. In that sense, this paper may be
considered as an excursion, for non specialists, into nuclear and particle
physics.

categories: quant-ph hep-th physics.chem-ph physics.hist-ph


title: Quantum and classical advantage distillation are not equivalent

abstract:
  We report that, for the generation of a secure cryptographic key from
correlations established through a noisy quantum channel, the quantum and
classical advantage distillation procedures are not equivalent, when coherent
eavesdropping attacks are duly taken into account. The quantum procedure can
tolerate markedly more noise in the channel than the classical procedure.


title: Low Energy Quantum System Simulation

abstract:
  A numerical method for solving Schrodinger's equation based upon a
Baker-Campbell-Hausdorff (BCH) expansion of the time evolution operator is
presented herein. The technique manifestly preserves wavefunction norm, and it
can be applied to problems in any number of spatial dimensions. We also
identify a particular dimensionless ratio of potential to kinetic energies as a
key coupling constant. This coupling establishes characteristic length and time
scales for a large class of low energy quantum states, and it guides the choice
of step sizes in numerical work. Using the BCH method in conjunction with an
imaginary time rotation, we compute low energy eigenstates for several quantum
systems coupled to non-trivial background potentials. The approach is
subsequently applied to the study of 1D propagating wave packets and 2D bound
state time development. Failures of classical expectations uncovered by
simulations of these simple systems help develop quantum intuition.
  Finally, we investigate the response of a Superconducting Quantum
Interference Device (SQUID) to a time dependent potential. We discuss how to
engineer the potential's energy and time scales so that the SQUID acts as a
quantum NOT gate. The notional simulation we present for this gate provides
useful insight into the design of one candidate building block for a quantum
computer.


title: Quantum-Mechanical Dualities on the Torus

abstract:
  On classical phase spaces admitting just one complex-differentiable
structure, there is no indeterminacy in the choice of the creation operators
that create quanta out of a given vacuum. In these cases the notion of a
quantum is universal, i.e., independent of the observer on classical phase
space. Such is the case in all standard applications of quantum mechanics.
However, recent developments suggest that the notion of a quantum may not be
universal. Transformations between observers that do not agree on the notion of
an elementary quantum are called dualities. Classical phase spaces admitting
more than one complex-differentiable structure thus provide a natural framework
to study dualities in quantum mechanics. As an example we quantise a classical
mechanics whose phase space is a torus and prove explicitly that it exhibits
dualities.


title: Energy-momentum operators with eigenfunctions localized along a line

abstract:
  The momentum operator $ {\bf p} = - i {\bx \nabla} $ has radial component $
{\bf \tilde p} \equiv - i {\bf \hat{r}} ({1 \over r} \partial_r r).$ We show
that ${\bf \tilde p} $ is the space part of a 4-vector operator, the zero
component of which is a positive operator. Their eigenfunctions are localized
along an axis through the origin. The solutions of the evolution equation $ i
\partial_t \psi = {\tilde p^0} \psi $ are waves along the propagation axis.
Lorentz transformations of these waves yield the aberration and Doppler shift.
We briefly consider spin-half and spin-one representations.


title:
Optical discrimination between spatial decoherence and thermalization of
  a massive object

abstract:
  We propose an optical ring interferometer to observe environment-induced
spatial decoherence of massive objects. The object is held in a harmonic trap
and scatters light between degenerate modes of a ring cavity. The output signal
of the interferometer permits to monitor the spatial width of the object's wave
function. It shows oscillations that arise from coherences between energy
eigenstates and that reveal the difference between pure spatial decoherence and
that coinciding with energy transfer and heating. Our method is designed to
work with a wide variety of masses, ranging from the atomic scale to
nano-fabricated structures. We give a thorough discussion of its experimental
feasibility.


title: Towards photostatistics from photon-number discriminating detectors

abstract:
  We study the properties of a photodetector that has a number-resolving
capability. In the absence of dark counts, due to its finite quantum
efficiency, photodetection with such a detector can only eliminate the
possibility that the incident field corresponds to a number of photons less
than the detected photon number. We show that such a {\em non-photon}
number-discriminating detector, however, provides a useful tool in the
reconstruction of the photon number distribution of the incident field even in
the presence of dark counts.


title: Coarse grained and fine dynamics in trapped ion Raman schemes

abstract:
  A novel result concerning Raman coupling schemes in the context of trapped
ions is obtained. By means of an operator perturbative approach, it is shown
that the complete time evolution of these systems (in the interaction picture)
can be expressed, with a high degree of accuracy, as the product of two unitary
evolutions. The first one describes the time evolution related to an effective
coarse grained dynamics. The second is a suitable correction restoring the {\em
fine} dynamics suppressed by the coarse graining performed to adiabatically
eliminate the nonresonantly coupled atomic level.


title: Stability of quantum Fourier transformation on Ising quantum computer

abstract:
  We analyze the influence of errors on the implementation of the quantum
Fourier transformation (QFT) on the Ising quantum computer (IQC). Two kinds of
errors are studied: (i) due to spurious transitions caused by pulses and (ii)
due to external perturbation. The scaling of errors with system parameters and
number of qubits is explained. We use two different procedures to fight each of
them. To suppress spurious transitions we use correcting pulses (generalized
$2\pi k$ method) while to suppress errors due to external perturbation we use
an improved QFT algorithm. As a result, the fidelity of quantum computation is
increased by several orders of magnitude and is thus stable in a much wider
range of physical parameters.


title: A Critique of PT-Symmetric Quantum Mechanics

abstract:
  We study the physical content of the PT-symmetric complex extension of
quantum mechanics as proposed in Bender et al, Phys. Rev. Lett. 80, 5243 (1998)
and 89, 270401 (2002), and show that as a fundamental probabilistic physical
theory it is neither an alternative to nor an extension of ordinary quantum
mechanics. We demonstrate that the definition of a physical observable given in
the above papers is inconsistent with the dynamical aspect of the theory and
offer a consistent notion of an observable.


title: Acceleration of quantum algorithms using three-qubit gates

abstract:
  Quantum-circuit optimization is essential for any practical realization of
quantum computation, in order to beat decoherence. We present a scheme for
implementing the final stage in the compilation of quantum circuits, i.e., for
finding the actual physical realizations of the individual modules in the
quantum-gate library. We find that numerical optimization can be efficiently
utilized in order to generate the appropriate control-parameter sequences which
produce the desired three-qubit modules within the Josephson charge-qubit
model. Our work suggests ways in which one can in fact considerably reduce the
number of gates required to implement a given quantum circuit, hence
diminishing idle time and significantly accelerating the execution of quantum
algorithms.


title: Bell's inequalities detect efficient entanglement

abstract:
  We review the status of Bell's inequalities in quantum information, stressing
mainly the links with quantum key distribution and distillation of
entanglement. We also prove that for all the eavesdropping attacks using one
qubit, and for a family of attacks of two qubits, acting on half of a maximally
entangled state of two qubits, the violation of a Bell inequality implies the
possibility of an efficient secret-key extraction.


title:
Two independent photon pairs versus four-photon entangled states in
  parametric down conversion

abstract:
  We study the physics of four-photon states generated in spontaneous
parametric down-conversion with a pulsed pump field. In the limit where the
coherence time of the photons t_c is much shorter than the duration of the pump
pulse Delta t, the four photons can be described as two independent pairs. In
the opposite limit, the four photons are in a four-particle entangled state.
Any intermediate case can be characterized by a single parameter chi, which is
a function of t_c/Delta t. We present a direct measurement of chi through a
simple experimental setup. The full theoretical analysis is also provided.


title: How much security does Y-00 protocol provide us ?

abstract:
  New quantum cryptography, often called Y-00 protocol, has much higher
performance than the conventional quantum cryptographies. It seems that the
conventional quantum cryptographic attacks are inefficient at Y-00 protocol as
its security is based on the different grounds from that of the conventional
ones. We have, then, tried to cryptoanalyze Y-00 protocol in the view of
cryptographic communication system. As a result, it turns out that the security
of Y-00 protocol is equivalent to that of classical stream cipher.


title:
Thermal entanglement of Bosonic atoms in an optical lattice with
  nonlinear couplings

abstract:
  The thermal entanglement of two spin-1 atoms with nonlinear couplings in
optical lattices is investigated in this paper. It is found that the nonlinear
couplings favor the thermal entanglement creating. The dependence of the
thermal entanglement in this system on the linear coupling, the nonlinear
coupling, the magnetic field and temperature is also presented. The results
show that the nonlinear couplings really change the feature of the thermal
entanglement in the system, increasing the nonlinear coupling constant
increases the critical magnetic field and the threshold temperature.


title: Field correlations and effective two level atom-cavity systems

abstract:
  We analyse the properties of the second order correlation functions of the
electromagnetic field in atom-cavity systems that approximate two-level
systems. It is shown that a recently-developed polariton formalism can be used
to account for all the properties of the correlations, if the analysis is
extended to include two manifolds - corresponding to the ground state and the
states excited by a single photon - rather than just two levels.


title: Quantum random walk on the line as a markovian process

abstract:
  We analyze in detail the discrete--time quantum walk on the line by
separating the quantum evolution equation into Markovian and interference
terms. As a result of this separation, it is possible to show analytically that
the quadratic increase in the variance of the quantum walker's position with
time is a direct consequence of the coherence of the quantum evolution. If the
evolution is decoherent, as in the classical case, the variance is shown to
increase linearly with time, as expected. Furthermore we show that this system
has an evolution operator analogous to that of a resonant quantum kicked rotor.
As this rotator may be described through a quantum computational algorithm, one
may employ this algorithm to describe the time evolution of the quantum walker.


title:
Unextendible product bases and locally unconvertible bound entangled
  states

abstract:
  Mutual convertibility of bound entangled states under local quantum
operations and classical communication (LOCC) is studied. We focus on states
associated with unextendible product bases (UPB) in a system of three qubits. A
complete classification of such UPBs is suggested. We prove that for any pair
of UPBs $S$ and $T$ the associated bound entangled states $\rho_S$ and $\rho_T$
can not be converted to each other by LOCC, unless $S$ and $T$ coincide up to
local unitaries. More specifically, there exists a finite precision
$\epsilon>0$ such that for any LOCC protocol mapping $\rho_S$ into a
probabilistic ensemble $(p_j,\rho_j)$, the fidelity between $\rho_T$ and any
possible final state $\rho_j$ is smaller than $1-\epsilon$.


title:
Entanglement production by quantum error correction in the presence of
  correlated environment

abstract:
  We analyze the effect of a quantum error correcting code on the entanglement
of encoded logical qubits in the presence of a dephasing interaction with a
correlated environment. Such correlated reservoir introduces entanglement
between physical qubits. We show that for short times the quantum error
correction interprets such entanglement as errors and suppresses it. However
for longer time, although quantum error correction is no longer able to correct
errors, it enhances the rate of entanglement production due to the interaction
with the environment.


title: Combinatorial Physics, Normal Order and Model Feynman Graphs

abstract:
  The general normal ordering problem for boson strings is a combinatorial
problem. In this note we restrict ourselves to single-mode boson monomials.
This problem leads to elegant generalisations of well-known combinatorial
numbers, such as Bell and Stirling numbers. We explicitly give the generating
functions for some classes of these numbers. Finally we show that a graphical
representation of these combinatorial numbers leads to sets of model field
theories, for which the graphs may be interpreted as Feynman diagrams
corresponding to the bosons of the theory. The generating functions are the
generators of the classes of Feynman diagrams.


title: On the concept of pressure in quantum mechanics

abstract:
  Heat and work are fundamental concepts for thermodynamical systems. When
these are scaled down to the quantum level they require appropriate embeddings.
Here we show that the dependence of the particle spectrum on system size giving
rise to a formal definition of pressure can, indeed, be correlated with an
external mechanical degree of freedom, modelled as a spatial coordinate of a
quantum oscillator. Under specific conditions this correlation is reminiscent
of that occurring in the classical manometer.


title: Relaxation into equilibrium under pure Schr\"odinger dynamics

abstract:
  We consider bipartite quantum systems that are described completely by a
state vector $|\Psi(t)>$ and the fully deterministic Schr\"odinger equation.
Under weak constraints and without any artificially introduced decoherence or
irreversibility, the smaller of the two subsystems shows thermodynamic
behaviour like relaxation into an equilibrium, maximization of entropy and the
emergence of the Boltzmann energy distribution. This generic behaviour results
from entanglement.


title: Entanglement versus chaos in disordered spin chains

abstract:
  We use a Heisenberg spin-1/2 chain to investigate how chaos and localization
may affect the entanglement of pairs of qubits. To measure how much entangled a
pair is, we compute its concurrence, which is then analyzed in the
delocalized/localized and in the chaotic/non-chaotic regimes. Our results
indicate that chaos reduces entanglement and that entanglement decreases in the
region of strong localization. In the transition region from a chaotic to a
non-chaotic regime localization increases entanglement. We also show that
entanglement is larger for strongly interacting qubits (nearest neighbors) than
for weakly interacting qubits (next and next-next neighbors).


title: Competition of Two Terms in Exchange Hamiltonian for magnetic substances

abstract:
  The unjustifiable or wrong in the previous magnetism theories has been
indicated in this paper. For a N electrons system with Heisenberg exchange
integral, the correct exchange Hamilton should be of two terms, not only one as
in the previous magnetism theories. The role of the minor term in the exchange
Hamilton was considered. Based on the principle of superposition of state, the
eigenstate of the system with Heisenberg exchange integral, the sum of a
positive term and a negative term, and the energy (relative to exchange
interaction) eigenvalue were attained. When the positive term is equal to the
absolute value of the negative term, the system is in the spin glass state, the
probabilities of parallel and antiparallel arrange for every pair of spins of
electron of nearest neighbours in the system are equal. When the positive term
is not equal to the absolute value of the negative term,the probabilities are
not equal, and there coexist the ferromagnetic states and spin glass or
antiferromagnetic state and spin glass,when ferromagnetic states and spin glass
or antiferromagnetic state and spin glass coexist, the energy of the system is
lower than that when only ferromagnetic states or antiferromagnetic state
exists as in previous theory. Weiss ferromagnetic state or Neel anti
ferromagnetic state is just a special state as the positive term is equal to
zero or negative term is equal to zero.


title:
Solutions of the Schr\"{o}dinger equation for the time-dependent linear
  potential

abstract:
  By making use of the Lewis-Riesenfeld invariant theory, the solution of the
Schr\"{o}dinger equation for the time-dependent linear potential corresponding
to the quadratic-form Lewis-Riesenfeld invariant $I_{\rm q}(t)$ is obtained in
the present paper. It is emphasized that in order to obtain the general
solutions of the time-dependent Schr\"{o}dinger equation, one should first find
the complete set of Lewis-Riesenfeld invariants. For the present quantum system
with a time-dependent linear potential, the linear $I_{\rm l}(t)$ and quadratic
$I_{\rm q}(t)$ (where the latter $I_{\rm q}(t)$ cannot be written as the
squared of the former $I_{\rm l}(t)$, {\it i.e.}, the relation $I_{\rm q}(t)=
cI_{\rm l}^{2}(t)$ does not hold true always) will form a complete set of
Lewis-Riesenfeld invariants. It is also shown that the solution obtained by
Bekkar {\it et al.} more recently is the one corresponding to the linear
$I_{\rm l}(t)$, one of the invariants that form the complete set. In addition,
we discuss some related topics regarding the comment [Phys. Rev. A {\bf 68},
016101 (2003)] of Bekkar {\it et al.} on Guedes's work [Phys. Rev. A {\bf 63},
034102 (2001)] and Guedes's corresponding reply [Phys. Rev. A {\bf 68}, 016102
(2003)].


title: Strategies to measure a quantum state

abstract:
  We consider the problem of determining the mixed quantum state of a large but
finite number of identically prepared quantum systems from data obtained in a
sequence of ideal (von Neumann) measurements, each performed on an individual
copy of the system. In contrast to previous approaches, we do not average over
the possible unknown states but work out a ``typical'' probability distribution
on the set of states, as implied by the experimental data. As a consequence,
any measure of knowledge about the unknown state and thus any notion of ``best
strategy'' (i.e. the choice of observables to be measured, and the number of
times they are measured) depend on the unknown state. By learning from
previously obtained data, the experimentalist re-adjusts the observable to be
measured in the next step, eventually approaching an optimal strategy. We
consider two measures of knowledge and exhibit all ``best'' strategies for the
case of a two-dimensional Hilbert space. Finally, we discuss some features of
the problem in higher dimensions and in the infinite dimensional case.


title: Anomalies of weakened decoherence criteria for quantum histories

abstract:
  The theory of decoherent histories is checked for the requirement of
statistical independence of subsystems. Strikingly, this is satisfied only when
the decoherence functional is diagonal in both its real a n d imaginary parts.
In particular, the condition of consistency (or weak decoherence) required for
the assignment of probabilities appears to be ruled out. The same conclusion is
obtained independently, by claiming a plausible dynamical robustness of
decoherent histories.


title:
Dynamics of entanglement between two atomic samples with spontaneous
  scattering

abstract:
  We investigate the effects of spontaneous scattering on the evolution of
entanglement of two atomic samples, probed by phase shift measurements on
optical beams interacting with both samples. We develop a formalism of
conditional quantum evolutions and present a wave function analysis implemented
in numerical simulations of the state vector dynamics. This method allows to
track the evolution of entanglement and to compare it with the predictions
obtained when spontaneous scattering is neglected. We provide numerical
evidence that the interferometric scheme to entangle atomic samples is only
marginally affected by the presence of spontaneous scattering, and should thus
be robust even in more realistic situations.


title: Photon number resolving detection using time-multiplexing

abstract:
  Detectors that can resolve photon number are needed in many quantum
information technologies. In order to be useful in quantum information
processing, such detectors should be simple, easy to use, and be scalable to
resolve any number of photons, as the application may require great portability
such as in quantum cryptography. Here we describe the construction of a
time-multiplexed detector, which uses a pair of standard avalanche photodiodes
operated in Geiger mode. The detection technique is analysed theoretically and
tested experimentally using a pulsed source of weak coherent light.


title: Casimir force on a piston

abstract:
  We consider a massless scalar field obeying Dirichlet boundary conditions on
the walls of a two-dimensional L x b rectangular box, divided by a movable
partition (piston) into two compartments of dimensions a x b and (L-a) x b. We
compute the Casimir force on the piston in the limit L -> infinity. Regardless
of the value of a/b, the piston is attracted to the nearest end of the box.
Asymptotic expressions for the Casimir force on the piston are derived for a <<
b and a >> b.


title: Communication through measurements and unitary transformations

abstract:
  It is generally accepted that no `faster than light signalling' (FTLS) using
two entangled spin 1/2 particles is possible because of indeterminism in a
quantum measurement and linearity of standard quantum mechanics. We show how in
principle one bit of information could be transmitted using local measurements
and a global unitary transformation of the state of two entangled spatially
separated spin 1/2 particles. Assuming that the postulate of a state collapse
due to measurement is valid, the no FTLS condition is saved if we do not have
physical access to the required global unitary transformation. This means that
the no FTLS condition is also present on the operational level, namely as
imposing a physical restriction on the possible realizable unitary
transformations, in this case of two entangled but spatially separated spin
1/2.


title: There Is No Basis Ambiguity in Everett Quantum Mechanics

abstract:
  The Everett-interpretation description of isolated measurements, i.e.,
measurements involving interaction between a measuring apparatus and a measured
system but not interaction with the environment, is shown to be unambiguous,
claims in the literature to the contrary notwithstanding. The appearance of
ambiguity in such measurements is engendered by the fact that, in the
Schroedinger picture, information on splitting into Everett copies must be
inferred from the history of the combined system. In the Heisenberg picture
this information is contained in mathematical quantities associated with a
single time.


title:
Highly efficient generation of pulsed photon pair using a bulk
  Periodically Poled Potassium Titanyl Phosphate

abstract:
  In this paper, we demonstrate efficient generation of collinearly
propagating, degenerate pulsed photon pairs based on a bulk Periodically Poled
Potassium Titanyl Phosphate pumped by an ultrashort pulse laser. Using a
single-mode fiber as a spatial mode filter, we detect about 3200 coincidence
counts per second per milliwatt pump power. After we consider main losses in
our experiment, the inferred coincidence counts are about 109000 per second per
milliwatt pump power. This is the very promising for realization of sources for
quantum communication and metrology.


title: Simulation of quantum interference by reactions of chemical type

abstract:
  A quantum unitary evolution alternated with measurements is simulated by a
bubble filled with fictitious particles called amplitude quanta that move
chaotically and can be transformed by the simple rules that look like chemical
reactions. A basic state of simulated system is treated as a collision of the
two corresponding amplitude quanta, that gives the quantum statistics of
measurements. The movement of the external membrane of the bubble corresponds
to the classical dynamics of the simulated system. Measurements are treated as
the membrane perforations and they are completely determined by initial
conditions. An identity of particles and an entanglement is simulated by the
membranes touching. The required memory grows linearly where the number of
particles increases, but entangled states of the big number of particles can be
simulated. The method can be used for a visualization of quantum dynamics.


title: Quantum computation by measurements

abstract:
  We first consider various methods for the indirect implementation of unitary
gates. We apply these methods to rederive the universality of 4-qubit
measurements based on a scheme much simpler than Nielsen's original
construction [quant-ph/0108020]. Then, we prove the universality of simple
discrete sets of 2-qubit measurements, again using a scheme simplifying the
initial construction [quant-ph/0111122]. Finally, we show how to use a single
4-qubit measurement to achieve universal quantum computation, and outline a
proof for the universality of almost all maximally entangling 4-qubit
measurements.


title:
On the alleged nonlocal and topological nature of the molecular
  Aharonov-Bohm effect

abstract:
  The nonlocal and topological nature of the molecular Aharonov-Bohm (MAB)
effect is examined for real electronic Hamiltonians. A notion of preferred
gauge for MAB is suggested. The MAB effect in the linear + quadratic $E\otimes
\epsilon$ Jahn-Teller system is shown to be essentially analogues to an
anisotropic Aharonov-Casher effect for an electrically neutral spin$-{1/2}$
particle encircling a certain configuration of lines of charge.


title:
Limit theorems and absorption problems for one-dimensional correlated
  random walks

abstract:
  There has recently been considerable interest in quantum walks in connection
with quantum computing. The walk can be considered as a quantum version of the
so-called correlated random walk. We clarify a strong structural similarity
between both walks and study limit theorems and absorption problems for
correlated random walks by our PQRS method, which was used in our analysis of
quantum walks.


title: Observation of Bell Inequality violation in B mesons

abstract:
  A pair of $B^0\bar B^0$ mesons from $\Upsilon(4S)$ decay exhibit EPR type
non-local particle-antiparticle (flavor) correlation. It is possible to write
down Bell Inequality (in the CHSH form: $S\le2$) to test the non-locality
assumption of EPR. Using semileptonic $B^0$ decays of $\Upsilon(4S)$ at Belle
experiment, a clear violation of Bell Inequality in particle-antiparticle
correlation is observed:
  S=2.725+-0.167(stat)+-0.092(syst)


title: A size criterion for macroscopic superposition states

abstract:
  An operational measure to quantify the sizes of some ``macroscopic quantum
superpositions'', realized in recent experiments, is proposed. The measure is
based on the fact that a superposition presents greater sensitivity in
interferometric applications than its superposed constituent states. This
enhanced sensitivity, or ``interference utility'', may then be used as a size
criterion among superpositions.


title: The Casimir Effect and Geometric Optics

abstract:
  We propose a new approach to the Casimir effect based on classical ray
optics. We define and compute the contribution of classical optical paths to
the Casimir force between rigid bodies. We reproduce the standard result for
parallel plates and agree over a wide range of parameters with a recent
numerical treatment of the sphere and plate with Dirichlet boundary conditions.
Our approach improves upon proximity force approximation. It can be generalized
easily to other geometries, other boundary conditions, to the computation of
Casimir energy densities and to many other situations.


title:
Solutions of the Logarithmic Schrodinger Equation in a Rotating Harmonic
  Trap

abstract:
  We study the influence of the nonlinearity in the Schrodinger equation on the
motion of quantum particles in a harmonic trap. In order to obtain exact
analytic solutions, we have chosen the logarithmic nonlinearity. The unexpected
result of our study is the existence in the presence of nonlinearity of two or
even three coexisting Gaussian solutions.


title: Quantum walk algorithm for element distinctness

abstract:
  We use quantum walks to construct a new quantum algorithm for element
distinctness and its generalization. For element distinctness (the problem of
finding two equal items among N given items), we get an O(N^{2/3}) query
quantum algorithm. This improves the previous O(N^{3/4}) query quantum
algorithm of Buhrman et.al. (quant-ph/0007016) and matches the lower bound by
Shi (quant-ph/0112086). The algorithm also solves the generalization of element
distinctness in which we have to find k equal items among N items. For this
problem, we get an O(N^{k/(k+1)}) query quantum algorithm.


title:
Comment on "Solutions of the Schr\"{o}dinger equation for the
  time-dependent linear potential''

abstract:
  We show that the solution obtained by Bekkar {\it et al.} in their comment
[Phys. Rev. A {\bf 68}, 016101 (2003)] on Guedes's work of solving the quantum
system with a time-dependent linear potential is still {\it not} the {\it
general} one of the Schr\"{o}dinger equation. It is concluded that Bekkar {\it
et al.}'s solution (corresponding to the linear Lewis-Riesenfeld invariant) and
our solution (corresponding to the quadratic-form Lewis-Riesenfeld invariant)
presented here will constitute together a complete set of solutions (general
solutions) of the time-dependent Schr\"{o}dinger equation of the system under
consideration.