title:
Von Neumann Measurement is Optimal for Detecting Linearly Independent
  Mixed Quantum States

abstract:
  We consider the problem of designing a measurement to minimize the
probability of a detection error when distinguishing between a collection of
possibly non-orthogonal mixed quantum states. We show that if the quantum state
ensemble consists of linearly independent density operators then the optimal
measurement is an orthogonal Von Neumann measurement consisting of mutually
orthogonal projection operators and not a more general positive operator-valued
measure.


title: The Controlled-U and Unitary Transformation in Two-Qudit

abstract:
  We concretely construct an extension of the controlled-U gate in qudit from
some elementary gates. We also construct unitary transformation in two-qudit by
means of the extended controlled-U gate and show the universality of it.


Comments On "Three Paradox of Quantum Information"


title: Exact PT-Symmetry Is Equivalent to Hermiticity

abstract:
  We show that a quantum system possessing an exact antilinear symmetry, in
particular PT-symmetry, is equivalent to a quantum system having a Hermitian
Hamiltonian. We construct the unitary operator relating an arbitrary
non-Hermitian Hamiltonian with exact PT-symmetry to a Hermitian Hamiltonian. We
apply our general results to PT-symmetry in finite-dimensions and give the
explicit form of the above-mentioned unitary operator and Hermitian Hamiltonian
in two dimensions. Our findings lead to the conjecture that non-Hermitian
CPT-symmetric field theories are equivalent to certain nonlocal Hermitian field
theories.


title:
Coherence properties and quantum state transportation in an optical
  conveyor belt

abstract:
  We have prepared and detected quantum coherences with long dephasing times at
the level of single trapped cesium atoms. Controlled transport by an "optical
conveyor belt" over macroscopic distances preserves the atomic coherence with
slight reduction of coherence time. The limiting dephasing effects are
experimentally identified and are of technical rather than fundamental nature.
We present an analytical model of the reversible and irreversible dephasing
mechanisms. Coherent quantum bit operations along with quantum state transport
open the route towards a "quantum shift register" of individual neutral atoms.


title: Decidable and undecidable problems about quantum automata

abstract:
  We study the following decision problem: is the language recognized by a
quantum finite automaton empty or non-empty? We prove that this problem is
decidable or undecidable depending on whether recognition is defined by strict
or non-strict thresholds. This result is in contrast with the corresponding
situation for probabilistic finite automata for which it is known that strict
and non-strict thresholds both lead to undecidable problems.


title: Physical-resource demands for scalable quantum computation

abstract:
  The primary resource for quantum computation is Hilbert-space dimension.
Whereas Hilbert space itself is an abstract construction, the number of
dimensions available to a system is a physical quantity that requires physical
resources. Avoiding a demand for an exponential amount of these resources
places a fundamental constraint on the systems that are suitable for scalable
quantum computation. To be scalable, the number of degrees of freedom in the
computer must grow nearly linearly with the number of qubits in an equivalent
qubit-based quantum computer.


title: Countinuous Quantum Hidden Subgroup Algorithms

abstract:
  In this paper we show how to construct two continuous variable and one
continuous functional quantum hidden subgroup (QHS) algorithms. These are
respectively quantum algorithms on the additive group of reals R, the additive
group R/Z of the reals R mod 1, i.e., the circle, and the additive group Paths
of L^2 paths x:[0,1]-->R^n in real n-space R^n. Also included is a curious
discrete QHS algorithm which is dual to Shor's algorithm.


title: The Semi-Quantum Computer

abstract:
  We discuss the performance of the Search and Fourier Transform algorithms on
a hybrid computer constituted of classical and quantum processors working
together. We show that this semi-quantum computer would be an improvement over
a pure classical architecture, no matter how few qubits are available and,
therefore, it suggests an easier implementable technology than a pure quantum
computer with arbitrary number of qubits.


title:
Quantum interference with distinguishable photons through
  indistinguishable pathways

abstract:
  We report a two-photon interference experiment in which the detected photons
have very different properties. The interference is observed even when no
effort is made to mask the distinguishing features before the photons are
detected. The results can only be explained in terms of indistinguishable
two-photon amplitudes.


title: Symplectic evolution of Wigner functions in markovian open systems

abstract:
  The Wigner function is known to evolve classically under the exclusive action
of a quadratic hamiltonian. If the system does interact with the environment
through Lindblad operators that are linear functions of position and momentum,
we show that the general evolution is the convolution of the classically
evolving Wigner function with a phase space gaussian that broadens in time. We
analyze the three generic cases of elliptic, hyperbolic and parabolic
Hamiltonians. The Wigner function always becomes positive in a definite time,
which is shortest in the hyperbolic case. We also derive an exact formula for
the evolving linear entropy as the average of a narrowing gaussian taken over a
probability distribution that depends only on the initial state. This leads to
a long time asymptotic formula for the growth of linear entropy.


title: No spin-statistics connection in nonrelativistic quantum mechanics

abstract:
  We emphasize that there is no spin-statistics connection in nonrelativistic
quantum mechanics. In several recent papers, including Phys. Rev. A 67, 042102
(2003) [quant-ph/0207017], quantum mechanics is modified so as to force a
spin-statistics connection, but the resulting theory is quite different from
standard physics.


title: Alternative Method for Quantum Feedback-Control

abstract:
  A new method for doing feedback control of single quantum systems was
proposed. Instead of feeding back precisely the process output, a cloning
machine served to obtain the feedback signal and the output. A simple example
was given to demonstrate the method.


title: Hidden symmetry detection on a quantum computer

abstract:
  The fastest quantum algorithms (for the solution of classical computational
tasks) known so far are basically variations of the hidden subgroup problem
with {$f(U[x])=f(x)$}. Following a discussion regarding which tasks might be
solved efficiently by quantum computers, it will be demonstrated by means of a
simple example, that the detection of more general hidden (two-point)
symmetries {$V\{f(x),f(U[x])\}=0$} by a quantum algorithm can also admit an
exponential speed-up. E.g., one member of this class of symmetries
{$V\{f(x),f(U[x])\}=0$} is discrete self-similarity (or discrete scale
invariance). PACS: 03.67.Lx, 89.70.+c.


title: Entanglement Criteria - Quantum and Topological

abstract:
  This paper gives a criterion for detecting the entanglement of a quantum
state, and uses it to study the relationship between topological and quantum
entanglement. It is fundamental to view topological entanglements such as
braids as entanglement operators and to associate to them unitary operators
that are capable of creating quantum entanglement. The entanglement criterion
is used to explore this connection. The paper discusses non-locality in the
light of this criterion.


title:
Mapping the Wigner distribution function of the Morse oscillator into a
  semi-classical distribution function

abstract:
  The mapping of the Wigner distribution function (WDF) for a given bound-state
onto a semiclassical distribution function (SDF) satisfying the Liouville
equation introduced previously by us is applied to the ground state of the
Morse oscillator. Here we give results showing that the SDF gets closer to the
corresponding WDF as the number of levels of the Morse oscillator increases. We
find that for a Morse oscillator with one level only, the agreement between the
WDF and the mapped SDF is very poor but for a Morse oscillator of ten levels it
becomes satisfactory.


title:
Quantum State Control via Trap-induced Shape Resonance in Ultracold
  Atomic Collisions

abstract:
  We investigate controlled collisions between trapped but separated ultracold
atoms. The interaction between atoms is treated self-consistently using an
energy-dependent delta-function pseudopotential model, whose validity we
establish. At a critical separation, a "trap-induced shape resonance" between a
molecular bound states and a vibrational eigenstate of the trap can occur. This
resonance leads to an avoided crossing in the eigenspectrum as a function of
separation. We investigate how this new resonance can be employed for quantum
control.


title: A New Symmetric Expression of Weyl Ordering

abstract:
  For the creation operator $\adag $ and the annihilation operator $a$ of a
harmonic oscillator, we consider Weyl ordering expression of $(\adag a)^n$ and
obtain a new symmetric expression of Weyl ordering w.r.t. $\adag a \equiv N$
and $a\adag =N+1$ where $N$ is the number operator. Moreover, we interpret
intertwining formulas of various orderings in view of the difference theory.
Then we find that the noncommutative parameter corresponds to the increment of
the difference operator w.r.t. variable $N$. Therefore, quantum
(noncommutative) calculations of harmonic oscillators are done by classical
(commutative) ones of the number operator by using the difference theory. As a
by-product, nontrivial relations including the Stirling number of the first
kind are also obtained.


title: Entanglement of Formation for a Class of Quantum States

abstract:
  Entanglement of formation for a class of higher dimensional quantum mixed
states is studied in terms of a generalized formula of concurrence for
$N$-dimensional quantum systems. As applications, the entanglement of formation
for a class of $16\times 16$ density matrices are calculated.


title: Schroedinger Proof in Minplus Complex Analysis

abstract:
  We are presenting an internal trajectory model for a quantum particle in the
Schroedinger non-relativistic approximation. This model is based on two new
mathematical concepts: a complex analytical mechanics in Minplus complex
analysis and a periodical non random process which gives a complex Ito formula.
  This model naturally generates a concept of spin or isospin and the
Heisenberg inequalities, and leads to the Schroedinger equation using a
generalization of the least action principle adapted to the trajectories of
this type.


title:
Einstein, Wigner, and Feynman: From E = mc^{2} to Feynman's decoherence
  via Wigner's little groups

abstract:
  The 20th-century physics starts with Einstein and ends with Feynman. Einstein
introduced the Lorentz-covariant world with E = mc^{2}. Feynman observed that
fast-moving hadrons consist of partons which act incoherently with external
signals. If quarks and partons are the same entities observed in different
Lorentz frames, the question then is why partons are incoherent while quarks
are coherent. This is the most puzzling question Feynman left for us to solve.
In this report, we discuss Wigner's role in settling this question. Einstein's
E = mc^{2}, which takes the form E = \sqrt{m^{2} + p^{2}}, unifies the
energy-momentum relations for massive and massless particles, but it does not
take into account internal space-time structure of relativistic particles. It
is pointed out Wigner's 1939 paper on the inhomogeneous Lorentz group defines
particle spin and gauge degrees of freedom in the Lorentz-covariant world.
Within the Wigner framework, it is shown possible to construct the internal
space-time structure for hadrons in the quark model. It is then shown that the
quark model and the parton model are two different manifestations of the same
covariant entity. It is shown therefore that the lack of coherence in Feynman's
parton picture is an effect of the Lorentz covariance.


title: Ground state entanglement in quantum spin chains

abstract:
  A microscopic calculation of ground state entanglement for the XY and
Heisenberg models shows the emergence of universal scaling behavior at quantum
phase transitions. Entanglement is thus controlled by conformal symmetry. Away
from the critical point, entanglement gets saturated by a mass scale. Results
borrowed from conformal field theory imply irreversibility of entanglement loss
along renormalization group trajectories. Entanglement does not saturate in
higher dimensions which appears to limit the success of the density matrix
renormalization group technique. A possible connection between majorization and
renormalization group irreversibility emerges from our numerical analysis.


title:
Automated Method for Building CNOT Based Quantum Circuits for Boolean
  Functions

abstract:
  In this paper we discuss an efficient technique that can implement any given
Boolean function as a quantum circuit. The method converts a truth table of a
Boolean function to the corresponding quantum circuit using a minimal number of
auxiliary qubits. We give examples of some circuits synthesized with this
technique. A direct result that follows from the technique is a new way to
convert any classical digital circuit to its classical reversible form.


title:
Decoherence, irreversibility and the selection by decoherence of quantum
  states with definite probabilities

abstract:
  The problem investigated in this paper is einselection, i. e. the selection
of mutually exclusive quantum states with definite probabilities through
decoherence. Its study is based on a theory of decoherence resulting from the
projection method in the quantum theory of irreversible processes, which is
general enough for giving reliable predictions. This approach leads to a
definition (or redefinition) of the coupling with the environment involving
only fluctuations. The range of application of perturbation calculus is then
wide, resulting in a rather general master equation.
  Two distinct cases of decoherence are then found: (i) A ``degenerate'' case
(already encountered with solvable models) where decoherence amounts
essentially to approximate diagonalization; (ii) A general case where the
einselected states are essentially classical. They are mixed states. Their
density operators are proportional to microlocal projection operators (or
``quasi projectors'') which were previously introduced in the quantum
expression of classical properties.
  It is found at various places that the main limitation in our understanding
of decoherence is the lack of a systematic method for constructing collective
observables.


title: Cyclotomy and Ramanujan sums in quantum phase locking

abstract:
  Phase-locking governs the phase noise in classical clocks through effects
described in precise mathematical terms. We seek here a quantum counterpart of
these effects by working in a finite Hilbert space. We use a coprimality
condition to define phase-locked quantum states and the corresponding
Pegg-Barnett type phase operator. Cyclotomic symmetries in matrix elements are
revealed and related to Ramanujan sums in the theory of prime numbers. The
employed mathematical procedures also emphasize the isomorphism between
algebraic number theory and the theory of quantum entanglement


title: Capacities of Quantum Channels and How to Find Them

abstract:
  We survey what is known about the information transmitting capacities of
quantum channels, and give a proposal for how to calculate some of these
capacities using linear programming.


title: Estimating purity in terms of correlation functions

abstract:
  We prove a rigorous inequality estimating the purity of a reduced density
matrix of a composite quantum system in terms of cross-correlation of the same
state and an arbitrary product state. Various immediate applications of our
result are proposed, in particular concerning Gaussian wave-packet propagation
under classically regular dynamics.


title: Theory of quantum Loschmidt echoes

abstract:
  In this paper we review our recent work on the theoretical approach to
quantum Loschmidt echoes, i.e. various properties of the so called echo
dynamics -- the composition of forward and backward time evolutions generated
by two slightly different Hamiltonians, such as the state autocorrelation
function (fidelity) and the purity of a reduced density matrix traced over a
subsystem (purity fidelity). Our main theoretical result is a linear response
formalism, expressing the fidelity and purity fidelity in terms of integrated
time autocorrelation function of the generator of the perturbation.
Surprisingly, this relation predicts that the decay of fidelity is the slower
the faster the decay of correlations. In particular for a static
(time-independent) perturbation, and for non-ergodic and non-mixing dynamics
where asymptotic decay of correlations is absent, a qualitatively different and
faster decay of fidelity is predicted on a time scale 1/delta as opposed to
mixing dynamics where the fidelity is found to decay exponentially on a
time-scale 1/delta^2, where delta is a strength of perturbation. A detailed
discussion of a semi-classical regime of small effective values of Planck
constant is given where classical correlation functions can be used to predict
quantum fidelity decay. Note that the correct and intuitively expected
classical stability behavior is recovered in the classical limit, as the
perturbation and classical limits do not commute. The theoretical results are
demonstrated numerically for two models, the quantized kicked top and the
multi-level Jaynes Cummings model. Our method can for example be applied to the
stability analysis of quantum computation and quantum information processing.


title:
Quantum interference with beamlike type-II spontaneous parametric
  down-conversion

abstract:
  We implement experimentally a method to generate photon-number$-$path and
polarization entangled photon pairs using ``beamlike'' type-II spontaneous
parametric down-conversion (SPDC), in which the signal-idler photon pairs are
emitted as two separate circular beams with small emission angles rather than
as two diverging cones.


title:
Interference of Hydrogen Atom 2P(1/2) State in a Field of a Few Small
  Perturbations

abstract:
  The interference of hydrogen atom 2P(1/2) state in a field of a few small
overlapping perturbations is considered in view of further applications to
experimental data interpretation. On a basis of this model two new experiments
are proposed which can clarify some features of Sokolov effect.


title: Distillable entanglement in $d\otimes d$ dimension

abstract:
  Distillable entanglement ($E_d$) is one of the acceptable measures of
entanglement of mixed states. Based on discrimination through local operation
and classical communication, this paper gives $E_d$ for two classes of
orthogonal multipartite maximally entangled states.


title: Quantum Spin Chain, Toeplitz Determinants and Fisher-Hartwig Conjecture

abstract:
  We consider one-dimensional quantum spin chain, which is called XX model, XX0
model or isotropic XY model in a transverse magnetic field. We study the model
on the infinite lattice at zero temperature. We are interested in the entropy
of a subsystem [a block of L neighboring spins]. It describes entanglement of
the block with the rest of the ground state.
  G. Vidal, J.I. Latorre, E. Rico, and A. Kitaev showed that for large blocks
the entropy scales logarithmically. We prove the logarithmic formula for the
leading term and calculate the next term.
  We discovered that the dependence on the magnetic field interacting with
spins is very simple: the magnetic field effectively reduce the size of the
subsystem.
  We also calculate entropy of a subsystem of a small size. We also evaluated
Renyi and Tsallis entropies of the subsystem. We represented the entropy in
terms of a Toeplitz determinant and calculated the asymptotic analytically.

categories: quant-ph cond-mat.stat-mech math-ph math.MP


title: Laws, Symmetries, and Reality

abstract:
  It is argued that quantum mechanics follows naturally from the assumptions
that there are no fundamental causal laws but only probabilities for physical
processes that are constrained by symmetries, and reality is relational in the
sense that an object is real only in relation to another object that it is
interacting with. The first assumption makes it natural to include in the
action for a gauge theory all terms that are allowed by the symmetries,
enabling cancellation of infinities, with only the terms in the standard model
observable at the energies at which we presently do our experiments. In this
approach, it is also natural to have an infinite number of fundamental
interactions.


title: Non-positivity of the Wigner function and bounds on associated integrals

abstract:
  The Wigner function shares several properties with classical distribution
functions on phase space, but is not positive-definite. The integral of the
Wigner function over a given region of phase space can therefore lie outside
the interval [0,1]. The problem of finding best-possible upper and lower bounds
for a given region is the problem of finding the greatest and least eigenvalues
of an associated Hermitian operator. Exactly solvable examples are described,
and possible extensions are indicated.


title:
Conditional preparation of a quantum state in the continuous variable
  regime: generation of a sub-Poissonian state from twin beams

abstract:
  We report the first experimental demonstration of conditional preparation of
a non classical state of light in the continuous variable regime. Starting from
a non degenerate OPO which generates above threshold quantum intensity
correlated signal and idler "twin beams", we keep the recorded values of the
signal intensity only when the idler falls inside a band of values narrower
than its standard deviation. By this very simple technique, we generate a
sub-Poissonian state 4.4dB below shot noise from twin beams exhibiting 7.5dB of
noise reduction in the intensity difference.


title: Multiparty Quantum Coin Flipping

abstract:
  We investigate coin-flipping protocols for multiple parties in a quantum
broadcast setting:
  (1) We propose and motivate a definition for quantum broadcast. Our model of
quantum broadcast channel is new.
  (2) We discovered that quantum broadcast is essentially a combination of
pairwise quantum channels and a classical broadcast channel. This is a somewhat
surprising conclusion, but helps us in both our lower and upper bounds.
  (3) We provide tight upper and lower bounds on the optimal bias epsilon of a
coin which can be flipped by k parties of which exactly g parties are honest:
for any 1 <= g <= k, epsilon = 1/2 - Theta(g/k).
  Thus, as long as a constant fraction of the players are honest, they can
prevent the coin from being fixed with at least a constant probability. This
result stands in sharp contrast with the classical setting, where no
non-trivial coin-flipping is possible when g <= k/2.


title: Quantum walks on cycles

abstract:
  We consider asymptotic behaviour of a Hadamard walk on a cycle. For a walk
which starts with a state in which all the probability is concentrated on one
node, we find the explicit formula for the limiting distribution and discuss
its asymptotic behaviour when the length of the cycle tends to infinity. We
also demonstrate that for a carefully chosen initial state, the limiting
distribution of a quantum walk on cycle can lie further away from the uniform
distribution than its initial state.


title: Numerical simulations of a quantum algorithm for Hilbert's tenth problem

abstract:
  We employ quantum mechanical principles in the computability exploration of
the class of classically noncomputable Hilbert's tenth problem which is
equivalent to the Turing halting problem in Computer Science. The Quantum
Adiabatic Theorem enables us to establish a connection between the solution for
this class of problems and the asymptotic behaviour of solutions of a
particular type of time-dependent Schr\"odinger equations. We then present some
preliminary numerical simulation results for the quantum adiabatic processes
corresponding to various Diophantine equations.


title:
The Innsbruck EPR Experiment: A Time-Retarded Local Description of
  Space-like Separated Correlations

abstract:
  A local, time-retarded hidden variable model is described that fits the
recently measured EPR data from the Innsbruck collaboration. The model is based
on the idea that waves in the zero-point field convey information from the
detectors to the source, stimulating the spontaneous emission of photons with
definite polarizations. In order to match experimental data, the model is
augmented with a further local assumption that the ``master'' photon (going
back along the direction of the zero-point wave that triggered emission) will
not be detected if the polarizer is not in the same orientation as the
stimulated wave. This model predicts a ratio of coincidences to singles of 1/3
compared to standard quantum mechanics' 2/3 for the 2-fold choice of modulator
settings, and predicts that a 20-fold choice of settings will yield a
coincidence ratio of 1/40 with the SQM ratio unchanged. Such an outcome should
be easily distinguishable given the Innsbruck group's measured efficiency of
1/20 in their experiment. This model also predicts that a coincidence at
polarizer settings (a,b,t) will never be correlated with its time-retarded
complement setting, (a',b',t-2L/c), a prediction for whose test the limited
data publicly available at this time is inadequate.


title: Relativistic entanglement of Bell states with general momentum

abstract:
  In this paper, the Lorentz transformation of the entangled Bell states with
momentum, not necessarily orthogonal to the boost direction, and spin, is
studied. We extended quantum correlations and Bell's inequality to the
relativistic regime by considering normalized relativistic observables. It is
shown that quantum information, along the perpendicular direction to the boost,
is eventually lost and Bell's inequality is not always violated for entangled
states in special relativity. This could impose restrictions to certain quantum
information processing such as quantum cryptography using massive particles.


title: Minimum-error discrimination between symmetric mixed quantum states

abstract:
  We provide a solution of finding optimal measurement strategy for
distinguishing between symmetric mixed quantum states. It is assumed that the
matrix elements of at least one of the symmetric quantum states are all real
and nonnegative in the basis of the eigenstates of the symmetry operator.


title:
Dual Algebraic Pairs and Polynomial Lie Algebras in Quantum Physics:
  Foundations and Geometric Aspects

abstract:
  We discuss some aspects and examples of applications of dual algebraic pairs
$({\cal G}_1,{\cal G}_2)$ in quantum many-body physics. They arise in models
whose Hamiltonians $H$ have invariance groups $G_i$. Then one can take ${\cal
G}_1 = G_i$ whereas another dual partner ${\cal G}_2= g^D$ is generated by
$G_i$ invariants, possesses a Lie-algebraic structure and describes dynamic
symmetry of models; herewith polynomial Lie algebras $\hat g = g^D$ appear in
models with essentially nonlinear Hamiltonians. Such an approach leads to a
geometrization of model kinematics and dynamics.


title: Is quantum entanglement invariant in special relativity?

abstract:
  Quantum entanglements are of fundamental importance in quantum physics
ranging from the quantum information processing to the physics of black hole.
Here, we show that the quantum entanglement is not invariant in special
relativity. This suggests that nearly all aspects of quantum information
processing would be affected significantly when relativistic effects are
considered because present schemes are based on the general assumption that
entanglement is invariant. There should be additional protocols to compensate
the variances of entanglement in in quantum information processing.
Furthermore, extending our results to general relativity may provide clues to
the fate of the information contained in an entangled Hawking pair inside and
outside the event horizon as black hole evaporates.


title: Photon polarization and Wigner's little group

abstract:
  To discuss one-photon polarization states we find an explicit form of the
Wigner's little group element in the massless case for arbitrary Lorentz
transformation. As is well known, when analyzing the transformation properties
of the physical states, only the value of the phase factor is relevant. We show
that this phase factor depends only on the direction of the momentum
$\vec{k}/|\vec{k}|$ and does not depend on the frequency $k^0$. Finally, we use
this observation to discuss the transformation properties of the linearly
polarized photons and the corresponding reduced density matrix. We find that
they transform properly under Lorentz group.


title:
Efficient photon counting and single-photon generation using resonant
  nonlinear optics

abstract:
  The behavior of an atomic double lambda system in the presence of a strong
off-resonant classical field and a few-photon resonant quantum field is
examined. It is shown that the system possesses properties that allow a
single-photon state to be distilled from a multi-photon input wave packet. In
addition, the system is also capable of functioning as an efficient
photodetector discriminating between one- and two-photon wave packets with
arbitrarily high efficiency.


title: Simulatings POVMs on EPR pairs with six bits of expected communication

abstract:
  We present a classical protocol for simulating correlations obtained by
bipartite POVMs on an EPR pair. The protocol uses shared random variables (also
known as local hidden variables) augmented by six bits of expected
communication.


title:
Direct estimation of functionals of density operators by local
  operations and classical communication

abstract:
  We present a method of determining important properties of a shared bipartite
quantum state, within the ``distant labs'' paradigm, using \emph{only} local
operations and classical communication (LOCC). We apply this procedure to
spectrum estimation of shared states, and locally implementable structural
physical approximations to incompletely positive maps. This procedure can also
be applied to the estimation of channel capacity and measures of entanglement.


title:
Disturbance of operation in quantum estimation for the Gaussian
  P-function

abstract:
  For the quantum Gaussian state family, Hayashi proposed a quantum mechanical
operation using beam splitters to estimate the location and scale parameters of
the P-function, and he showed that it is asymptotically optimal. In this paper,
we analyze the effect of disturbance of his operation caused by the randomness
of the transparency of the beam splitters. It is shown that even if the
variance of the random transparency is small, Hayashi's estimators are improper
in a sense that they are biased and asymptotically inconsistent. In such a
case, we propose to stop the operation and correct the biases of estimators.


title:
The Clifford group, stabilizer states, and linear and quadratic
  operations over GF(2)

abstract:
  We describe stabilizer states and Clifford group operations using linear
operations and quadratic forms over binary vector spaces. We show how the
n-qubit Clifford group is isomorphic to a group with an operation that is
defined in terms of a (2n+1)x(2n+1) binary matrix product and binary quadratic
forms. As an application we give two schemes to efficiently decompose Clifford
group operations into one and two-qubit operations. We also show how the
coefficients of stabilizer states and Clifford group operations in a standard
basis expansion can be described by binary quadratic forms. Our results are
useful for quantum error correction, entanglement distillation and possibly
quantum computing.


title: Optimal estimation of multiple phases

abstract:
  We study the issue of simultaneous estimation of several phase shifts induced
by commuting operators on a quantum state. We derive the optimal positive
operator-valued measure corresponding to the multiple-phase estimation. In
particular, we discuss the explicit case of the optimal detection of double
phase for a system of identical qutrits and generalise these results to optimal
multiple phase detection for d-dimensional quantum states.


title: The private classical capacity and quantum capacity of a quantum channel

abstract:
  A formula for the capacity of a quantum channel for transmitting private
classical information is derived. This is shown to be equal to the capacity of
the channel for generating a secret key, and neither capacity is enhanced by
forward public classical communication. Motivated by the work of Schumacher and
Westmoreland on quantum privacy and quantum coherence, parallels between
private classical information and quantum information are exploited to obtain
an expression for the capacity of a quantum channel for generating pure
bipartite entanglement. The latter implies a new proof of the quantum channel
coding theorem and a simple proof of the converse. The coherent information
plays a role in all of the above mentioned capacities.


title: Transcending the Limits of Turing Computability

abstract:
  Hypercomputation or super-Turing computation is a ``computation'' that
transcends the limit imposed by Turing's model of computability. The field
still faces some basic questions, technical (can we mathematically and/or
physically build a hypercomputer?), cognitive (can hypercomputers realize the
AI dream?), philosophical (is thinking more than computing?). The aim of this
paper is to address the question: can we mathematically build a hypercomputer?
We will discuss the solutions of the Infinite Merchant Problem, a decision
problem equivalent to the Halting Problem, based on results obtained in
\cite{Coins,acp}. The accent will be on the new computational technique and
results rather than formal proofs.


title: The charge-dyon bound system in the spherical quantum well

abstract:
  The spherical wave functions of charge-dyon bounded system in a rectangular
spherical quantum dot of infinitely and finite height are calculated. The
transcendent equations, defining the energy spectra of the systems are
obtained. The dependence of the energy levels from the wall sizes is found.


title:
Perturbative Formulation and Non-adiabatic Corrections in Adiabatic
  Quantum Computing Schemes

abstract:
  Adiabatic limit is the presumption of the adiabatic geometric quantum
computation and of the adiabatic quantum algorithm. But in reality, the
variation speed of the Hamiltonian is finite. Here we develop a general
formulation of adiabatic quantum computing, which accurately describes the
evolution of the quantum state in a perturbative way, in which the adiabatic
limit is the zeroth-order approximation. As an application of this formulation,
non-adiabatic correction or error is estimated for several physical
implementations of the adiabatic geometric gates. A quantum computing process
consisting of many adiabatic gate operations is considered, for which the total
non-adiabatic error is found to be about the sum of those of all the gates.
This is a useful constraint on the computational power. The formalism is also
briefly applied to the adiabatic quantum algorithm.


title: Quantum Evaluation of Multi-Valued Boolean Functions

abstract:
  Our problem is to evaluate a multi-valued Boolean function $F$ through oracle
calls. If $F$ is one-to-one and the size of its domain and range is the same,
then our problem can be formulated as follows: Given an oracle $f(a,x):
\{0,1\}^n\times\{0,1\}^n \to \{0,1\}$ and a fixed (but hidden) value $a_0$, we
wish to obtain the value of $a_0$ by querying the oracle $f(a_0,x)$. Our goal
is to minimize the number of such oracle calls (the query complexity) using a
quantum mechanism.
  Two popular oracles are the EQ-oracle defined as $f(a,x)=1$ iff $x=a$ and the
IP-oracle defined as $f(a,x)= a\cdot x \mod 2$. It is also well-known that the
query complexity is $\Theta(\sqrt{N})$ ($N=2^n$) for the EQ-oracle while only
O(1) for the IP-oracle. The main purpose of this paper is to fill this gap or
to investigate what causes this large difference. To do so, we introduce a
parameter $K$ as the maximum number of 1's in a single column of $T_f$ where
$T_f$ is the $N\times N$ truth-table of the oracle $f(a,x)$. Our main result
shows that the (quantum) query complexity is heavily governed by this parameter
$K$: ($i$) The query complexity is $\Omega(\sqrt{N/K})$. ($ii$) This lower
bound is tight in the sense that we can construct an explicit oracle whose
query complexity is $O(\sqrt{N/K})$. ($iii$) The tight complexity,
$\Theta(\frac{N}{K}+\log{K})$, is also obtained for the classical case. Thus,
the quantum algorithm needs a quadratically less number of oracle calls when
$K$ is small and this merit becomes larger when $K$ is large, e.g., $\log{K}$
v.s. constant when $K = cN$.


title: Entangled subspaces and quantum symmetries

abstract:
  Entanglement is defined for each vector subspace of the tensor product of two
finite-dimensional Hilbert spaces, by applying the notion of operator
entanglement to the projection operator onto that subspace. The operator
Schmidt decomposition of the projection operator defines a string of Schmidt
coefficients for each subspace, and this string is assumed to characterize the
entanglement of the subspace, so that a first subspace is more entangled than a
second, if the Schmidt string of the second subspace majorizes the Schmidt
string of the first. The idea is applied to the antisymmetric and symmetric
tensor products of a finite-dimensional Hilbert space with itself, and also to
the tensor product of an angular momentum j with a spin 1/2. When adapted to
the subspaces of states of the nonrelativistic hydrogen atom with definite
total angular momentum (orbital plus spin), within the space of bound states
with a given total energy, this leads to a complete ordering of those subspaces
by their Schmidt strings.


title: A de Broglie-Bohm Like Model for Klein-Gordon Equation

abstract:
  A de Broglie-Bohm like model of Klein-Gordon equation, that leads to the
correct Schrodinger equation in the low-speed limit, is presented. Under this
theoretical framework, that affords an interpretation of the quantum potential,
the main assumption of the de Broglie-Bohm interpretation--that the local
momentum of particles is given by the gradient of the phase of the wave
function--is not but approximately correct. Also, the number of particles is
not locally conserved. Furthermore, the representation of physical systems
through wave functions wont be complete.


title:
Comment on "Propagator of two coupled general driven time-dependent
  oscillators" by C. F. Lo and Y. J.Wong

abstract:
  We comment on several incorrect results given in a recent paper by Lo and
Wong. In particular, it is pointed out that their evaluation of the propagator
for two coupled general driven time-dependent oscillators is not satisfactory.
The correct expression can be obtained by applying an appropriate
time-dependent canonical transformation.


title:
Creation of maximally entangled photon-number states using optical fiber
  multiports

abstract:
  We theoretically demonstrate a method for producing the maximally
path-entangled state (1/Sqrt[2]) (|N,0> + exp[iN phi] |0,N>) using
intensity-symmetric multiport beamsplitters, single photon inputs, and either
photon-counting postselection or conditional measurement. The use of
postselection enables successful implementation with non-unit efficiency
detectors. We also demonstrate how to make the same state more conveniently by
replacing one of the single photon inputs by a coherent state.


title: Beyond Quantum Computation and Towards Quantum Field Computation

abstract:
  Because the subject of relativistic quantum field theory (QFT) contains all
of non-relativistic quantum mechanics, we expect quantum field computation to
contain (non-relativistic) quantum computation. Although we do not yet have a
quantum theory of the gravitational field, and are far from a practical
implementation of a quantum field computer, some pieces of the puzzle (without
gravity) are now available. We consider a general model for computation with
quantum field theory, and obtain some results for relativistic quantum
computation. Moreover, it is possible to see new connections between principal
models of computation, namely, computation over the continuum and computation
over the integers (Turing computation). Thus we identify a basic problem in
QFT, namely Wightman's computation problem for domains of holomorphy, which we
call WHOLO. Inspired by the same analytic functions which are central to the
famous CPT theorem of QFT, it is possible to obtain a computational complexity
structure for QFT and shed new light on certain complexity classes for this
problem WHOLO.


title: Quantum processes, space-time representation and brain dynamics

abstract:
  The recent controversy of applicability of quantum formalism to brain
dynamics has been critically analysed. The prerequisites for any type of
quantum formalism or quantum field theory is to investigate whether the
anatomical structure of brain permits any kind of smooth geometric notion like
Hilbert structure or four dimensional Minkowskian structure for quantum field
theory. The present understanding of brain function clearly denies any kind of
space-time representation in Minkowskian sense. However, three dimensional
space and one time can be assigned to the neuromanifold and the concept of
probabilistic geometry is shown to be appropriate framework to understand the
brain dynamics. The possibility of quantum structure is also discussed in this
framework.


title: Effects of Noisy Oracle on Search Algorithm Complexity

abstract:
  Grover's algorithm provides a quadratic speed-up over classical algorithms
for unstructured database or library searches. This paper examines the
robustness of Grover's search algorithm to a random phase error in the oracle
and analyzes the complexity of the search process as a function of the scaling
of the oracle error with database or library size. Both the discrete- and
continuous-time implementations of the search algorithm are investigated. It is
shown that unless the oracle phase error scales as O(N^(-1/4)), neither the
discrete- nor the continuous-time implementation of Grover's algorithm is
scalably robust to this error in the absence of error correction.


title: Quantum hamiltonians and prime numbers

abstract:
  A short review of Schroedinger hamiltonians for which the spectral problem
has been related in the literature to the distribution of the prime numbers is
presented here. We notice a possible connection between prime numbers and
centrifugal inversions in black holes and suggest that this remarkable link
could be directly studied within trapped Bose-Einstein condensates. In
addition, when referring to the factorizing operators of Pitkanen and Castro
and collaborators, we perform a mathematical extension allowing a more standard
supersymmetric approach


title: Quantum Joint Distributions

abstract:
  In this paper we provide a method for constructing joint distributions for an
arbitrary set of observables on finite dimensional Hilbert spaces irrespective
of whether the observables commute or not. These distributions have a number of
desirable properties: they agree with the standard quantum mechanical ones if
the observables commute, they also depend continuously on the observables, and
under unitary transformations they behave in a reasonable manner.


title: Deterministic secure communication protocol without using entanglement

abstract:
  We show a deterministic secure direct communication protocol using single
qubit in mixed state. The security of this protocol is based on the security
proof of BB84 protocol. It can be realized with current technologies.


title: Algorithm of Reduction

abstract:
  We show that the von Neumann's algorithm of reduction (i.e. the algorithm of
calculating the density matrix of the observable subsystem from the density
matrix of the closed quantum system) corresponds to the special approximation
at which the unobservable subsystem is supposed to be in the steady state of
minimum information (infinite temperature). We formulate the generalized
algorithm of reduction that includes as limiting cases the von Neumann's
reduction and the self-congruent correlated reduction most corresponding to the
quantum nondemolition measurement. We demonstrate the correlation in dynamics
of subsystems with exactly soluble models of quantum optics: 1) about the
dynamics of a pair of interacting two-level atoms, and 2) about the dynamics of
a two-level atom interacting with a single-mode resonant field.


title: Duality, Quantum Mechanics and (Almost) Complex Manifolds

abstract:
  The classical mechanics of a finite number of degrees of freedom requires a
symplectic structure on phase space C, but it is independent of any complex
structure. On the contrary, the quantum theory is intimately linked with the
choice of a complex structure on C. When the latter is a complex-analytic
manifold admitting just one complex structure, there is a unique quantisation
whose classical limit is C. Then the notion of coherence is the same for all
observers. However, when C admits two or more nonbiholomorphic complex
structures, there is one different quantisation per different complex structure
on C. The lack of analyticity in transforming between nonbiholomorphic complex
structures can be interpreted as the loss of quantum-mechanical coherence under
the corresponding transformation. Observers using one complex structure
perceive as coherent the states that other observers, using a different complex
structure, do not perceive as such. This is the notion of a quantum-mechanical
duality transformation: the relativity of the notion of a quantum.


title:
Supersymmetric manipulation of quasienergy states. Application to the
  Berry phase

abstract:
  Time-dependent supersymmetry allows one to delete quasienergy levels for
time-periodic Hamiltonians and to create new ones. We illustrate this by
examining an exactly solvable model related to the simple harmonic oscillator
with a time-varying frequency. For an interesting nonharmonic example we
present the change of the Berry phase due to a supersymmetry transformation.


title:
Quantum operation, quantum Fourier transform and semi-definite
  programming

abstract:
  We analyze a class of quantum operations based on a geometrical
representation of $d-$level quantum system (or qudit for short). A sufficient
and necessary condition of complete positivity, expressed in terms of the
quantum Fourier transform, is found for this class of operations. A more
general class of operations on qudits is also considered and its completely
positive condition is reduced to the well-known semi-definite programming
problem.


title: Solving a Maze With a Quantum Computer

abstract:
  It is well known, and appreciated, that quantum computers have the potential
to be the most powerful computational devices ever created. This newfound power
comes from a quantum parallelism effect that allows the computer to be in
multiple states at the same time. This property of quantum parallelism, while
suited to handle common problems such as factoring and searching an unorganized
database, is extremely well-suited to handle the task of solving a binary maze.
I propose an algorithm that can be used to solve a binary maze on a quantum
computer, with guaranteed accuracy. While it does work, it does come with a few
setbacks, in that the maze must have no flaws, and that the computer requires a
number of qubits equal to the number of decisions in the maze, plus log 2 of
the decisions.


title:
S-matrix theory for transmission through billiards in tight-binding
  approach

abstract:
  In the tight-binding approximation we consider multi-channel transmission
through a billiard coupled to leads. Following Dittes we derive the coupling
matrix, the scattering matrix and the effective Hamiltonian, but take into
account the energy restriction of the conductance band. The complex eigenvalues
of the effective Hamiltonian define the poles of the scattering matrix. For
some simple cases, we present exact values for the poles. We derive also the
condition for the appearance of double poles.


title:
Continuous-Variable Quantum Teleportation with a Conventional Laser
  (Rev. Ver.)

abstract:
  We give a description of balanced homodyne detection (BHD) using a
conventional laser as a local oscillator (LO), where the laser field outside
the cavity is a mixed state whose phase is completely unknown. Our description
is based on the standard interpretation of the quantum theory for measurement,
and accords with the experimental result in the squeezed state generation
scheme. We apply our description of BHD to continuous-variable quantum
teleportation (CVQT) with a conventional laser to analyze the CVQT experiment
[A. Furusawa et al., Science 282, 706 (1998)], whose validity has been
questioned on the ground of intrinsic phase indeterminacy of the laser field
[T. Rudolph and B.C. Sanders, Phys. Rev. Lett. 87, 077903 (2001)]. We show that
CVQT with a laser is valid only if the unknown phase of the laser field is
shared among sender's LOs, the EPR state, and receiver's LO. The CVQT
experiment is considered valid with the aid of an optical path other than the
EPR channel and a classical channel, directly linking between a sender and a
receiver. We also propose a method to probabilistically generate a strongly
phase-correlated quantum state via continuous measurement of independent
lasers, which is applicable to realizing CVQT without the additional optical
path.


title: About Covariant Quartit Cloning Machines

abstract:
  The study of quantum cryptography and quantum entanglement has traditionally
been based on two-level quantum systems (qubits) and more recently on
three-level systems (qutrits). We investigate several classes of
state-dependent quantum cloners for four-level systems (quartits). These
results apply to symmetric as well as asymmetric cloners, so that the balance
between the fidelity of the two clones can also be analyzed. We extend Cerf's
formalism for cloning states in order to derive cloning machines that remain
invariant under certain unitary transformations. Our results show that a
different cloner has to be used for two mutually unbiased bases which are
related by a double Hadamard transformation, than for two mutually unbiased
bases that are related by a Fourier transformation. This different cloner is
obtained thanks to a redefinition of Bell states that respects the intrinsic
symmetries of the Hadamard transformation.


title: Robust Quantum Computation with Quantum Dots

abstract:
  Quantum computation in solid state quantum dots faces two significant
challenges: Decoherence from interactions with the environment and the
difficulty of generating local magnetic fields for the single qubit rotations.
This paper presents a design of composite qubits to overcome both challenges.
Each qubit is encoded in the degenerate ground-state of four (or six) electrons
in a system of five quantum dots arranged in a two-dimensional pattern. This
decoherence-free subspace is immune to both collective and local decoherence,
and resists other forms of decoherence, which must raise the energy. The gate
operations for universal computation are simple and physically intuitive, and
are controlled by modifying the tunneling barriers between the dots--Control of
local magnetic fields is not required. A controlled-phase gate can be
implemented in a single pulse.


title: Mode Entanglement and Entangling power in Bosonic Graphs

abstract:
  We analyze the quantum entanglement properties of bosonic particles hopping
over graph structures.Mode-entanglement of a graph vertex with respect the rest
of the graph is generated, starting from a product state, by turning on for a
finite time a tunneling along the graph edges. The maximum achieved during the
dynamical evolution by this bi-partite entanglement characterizes the
entangling power of a given hopping hamiltonian. We studied this entangling
power as a function of the self-interaction parameters i.e., non-linearities,
for all the graphs up to four vertices and for two different natural choices of
the initial state. The role of graph topology and self-interaction strengths in
optimizing entanglement generation is extensively studied by means of exact
numerical simulations and by perturbative calculations.


title: Exceptional Points of Non-hermitian Operators

abstract:
  Exceptional points associated with non-hermitian operators, i.e. operators
being non-hermitian for real parameter values, are investigated. The specific
characteristics of the eigenfunctions at the exceptional point are worked out.
  Within the domain of real parameters the exceptional points are the points
where eigenvalues switch from real to complex values. These and other results
are exemplified by a classical problem leading to exceptional points of a
non-hermitian matrix.


title: Permutationally Invariant Codes for Quantum Error Correction

abstract:
  A permutationally invariant n-bit code for quantum error correction can be
realized as a subspace stabilized by the non-Abelian group S_n. The code
corresponds to bases for the trivial representation, and all other irreducible
representations, both those of higher dimension and orthogonal bases for the
trivial representation, are available for error correction.
  A number of new (non-additive) binary codes are obtained, including two new
7-bit codes and a large family of new 9-bit codes. It is shown that the
degeneracy arising from permutational symmetry facilitates the correction of
certain types of two-bit errors. The correction of two-bit errors of the same
type is considered in detail, but is shown not to be compatible with single-bit
error correction using 9-bit codes.


title: Partial Wave Analysis of Scattering with Nonlocal Aharonov-Bohm Effect

abstract:
  Partial wave theory of a two dimensional scattering problem for an arbitray
short range potential and a nonlocal Aharonov-Bohm magnetic flux is
established. The scattering process of a ``hard disk'' like potential and the
magnetic flux is examined. Since the nonlocal influence of magnetic flux on the
charged particles is universal, the nonlocal effect in hard disk case is
expected to appear in quite general potential system and will be useful in
understanding some phenomena in mesoscopic phyiscs.


title: Rotational master equation for cold laser-driven molecules

abstract:
  The equations of motion for the molecular rotation are derived for
vibrationally cold dimers that are polarized by off-resonant laser light. It is
shown that, by eliminating electronic and vibrational degrees of freedom, a
quantum master equation for the reduced rotational density operator can be
obtained. The coherent rotational dynamics is caused by stimulated Raman
transitions, whereas spontaneous Raman transitions lead to decoherence in the
motion of the quantized angular momentum. As an example the molecular dynamics
for the optical Kerr effect is chosen, revealing decoherence and heating of the
molecular rotation.


title:
Testing Bell's inequality and measuring the entanglement using
  superconducting nanocircuits

abstract:
  An experimental scheme is proposed to test Bell's inequality by using
superconducting nanocircuits. In this scheme, quantum entanglement of a pair of
charge qubits separated in a sufficient long distance may be created by cavity
quantum electrodynamic techniques; the population of qubits is experimentally
measurable by dc currents through the probe junctions, and one measured outcome
may be recorded for every experiment. Therefore, both locality and detection
efficiency loopholes should be closed in the same experiment. We also propose a
useful method to measure the amount of entanglement based on the concurrence
between Josephson qubits. The measurable variables for Bell's inequality as
well as the entanglement are expressed in terms of a useful phase-space Q
function.


title: On the quantum phase problem

abstract:
  We present a phase formalism that passes the Barnett-Pegg acid test, i.e.
phase fluctuations for a number state are the expected value $\pi^2/3$ which
are the fluctuations for a classical random phase distribution. The formalism
is shown to have consistency subjected to different approaches.


title: What is actually teleported?

abstract:
  There are no ``unknown quantum states.'' It's a contradiction in terms.
Moreover, Alice and Bob are only inanimate objects. They know nothing. What is
teleported instantaneously from one system (Alice) to another system (Bob) is
the applicability of the preparer's knowledge to the state of a particular
qubit in these systems. The operation necessitates dual classical and quantum
channels. Other examples of dual transmission, including ``unspeakable
information,'' will be presented and discussed. This article also includes a
narrative of how I remember that quantum teleportation was conceived.


title:
Quantum information processing, operational quantum logic, convexity,
  and the foundations of physics

abstract:
  Quantum information science is a source of task-related axioms whose
consequences can be explored in general settings encompassing quantum
mechanics, classical theory, and more. Quantum states are compendia of
probabilities for the outcomes of possible operations we may perform a system:
``operational states.'' I discuss general frameworks for ``operational
theories'' (sets of possible operational states of a system), in which
convexity plays key role. The main technical content of the paper is in a
theorem that any such theory naturally gives rise to a ``weak effect algebra''
when outcomes having the same probability in all states are identified, and in
the introduction of a notion of ``operation algebra'' that also takes account
of sequential and conditional operations. Such frameworks are appropriate for
investigating what things look like from an ``inside view,'' i.e. for
describing perspectival information that one subsystem of the world can have
about another. Understanding how such views can combine, and whether an overall
``geometric'' picture (``outside view'') coordinating them all can be had, even
if this picture is very different in structure from the perspectives within it,
is the key to whether we may be able to achieve a unified, ``objective''
physical view in which quantum mechanics is the appropriate description for
certain perspectives, or whether quantum mechanics is truly telling us we must
go beyond this ``geometric'' conception of physics.


title:
Demonstration of Dispersion-Cancelled Quantum-Optical Coherence
  Tomography

abstract:
  We present an experimental demonstration of quantum optical coherence
tomography (QOCT). The technique makes use of an entangled twin-photon light
source to carry out axial optical sectioning. QOCT is compared to conventional
optical co1herence tomography (OCT). The immunity of QOCT to dispersion, as
well as a factor of two enhancement in resolution, are experimentally
demonstrated.


title: Sparse Graph Codes for Quantum Error-Correction

abstract:
  We present sparse graph codes appropriate for use in quantum
error-correction. Quantum error-correcting codes based on sparse graphs are of
interest for three reasons. First, the best codes currently known for classical
channels are based on sparse graphs. Second, sparse graph codes keep the number
of quantum interactions associated with the quantum error correction process
small: a constant number per quantum bit, independent of the blocklength.
Third, sparse graph codes often offer great flexibility with respect to
blocklength and rate. We believe some of the codes we present are unsurpassed
by previously published quantum error-correcting codes.


title: A quantum lower bound for the collision problem

abstract:
  We extend Shi's 2002 quantum lower bound for collision in $r$-to-one
functions with $n$ inputs. Shi's bound of $\Omega((n/r)^{1/3})$ is tight, but
his proof applies only in the case where the range has size at least $3n/2$. We
give a modified version of Shi's argument which removes this restriction.


title:
Faraday spectroscopy in an optical lattice: a continuous probe of atom
  dynamics

abstract:
  The linear Faraday effect is used to implement a continuous measurement of
the spin of a sample of laser cooled atoms trapped in an optical lattice. One
of the optical lattice beams serves also as a probe beam, thereby allowing one
to monitor the atomic dynamics in real time and with minimal perturbation. A
simple theory is developed to predict the measurement sensitivity and
associated cost in terms of decoherence caused by the scattering of probe
photons. Calculated signal-to-noise ratios in measurements of Larmor precession
are found to agree with experimental data for a wide range of lattice intensity
and detuning. Finally, quantum backaction is estimated by comparing the
measurement sensitivity to spin projection noise, and shown to be insignificant
in the current experiment. A continuous quantum measurement based on Faraday
spectroscopy in optical lattices may open up new possibilities for the study of
quantum feedback and classically chaotic quantum systems.


title:
Teleportation-based number state manipulation with number sum
  measurement

abstract:
  We examine various manipulations of photon number states which can be
implemented by teleportation technique with number sum measurement. The
preparations of the Einstein-Podolsky-Rosen resources as well as the number sum
measurement resulting in projection to certain Bell state may be done
conditionally with linear optical elements, i.e., beam splitters, phase
shifters and zero-one-photon detectors. Squeezed vacuum states are used as
primary entanglement resource, while single-photon sources are not required.


title: Quantum teleportation using cluster states

abstract:
  A protocol of quantum communication is proposed in terms of the multi-qubit
quantum teleportation through cluster states (Phys. Rev. Lett. \textbf{86}, 910
(2001)). Extending the cluster state based quantum teleportation on the basic
unit of three qubits (or qudits), the corresponding multi-qubit network is
constructed for both the qubits and qudits (multi-level) cases. The classical
information costs to complete this communication task is also analyzed. It is
also shown that this quantum communication protocol can be implemented in the
spin-spin system on lattices.


title: Photon filters in a microwave cavity

abstract:
  In an earlier paper we have concluded that time-dependent parameters in
atom-mode interaction can be utilized to modify the quantum field in a cavity.
When an atom shoots through the cavity field, it is expected to experience a
trigonometric time dependence of its coupling constant. We investigate the
possibilities this offers to modify the field. As a point of comparison we use
the solvable Rosen-Zener model, which has parameter dependencies roughly
similar to the ones expected in a real cavity. We do confirm that by repeatedly
sending atoms through the cavity, we can obtain filters on the photon states.
Highly non-classical states can be obtained. We find that the Rosen-Zener model
is more sensitive to the detuning than the case of a trigonometric coupling.


title: Nonlinear Dirac equations and nonlinear gauge transformations

abstract:
  Nonlinear Dirac equations (NLDE) are derived through a group N^2 of nonlinear
(gauge) transformation acting in the corresponding state space. The
construction generalises a construction for nonlinear Schr\"odinger equations.
To relate N^2 with physically motivated principles we assume: locality (i.e. it
contains no explicit derivative and no derivatives of the wave function),
separability (i.e. it acts on product states componentwise) and Poincar\'e
invariance. Furthermore we want that a positional density is invariant under
N^2. Such nonlinear transformations yield NLDE which describe physically
equivalent systems. To get 'new' systems, we extend this NLDE (gauge extension)
and present a family of NLDE which is a slight nonlinear generalisation of the
Dirac equation. We discuss and comment the fact that nonlinear evolutions are
not consistent with the usual framework of quantum theory. To develop a
corresponding extended framework one needs models for nonlinear evolutions
which also indicate possible physical consequences of nonlinearities.


title: Ion-trap quantum computing in the presence of cooling

abstract:
  This paper discusses ways to implement two-qubit gate operations for quantum
computing with cold trapped ions within one step. The proposed scheme is widely
robust against parameter fluctuations and its simplicity might help to increase
the number of qubits in present experiments. Basic idea is to use the quantum
Zeno effect originating from continuous measurements on a common vibrational
mode to realise gate operations with very high fidelities. The gate success
rate can, in principle, be arbitrary high but operation times comparable to
other schemes can only be obtained by accepting success rates below 80%.


title:
Spin-based quantum gating with semiconductor quantum dots by bichromatic
  radiation method

abstract:
  A potential scheme is proposed for realizing a two-qubit quantum gate in
semiconductor quantum dots. Information is encoded in the spin degrees of
freedom of one excess conduction electron of each quantum dot. We propose to
use two lasers, radiation two neighboring QDs, and tuned to blue detuning with
respect to the resonant frequencies of individual excitons. The two-qubit phase
gate can be achieved by means of both Pauli-blocking effect and dipole-dipole
coupling between intermediate excitonic states.


title:
Multiparametric oscillator Hamiltonians with exact bound states in
  infinite-dimensional space

abstract:
  Central D-dimensional Hamiltonians $H = p^2 + a |\vec{r}|^2 + b |\vec{r}|^4 +
>... + z |\vec{r}|^{4q+2}$ (where z=1) are considered in the limit $D \to
\infty$ where numerical experiments revealed recently a new class of
q-parametric quasi-exact solutions at $q \leq 5$. We show how a systematic
construction of these "privileged" exact bound states may be extended to much
higher q (meaning an enhanced flexibility of the shape of the force) at a cost
of narrowing the set of wavefunctions (with degree N restricted to the first
few non-negative integers). At q=4K+3 we conjecture the validity of a closed
formula for the N=3 solutions at all K.


title: A relativistic variant of the Wigner function

abstract:
  The conventional Wigner function is inappropriate in a quantum field theory
setting because, as a quasiprobability density over phase space, it is not
manifestly Lorentz covariant. A manifestly relativistic variant is constructed
as a quasiprobability density over trajectories instead of over phase space.


title:
Monomode photon spin operators projected onto the fixed frame and
  quantum-vacuum geometric phases of photons inside a noncoplanar optical fibre

abstract:
  The propagation of monomode photons inside a coiled optical fibre was
regarded as a time-dependent quantum evolution process, which gives rise to a
geometric phase. It is well known that the investigation of non-adiabatic
geometric phases ought to be performed only in the Schr\"{o}dinger picture. So,
the projections of photon spin operators onto the fixed frame of reference is
discussed in this paper. In addition, we also treat the non-normal-order spin
operators and consider the potential effects (e.g., quantum-vacuum geometric
phases) of quantum fluctuation fields arising in a curved optical fibre. The
quantum-vacuum geometric phase, which is of physical interest, can be deducted
by using the operator normal product, and the doubt of validity and
universality for the normal-normal procedure applied to time-dependent quantum
systems is thus proposed. In the Appendix, the discussion of possible
experimental realizations of quantum-vacuum geometric phases is briefly
presented.


title:
Quantum information processing using Josephson junctions coupled through
  cavities

abstract:
  Josephson junctions have been shown to be a promising solid-state system for
implementation of quantum computation. The significant two-qubit gates are
generally realized by the capacitive coupling between the nearest neighbour
qubits. We propose an effective Hamiltonian to describe charge qubits coupled
through the cavity. We find that nontrivial two-qubit gates may be achieved by
this coupling. The ability to interconvert localized charge qubits and flying
qubits in the proposed scheme implies that quantum network can be constructed
using this large scalable solid-state system.


title:
Universal quantum gates based on both geometric and dynamic phases in
  quantum dots

abstract:
  A large-scalable quantum computer model, whose qubits are represented by the
subspace subtended by the ground state and the single exciton state on
semiconductor quantum dots, is proposed. A universal set of quantum gates in
this system may be achieved by a mixed approach, composed of dynamic evolution
and nonadibatic geometric phase.


title: Optimal realization of the transposition maps

abstract:
  We solve the problem of achieving the optimal physical approximation of the
transposition for pure states of arbitrary quantum systems for finite and
infinite dimensions. A unitary realization is also given for any finite
dimension, which provides the optimal quantum cloning map of the ancilla as
well.


title:
Violations of Bell inequalities as lower bounds on the communication
  cost of non-local correlations

abstract:
  To reproduce in a local hidden variables theory correlations that violate
Bell inequalities, communication must occur between the parties. We show that
the amount of violation of a Bell inequality imposes a lower bound on the
average communication needed to produce these correlations. Moreover, for every
probability distribution there exists an optimal inequality for which the
degree of violation gives the minimal average communication. As an example, to
produce using classical resources the correlations that maximally violate the
CHSH inequality, 0.4142 bits of communication are necessary and sufficient. For
Bell tests performed on two entangled states of dimension d>=3 where each party
has the choice between two measurements, our results suggest that more
communication is needed to simulate outcomes obtained from certain
non-maximally entangled states than maximally entangled ones.


title:
Blinking molecules: Determination of Photo-Physical Parameters from the
  Intensity Correlation Function

abstract:
  An explicit expression is given for the correlation function of blinking
systems, i.e. systems exhibiting light and dark periods in their fluorescence.
We show through the example of terrylene in a crystalline host that it is
possible to determine by means of this explicit expression photo-physical
parameters, like Einstein coefficients and the mean light and dark periods by a
simple fit. In addition we obtain further parameters like the frequency of the
various intensity periods and the probability density of photons scattered off
the host crystal. It turns out that this approach is simpler and allows greater
accuracy than previous procedures.


title:
Non-Markovian Decay of a Three Level Cascade Atom in a Structured
  Reservoir

abstract:
  We present a formalism that enables the study of the non-Markovian dynamics
of a three-level ladder system in a single structured reservoir. The
three-level system is strongly coupled to a bath of reservoir modes and two
quantum excitations of the reservoir are expected. We show that the dynamics
only depends on reservoir structure functions, which are products of the mode
density with the coupling constant squared. This result may enable pseudomode
theory to treat multiple excitations of a structured reservoir. The treatment
uses Laplace transforms and an elimination of variables to obtain a formal
solution. This can be evaluated numerically (with the help of a numerical
inverse Laplace transform) and an example is given. We also compare this result
with the case where the two transitions are coupled to two separate structured
reservoirs (where the example case is also analytically solvable).


title:
Reduction Theorems for Optimal Unambiguous State Discrimination of
  Density Matrices

abstract:
  We present reduction theorems for the problem of optimal unambiguous state
discrimination (USD) of two general density matrices. We show that this problem
can be reduced to that of two density matrices that have the same rank $n$ and
are described in a Hilbert space of dimensions $2n$. We also show how to use
the reduction theorems to discriminate unambiguously between N mixed states (N
\ge 2).


title: Control of conditional pattern with polarization entanglement

abstract:
  Conditional interference patterns can be obtained with twin photons from
spontaneous parametric down-conversion and the phase of the pattern can be
controlled by the relative transverse position of the signal and idler
detectors. Using a configuration that produces entangled photons in both
polarization and transverse momentum we report on the control of the
conditional patterns by acting on the polarization degree of freedom.


title:
Measurement of one-photon and two-photon wavepackets in spontaneous
  parametric down-conversion

abstract:
  One-photon and two-photon wavepackets of entangled two-photon states in
spontaneous parametric down-conversion (SPDC) fields are calculated and
measured experimentally. For type-II SPDC, measured one-photon and two-photon
wavepackets agree well with theory. For type-I SPDC, the measured one-photon
wavepacket agree with the theory. However, the two-photon wavepacket is much
bigger than the expected value and the visibility of interference is low. We
identify the sources of this discrepancy as the spatial filtering of the
two-photon bandwidth and non-pair detection events caused by the detector
apertures and the tuning curve characteristics of the type-I SPDC.


title: Quantum probability measures and tomographic probability densities

abstract:
  Introduced recently approach based on tomographic probability distribution of
quantum states is shown to be closely related with the known notion of the
quantum probability measures discussed in quantum information theory and
positive operator valued measures approach. Partial derivative of the
distribution function of quantum probability measure associated with the
homodyne quadrature (symplectic quantum measure) is shown to be equal the
tomogram of the quantum state. Analogous relation of the spin tomogram to
quantum probability measure associated with spin state is obtained.
Star-product of symplectic quantum measures is studied. Evolution equation for
symplectic quantum measures is derived.


title: On entanglement at tripartite states

abstract:
  Article presents general formulation of entanglement measures problem in
terms of correlation function. Description of entanglement in probabilistic
framework allow us to introduce new quantity which describes quantum and
classical correlations. This formalism is applied to calculate bipartite and
tripartite correlations in two special cases of entangled states of tripartite
systems.


title: Bell States, Dense Coding, and Teleportation

abstract:
  The question of the measurements on the Bell states by making use of mode
change (from mixed to pure) of one qubit is considered. Such a mode change
cannot be taken advantage of for superluminal communication in teleportation,
and it may define constraints on the size of the gates.


title:
Decoherence effects on the tunneling rate of paramagnetic and
  superparamagnetic particles

abstract:
  We analyze the effects of the environment on the spin tunneling process of
paramagnetic and superparamagnetic particles and conclude that the non assisted
macroscopic tunneling rate is hardly affected in such case, but other more
effective (phonon mediated) processes change the magnetization state of the
particle. We conclude that for both, paramagnetic and superparamagnetic
particles, the decoherence time scale is extremely short (~ 10^(-8..-16)seg),
indicating thar coherent tunneling should be strongly suppressed in favor of
incoherent tunneling, i.e., the population of higher levels with subsequent
decay.


title: Quantum correlations between separated particles

abstract:
  Long-range quantum correlations between particles are usually formulated by
assuming the persistence of an entangled state after the particles have
spearated. Here this approach is re-examined based upon studying the
correlations present in a pair of EPR spins. Two types of correltions are
identified. The first, due to the quantum interference terms is parity. This
symmetry property characterizes entanglement. Second is correlation due to
conservation of angular momentum. The two contributions are equal and have the
same functional form. When entanglement is present, Bell's inequalities are
violated but when parity is destroyed by disentanglement, Bell's inequalities
are satisfied. It is shown tht some experiments which have hiterto been
interpreted by entangled states can be better described by disentanglement.
Implications for quantum non-locality are discussed.


title: Quantum "Teleportation" using local correlations

abstract:
  The phenomenon called quantum "teleportation" has been formulated assuming
the presence of entangled states and is interpreted as a realization of quantum
non-locality. In contrast, correlations from both entanglement and
disentanglement upon particle spearation exists and both of these are built
into the EPR pair as they move apart. Here it is shown that quantum
"teleportaton" can be formulated and interpreted without invoking a non-local
hypothesis of quantum mechanics, and is better descrited as "quantum state
selection".


title: Atomic Qubit Manipulations with an Electro-Optic Modulator

abstract:
  We report new techniques for driving high-fidelity stimulated Raman
transitions in trapped ion qubits. An electro-optic modulator induces sidebands
on an optical source, and interference between the sidebands allows coherent
Rabi transitions to be efficiently driven between hyperfine ground states
separated by 14.53 GHz in a single trapped 111Cd+ ion.


title: Description of a quantum convolutional code

abstract:
  We describe a quantum error correction scheme aimed at protecting a flow of
quantum information over long distance communication. It is largely inspired by
the theory of classical convolutional codes which are used in similar
circumstances in classical communication. The particular example shown here
uses the stabilizer formalism, which provides an explicit encoding circuit. An
associated error estimation algorithm is given explicitly and shown to provide
the most likely error over any memoryless quantum channel, while its complexity
grows only linearly with the number of encoded qubits.


title: Stability of stationary solutions of the Schrodinger-Langevin equation

abstract:
  The stability properties of a class of dissipative quantum mechanical systems
are investigated. The nonlinear stability and asymptotic stability of
stationary states (with zero and nonzero dissipation respectively) is
investigated by Liapunov's direct method. The results are demonstrated by
numerical calculations on the example of the damped harmonic oscillator.


title: Muon transfer from muonic hydrogen to atomic oxygen

abstract:
  The muon transfer probabilities between muonic hydrogen and an oxygen atom
are calculated in a constrained geometry one dimensional model for collision
between 10^-6 and 10^3 eV. These estimated rates are discussed in the light of
previous model calculations and available experimental data for this process.


title: Stored light and released fiction

abstract:
  It is shown that the interpretation of the experimental results reported in
the publication Storage of Light in Atomic Vapor" by D.F.Phillips et al., Phys.
Rev.Lett. 86, 783 (2001) is incorrect. The experimental observation of this
paper can be consistently explained in the framework of standard concepts of
the physics of optical pumping and have nothing to do with "storage of light'',
or "dynamic reduction of the group velocity'', or "light pulse compression''.


title: Generation of spatial antibunching with free propagating twin beams

abstract:
  We propose and implement a novel method to produce a spatial anti-bunched
field with free propagating twin beams from spontaneous parametric
down-conversion. The method consists in changing the spatial propagation by
manipulating the transverse degrees of freedom through reflections of one of
the twin beams. Our method use reflective elements eliminating losses from
absorption by the objects inserted in the beams.


title: Mixture of multiple copies of maximally entangled states is quasi-pure

abstract:
  Employing the general BXOR operation and local state discrimination, the
mixed state of the form
\rho^{(k)}_{d}=\frac{1}{d^{2}}\sum_{m,n=0}^{d-1}(|\phi_{mn}><\phi_{mn}|)^{\otim
es k} is proved to be quasi-pure, where $\{|\phi_{mn}>\}$ is the canonical set
of mutually orthogonal maximally entangled states in $d\times d$. Therefore
irreversibility does not occur in the process of distillation for this family
of states. Also, the distillable entanglement is calculated explicitly.


title: A de Broglie-Bohm Like Model for Dirac Equation

abstract:
  A de Broglie-Bohm like model of Dirac equation, that leads to the correct
Pauli equations for electrons and positrons in the low-speed limit, is
presented. Under this theoretical framework, that affords an interpretation of
the quantum potential, the main assumption of the de Broglie-Bohm theory--that
the local momentum of particles is given by the gradient of the phase of the
wave function--wont be accurate. Also, the number of particles wont be locally
conserved. Furthermore, the representation of physical systems through wave
functions wont be complete.


title: Distilling common randomness from bipartite quantum states

abstract:
  The problem of converting noisy quantum correlations between two parties into
noiseless classical ones using a limited amount of one-way classical
communication is addressed. A single-letter formula for the optimal trade-off
between the extracted common randomness and classical communication rate is
obtained for the special case of classical-quantum correlations. The resulting
curve is intimately related to the quantum compression with classical side
information trade-off curve $Q^*(R)$ of Hayden, Jozsa and Winter. For a general
initial state we obtain a similar result, with a single-letter formula, when we
impose a tensor product restriction on the measurements performed by the
sender; without this restriction the trade-off is given by the regularization
of this function. Of particular interest is a quantity we call ``distillable
common randomness'' of a state: the maximum overhead of the common randomness
over the one-way classical communication if the latter is unbounded. It is an
operational measure of (total) correlation in a quantum state. For
classical-quantum correlations it is given by the Holevo mutual information of
its associated ensemble, for pure states it is the entropy of entanglement. In
general, it is given by an optimization problem over measurements and
regularization; for the case of separable states we show that this can be
single-letterized.


title: Effective Hamiltonian and unitarity of the S matrix

abstract:
  The properties of open quantum systems are described well by an effective
Hamiltonian ${\cal H}$ that consists of two parts: the Hamiltonian $H$ of the
closed system with discrete eigenstates and the coupling matrix $W$ between
discrete states and continuum. The eigenvalues of ${\cal H}$ determine the
poles of the $S$ matrix. The coupling matrix elements $\tilde W_k^{cc'}$
between the eigenstates $k$ of ${\cal H}$ and the continuum may be very
different from the coupling matrix elements $W_k^{cc'}$ between the eigenstates
of $H$ and the continuum. Due to the unitarity of the $S$ matrix, the
$\TW_k^{cc'}$ depend on energy in a non-trivial manner, that conflicts with the
assumptions of some approaches to reactions in the overlapping regime. Explicit
expressions for the wave functions of the resonance states and for their phases
in the neighbourhood of, respectively, avoided level crossings in the complex
plane and double poles of the $S$ matrix are given.


title:
Spin-dependent Bohm trajectories for Pauli and Dirac eigenstates of
  hydrogen

abstract:
  The de Broglie-Bohm causal theory of quantum mechanics is applied to the
hydrogen atom in the fully spin-dependent and relativistic framework of the
Dirac equation, and in the nonrelativistic but spin-dependent framework of the
Pauli equation. Eigenstates are chosen which are simultaneous eigenstates of
the energy H, total angular momentum M, and z component of the total angular
momentum M_z. We find the trajectories of the electron, and show that in these
eigenstates, motion is circular about the z-axis, with constant angular
velocity. We compute the rates of revolution for the ground (n=1) state and the
n=2 states, and show that there is agreement in the relevant cases between the
Dirac and Pauli results, and with earlier results on the Schrodinger equation.


title: Quantum gates with topological phases

abstract:
  We investigate two models for performing topological quantum gates with the
Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects. Topological one- and
two-qubit Abelian phases can be enacted with the AB effect using charge qubits,
whereas the AC effect can be used to perform all single-qubit gates (Abelian
and non-Abelian) for spin qubits. Possible experimental setups suitable for a
solid state implementation are briefly discussed.


title:
On the properties of information gathering in quantum and classical
  measurements

abstract:
  The information provided by a classical measurement is unambiguously
determined by the mutual information between the output results and the
measured quantity. However, quantum mechanically there are at least two notions
of information gathering which can be considered, one characterizing the
information provided about the initial preparation, useful in communication,
and the other characterizing the information about the final state, useful in
state-preparation and control. Here we are interested in understanding the
properties of these measures, and the information gathering capacities of
quantum and classical measurements. We provide a partial answer to the question
`in what sense does information gain increase with initial uncertainty?' by
showing that, for classical and quantum measurements which are symmetric with
respect to reversible transformations of the state space, the information gain
regarding the initial state always increases with the observer's initial
uncertainty. In addition, we calculate the capacity of all unitarily covariant
and commutative permutation-symmetric measurements for obtaining classical
information. While it is the von Neumann entropy of the effects which appears
in the latter capacity, it is the subentropy which appears in the expression
for the former.


title: Quantum walk on the line as an interference phenomenon

abstract:
  We show that the coined quantum walk on a line can be understood as an
interference phenomenon, can be classically implemented, and indeed already has
been. The walk is essentially two independent walks associated with the
different coin sides, coupled only at initiation. There is a simple analogy
between the evolution of walker positions and the propagation of light in a
dispersive optical fiber.


title: That strange procedure called quantisation

abstract:
  This is a pedagogical and (almost) self-contained introduction into the
theorem of Groenewold and van Howe, which states that a naive transcription of
Dirac's quantisation rules cannot work. Some related issues in quantisation
theory are also discussed. First-class constrained systems are briefly
described in a slightly more `global' fashion.


title:
Spin-dependent Bohm trajectories associated with an electronic
  transition in hydrogen

abstract:
  The Bohm causal theory of quantum mechanics with spin-dependence is used to
determine electron trajectories when a hydrogen atom is subjected to
(semi-classical) radiation. The transition between the 1s ground state and the
2p0 state is examined. It is found that transitions can be identified along
Bohm trajectories. The trajectories lie on invariant hyperboloid surfaces of
revolution in R^3. The energy along the trajectories is also discussed in
relation to the hydrogen energy eigenvalues.


title: Controlling discrete quantum walks: coins and intitial states

abstract:
  In discrete time, coined quantum walks, the coin degrees of freedom offer the
potential for a wider range of controls over the evolution of the walk than are
available in the continuous time quantum walk. This paper explores some of the
possibilities on regular graphs, and also reports periodic behaviour on small
cyclic graphs.


title: Entangled light in transition through the generation threshold

abstract:
  We investigate continuous variable entangling resources on the base of
two-mode squeezing for all operational regimes of a nondegenerate optical
parametric oscillator with allowance for quantum noise of arbitrary level. The
results for the quadrature variances of a pair of generated modes are obtained
by using the exact steady-state solution of Fokker-Planck equation for the
complex P-quasiprobability distribution function. We find a simple expression
for the squeezed variances in the near-threshold range and conclude that the
maximal two-mode squeezing reaches 50% relative to the level of vacuum
fluctuations and is achieved at the pump field intensity close to the
generation threshold. The distinction between the degree of two-mode squeezing
for monostable and bistable operational regimes is cleared up.


title: Harmonic inversion helps to beat time-energy uncertainty relations

abstract:
  It is impossible to obtain accurate frequencies from time signals of a very
short duration. This is a common believe among contemporary physicists. Here I
present a practical way of extracting energies to a high precision from very
short time signals produced by a quantum system. The product of time span of
the signal and the precision of found energies is well bellow the limit imposed
by the time-energy uncertainty relation.


title:
Diagnosis, prescription and prognosis of a Bell-state filter by quantum
  process tomography

abstract:
  Using a Hong-Ou-Mandel interferometer, we apply the techniques of quantum
process tomography to characterize errors and decoherence in a prototypical
two-photon operation, a singlet-state filter. The quantum process tomography
results indicate a large asymmetry in the process and also the required
operation to correct for this asymmetry. Finally, we quantify errors and
decoherence of the filtering operation after this modification.


title:
Characterization of entanglement using sum uncertainty relations for
  N-level systems

abstract:
  The efficient experimental verification of entanglement requires an
identification of the essential physical properties that distinguish entangled
states from non-entangled states. Since the most characteristic feature of
entanglement is the extreme precision of correlations between spatially
separated systems, we propose a quantitative criterion based on local
uncertainty relations (quant-ph/0212090). Some basic sum uncertainty relations
for N-level systems are introduced and the amount of entanglement that can be
verified by violations of the corresponding local uncertainty limit is
discussed.


title:
Bound entangled states violate a non-symmetric local uncertainty
  relation

abstract:
  As a consequence of having a positive partial transpose, bound entangled
states lack many of the properties otherwise associated with entanglement. It
is therefore interesting to identify properties that distinguish bound
entangled states from separable states. In this paper, it is shown that some
bound entangled states violate a non-symmetric class of local uncertainty
relations (quant-ph/0212090). This result indicates that the asymmetry of
non-classical correlations may be a characteristic feature of bound
entanglement.


title: An arbitrary-operation gate with a SQUID qubit

abstract:
  A novel approach is proposed for realizing an arbitrary-operation gate with a
SQUID qubit via pulsed-microwave manipulation. In this approach, the two
logical states of the qubit are represented by the two lowest levels of the
SQUID and an intermediate level is utilized for the gate manipulation. The
method does not involve population in the intermediate level or tunneling
between the two logical qubit states during the gate operation. Morever, we
show that the gate can be much faster than the conventional two-level gate. In
addition, to take the advantage of geometric quantum computing, we further show
how the method can be extended to implement an arbitrary quantum logic
operation in a SQUID qubit via geometric manipulation.


title:
Entangled states with positive partial transpose arising from
  indecomposable positive linear maps

abstract:
  We construct entangled states with positive partial transposes using
indecomposable positive linear maps between matrix algebras. We also exhibit
concrete examples of entangled states with positive partial transposes arising
in this way, and show that they generate extreme rays in the cone of all
positive semi-definite matrices with positive partial transposes. They also
have Schmidt numbers two.


title:
Eliminating ground-state dipole moments in quantum optics via canonical
  transformation

abstract:
  By means of a canonical transformation it is shown how it is possible to
recast the equations for molecular nonlinear optics to completely eliminate
ground-state static dipole coupling terms. Such dipoles can certainly play a
highly important role in nonlinear optical response - but equations derived by
standard methods, in which these dipoles emerge only as special cases of
transition moments, prove unnecessarily complex. It has been shown that the
elimination of ground-state static dipoles in favor of dipole shifts results in
a considerable simplification in form of the nonlinear optical
susceptibilities. In a fully quantum theoretical treatment the validity of such
a procedure has previously been verified using an expedient algorithm, whose
defense was afforded only by a highly intricate proof. In this paper it is
shown how a canonical transformation method entirely circumvents such an
approach; it also affords new insights into the formulation of quantum field
interactions.


title: Quantum Physics of Simple Optical Instruments

abstract:
  Simple optical instruments are linear optical networks where the incident
light modes are turned into equal numbers of outgoing modes by linear
transformations. For example, such instruments are beam splitters, multiports,
interferometers, fibre couplers, polarizers, gravitational lenses, parametric
amplifiers, phase-conjugating mirrors and also black holes. The article
develops the quantum theory of simple optical instruments and applies the
theory to a few characteristic situations, to the splitting and interference of
photons and to the manifestation of Einstein-Podolsky-Rosen correlations in
parametric downconversion. How to model irreversible devices such as absorbers
and amplifiers is also shown. Finally, the article develops the theory of
Hawking radiation for a simple optical black hole. The paper is intended as a
primer, as a nearly self-consistent tutorial. The reader should be familiar
with basic quantum mechanics and statistics, and perhaps with optics and some
elementary field theory. The quantum theory of light in dielectrics serves as
the starting point and, in the concluding section, as a guide to understand
quantum black holes.


title: Simulation of quantum random walks using interference of classical field

abstract:
  We suggest a theoretical scheme for the simulation of quantum random walks on
a line using beam splitters, phase shifters and photodetectors. Our model
enables us to simulate a quantum random walk with use of the wave nature of
classical light fields. Furthermore, the proposed set-up allows the analysis of
the effects of decoherence. The transition from a pure mean photon-number
distribution to a classical one is studied varying the decoherence parameters.