title: Analytic Representation of Finite Quantum Systems

abstract:
  A transform between functions in R and functions in Zd is used to define the
analogue of number and coherent states in the context of finite d-dimensional
quantum systems. The coherent states are used to define an analytic
representation in terms of theta functions. All states are represented by
entire functions with growth of order 2, which have exactly d zeros in each
cell. The analytic function of a state is constructed from its zeros. Results
about the completeness of finite sets of coherent states within a cell are
derived.


title: Phase space methods for particles on a circle

abstract:
  The phase space $S\times Z$ for a particle on a circle is considered.
Displacement operators in this phase space are introduced and their properties
are studied. Wigner and Weyl functions in this context are also considered and
their physical interpretation and properties are discussed. All results are
compared and contrasted with the corresponding ones for the harmonic oscillator
in the $R \times R$ phase space.


title: Optimal Time-Reversal of Multi-phase Equatorial States

abstract:
  Even though the time-reversal is unphysical (it corresponds to the complex
conjugation of the density matrix), for some restricted set of states it can be
achieved unitarily, typically when there is a common de-phasing in a n-level
system. However, in the presence of multiple phases (i. e. a different
de-phasing for each element of an orthogonal basis occurs) the time reversal is
no longer physically possible. In this paper we derive the channel which
optimally approaches in fidelity the time-reversal of multi-phase equatorial
states in arbitrary (finite) dimension. We show that, in contrast to the
customary case of the Universal-NOT on qubits (or the universal conjugation in
arbitrary dimension), the optimal phase covariant time-reversal for equatorial
states is a nonclassical channel, which cannot be achieved via a
measurement/preparation procedure. Unitary realizations of the optimal
time-reversal channel are given with minimal ancillary dimension, exploiting
the simplex structure of the optimal maps.


title: An Operator-Based Exact Treatment of Open Quantum Systems

abstract:
  "Quantum mechanics must be regarded as open systems. On one hand, this is due
to the fact that, like in classical physics, any realistic system is subjected
to a coupling to an uncontrollable environment which influences it in a
non-negligible way. The theory of open quantum systems thus plays a major role
in many applications of quantum physics since perfect isolation of quantum
system is not possible and since a complete microscopic description or control
of the environment degrees of freedom is not feasible or only partially so"
[1]. Practical considerations therefore force one to seek for a simpler,
effectively probabilistic description in terms of an open system. There is a
close physical and mathematical connection between the evolution of an open
system, the state changes induced by quantum measurements, and the classical
notion of a stochastic process. The paper provides a bibliographic review of
this interrelations, it shows the mathematical equivalence between markovian
master equation and generalized piecewise deterministic processes [1] and it
introduces the open system in an open observed environment model.


title: Comment on the Ghost State in the Lee Model

abstract:
  We examine the ghost state in the Lee model, and give the physically
meaningful interpretatation for norm of the ghost state. According to this
interpretation, the semi-positivity of the norm is guaranteed.


title:
Hidden measurements, hidden variables and the volume representation of
  transition probabilities

abstract:
  We construct, for any finite dimension $n$, a new hidden measurement model
for quantum mechanics based on representing quantum transition probabilities by
the volume of regions in projective Hilbert space. For $n=2$ our model is
equivalent to the Aerts sphere model and serves as a generalization of it for
dimensions $n \geq 3$. We also show how to construct a hidden variables scheme
based on hidden measurements and we discuss how joint distributions arise in
our hidden variables scheme and their relationship with the results of Fine.


title: Decoherence and localization in the double well model

abstract:
  We use a spin-1/2 model to analyze tunnelling in a double well system coupled
to an external reservoir. We consider different noise sources such as
fluctuations on the height and central position of the barrier and propose an
experiment to observe these effects in trapped ions or atoms.


title: Numerical Simulations of a Possible Hypercomputational Quantum Algorithm

abstract:
  The hypercomputers compute functions or numbers, or more generally solve
problems or carry out tasks, that cannot be computed or solved by a Turing
machine. Several numerical simulations of a possible hypercomputational
algorithm based on quantum computations previously constructed by the authors
are presented. The hypercomputability of our algorithm is based on the fact
that this algorithm could solve a classically non-computable decision problem,
Hilbert's tenth problem. The numerical simulations were realized for three
types of Diophantine equations: with and without solutions in non-negative
integers, and without solutions by way of various traditional mathematical
packages.


title: Coherent analysis of quantum optical sideband modes

abstract:
  We demonstrate a device that allows for the coherent analysis of a pair of
optical frequency sidebands in an arbitrary basis. We show that our device is
quantum noise limited and hence applications for this scheme may be found in
discrete and continuous variable optical quantum information experiments.


title:
On a parametrically extended entanglement-measure due to Tsallis
  relative entropy

abstract:
  In the previous paper \cite{FYK}, we mainly studied the mathematical
properties of Tsallis relative entropy with respect to the density operators.
As an application of it, we adopt a parametrically extended
entanglement-measure due to Tsallis relative entropy in order to measure the
degree of entanglement. Then we study its properies with respect to the
parameter $q$ appearing in Tsallis entropies. In addition, the relation between
it and the relative entropy of entanglement is studied.


title: Quantum Timing and Synchronization Problems

abstract:
  Feynman's model of a quantum computer provides an example of a
continuous-time quantum walk. Its clocking mechanism is an excitation of a
basically linear chain of spins with occasional controlled jumps which allow
for motion on a planar graph. The spreading of the wave packet poses
limitations on the probability of ever completing the $s$ elementary steps of a
computation: an additional amount of storage space $\delta$ is needed in order
to achieve an assigned completion probability. In this note we study the END
instruction, viewed as a measurement of the position of the clocking
excitation: a $\pi$-pulse indefinitely freezes the contents of the input/output
register, with a probability depending only on the ratio $\delta/s$.


title:
Representation theory and Wigner-Racah algebra of the SU(2) group in a
  noncanonical basis

abstract:
  The Lie algebra su(2) of the classical group SU(2) is built from two
commuting quon algebras for which the deformation parameter is a common root of
unity. This construction leads to (i) a not very well-known polar decomposition
of the ladder generators of the SU(2) group, in terms of a unitary operator and
a Hermitean operator, and (ii) a nonstandard quantization scheme, alternative
to the usual quantization scheme correponding to the diagonalization of the
Casimir of su(2) and of the z-generator. The representation theory of the SU(2)
group can be developed in this nonstandard scheme. The key ideas for developing
the Wigner-Racah algebra of the SU(2) group in the nonstandard scheme are
given. In particular, some properties of the coupling and recoupling
coefficients as well as the Wigner-Eckart theorem in the nonstandard scheme are
examined in great detail.


title:
Noiseless method for checking the Peres separability criterion by local
  operations and classical communication

abstract:
  We present a method for checking Peres separability criterion in an arbitrary
bipartite quantum state $\rho_{AB}$ within local operations and classical
communication scenario. The method does not require the prior state
reconstruction and the structural physical approximation. The main task for the
two observers, Alice and Bob, is to estimate some specific functions. After
getting these functions, they can determine the minimal eigenvalue of
$\rho^{T_{B}}_{AB}$, which serves as an entanglement indicator in lower
dimensions.


title: Reduction of Magnetic Noise in Atom Chips by Material Optimization

abstract:
  We discuss the contribution of the material type in metal wires to the
electromagnetic fluctuations in magnetic microtraps close to the surface of an
atom chip. We show that significant reduction of the magnetic noise can be
achieved by replacing the pure noble metal wires with their dilute alloys. The
alloy composition provides an additional degree of freedom which enables a
controlled reduction of both magnetic noise and resistivity if the atom chip is
cooled. In addition, we provide a careful re-analysis of the magnetically
induced trap loss observed by Yu-Ju Lin et al. [Phys. Rev. Lett. 92, 050404
(2004)] and find good agreement with an improved theory.


title:
A new approximation method for time-dependent problems in quantum
  mechanics

abstract:
  We propose an approximate solution of the time-dependent Schr\"odinger
equation using the method of stationary states combined with a variational
matrix method for finding the energies and eigenstates. We illustrate the
effectiveness of the method by applying it to the time development of the
wave-function in the quantum-mechanical version of the inflationary slow-roll
transition.


title: Chaotic Tunneling in a Laser Field

abstract:
  We study the driven tunneling of a one-dimensional charged particle confined
to a rectangular double-well. The numerical simulation of the Schr\"odinger
equation based on the Cranck-Nicholson finite-difference scheme, shows that the
modulation of the amplitude of the external field may result in the parametric
resonance. The latter is accompanied by the breakdown of the quasi-periodic
motion characteristic of the usual driven tunneling, and the emergence of an
irregular dynamics. We describe the above breakdown with the occupation
probability for the ground state of the unperturbed system, and make the
visualization of the irregular dynamics with the help of Shaw-Takens'
reconstruction of the state-space. Both approaches agree as to the values of
the resonant frequency for the parametric excitation. Our results indicate that
the shape of the laser pulse could be essential for generating chaotic
tunneling.


title:
On the Consequences of Retaining the General Validity of Locality in
  Physical Theory

abstract:
  The empirical validity of the locality (LOC) principle of relativity is used
to argue in favour of a local hidden variable theory (HVT) for individual
quantum processes. It is shown that such a HVT may reproduce the statistical
predictions of quantum mechanics (QM), provided the reproducibility of initial
hidden variable states is limited. This means that in a HVT limits should be
set to the validity of the notion of counterfactual definiteness (CFD). This is
supported by the empirical evidence that past, present, and future are
basically distinct. Our argumentation is contrasted with a recent one by Stapp
resulting in the opposite conclusion, i.e. nonlocality or the existence of
faster-than-light influences. We argue that Stapp's argumentation still depends
in an implicit, but crucial, way on both the notions of hidden variables and of
CFD. In addition, some implications of our results for the debate between Bohr
and Einstein, Podolsky and Rosen are discussed.


title:
Renninger's Thought Experiment: Implications for Quantum Ontology and
  for Quantum Mechanic's Interpretation

abstract:
  It is argued that the conclusions obtained by Renninger (Zeitschrift fur
Physik 136, 251 (1953)), by means of an interferometer thought experiment, have
important implications for a number of still ongoing discussions about quantum
mechanics (QM). To these belong the ontology underlying QM, Bohr's
complementarity principle, the significance of QM's wave function, the
"elements of reality" introduced by Einstein, Podolsky and Rosen (EPR), and
Bohm's version of QM (BQM). A slightly extended setup is used to make a
physical prediction at variance with the mathematical prediction of QM. An
english translation of Renninger's paper, which was originally published in
german language, follows the present paper. This should facilitate access to
that remarkable, apparently overlooked and forgotten, paper.


title:
Conditional transfer of quantum correlation in the intensity of twin
  beams

abstract:
  A conditional protocol of transferring quantum-correlation in continuous
variable regime was experimentally demonstrated. The quantum-correlation in two
pairs of twin beams, each characterized by intensity-difference squeezing of
7.0 dB, was transferred to two initially independent idler beams. The
quantum-correlation transfer resulted in intensity-difference squeezing of 4.0
dB between two idler beams. The dependence of preparation probability and
transfer fidellity on the selection bandwidth was also studied.


title: Higher order perturbation theory for decoherence in Grover's algorithm

abstract:
  In this paper, we study decoherence in Grover's quantum search algorithm
using a perturbative method. We assume that each two-state system (qubit) that
belongs to a register suffers a phase flip error (\sigma_{z} error) with
probability p independently at every step in the algorithm, where $0\leq p\leq
1$. Considering an n-qubit density operator to which Grover's iterative
operation is applied M times, we expand it in powers of 2Mnp and derive its
matrix element order by order under the large-n limit. [In this large-n limit,
we assume p is small enough, so that 2Mnp can take any real positive value or
zero. We regard $x\equiv 2Mnp(\geq 0)$ as a perturbative parameter.] We obtain
recurrence relations between terms in the perturbative expansion. By these
relations, we compute higher orders of the perturbation efficiently, so that we
extend the range of the perturbative parameter that provides a reliable
analysis. Calculating the matrix element numerically by this method, we derive
the maximum value of the perturbative parameter x at which the algorithm finds
a correct item with a given threshold of probability P_{th} or more. (We refer
to this maximum value of x as x_{c}, a critical point of x.) We obtain a curve
of x_{c} as a function of P_{th} by repeating this numerical calculation for
many points of P_{th} and find the following facts: a tangent of the obtained
curve at P_{th}=1 is given by x=(8/5)(1-P_{th}), and we have
x_{c}>-(8/5)\log_{e}P_{th} near P_{th}=0.


title:
Continuous optimal ensembles II. Reducing the separability condition to
  numerical equations

abstract:
  A density operator of a bipartite quantum system is called robustly separable
if it has a neighborhood of separable operators. Given a bipartite density
matrix, its property to be robustly separable is reduced, using the continuous
ensemble method, to a finite number of numerical equations. The solution of
this system exists for any robustly separable density operator and provides its
representation by a continuous mixture of pure product states.


title:
Change of decoherence scenario and appearance of localization due to
  reservoir anharmonicity

abstract:
  Although coupling to a super-Ohmic bosonic reservoir leads only to partial
dephasing on short time scales, exponential decay of coherence appears in the
Markovian limit (for long times) if anharmonicity of the reservoir is taken
into account. This effect not only qualitatively changes the decoherence
scenario but also leads to localization processes in which superpositions of
spatially separated states dephase with a rate that depends on the distance
between the localized states. As an example of the latter process, we study the
decay of coherence of an electron state delocalized over two semiconductor
quantum dots due to anharmonicity of phonon modes.


title: Universality of Measurements on Quantum Markets

abstract:
  We reason about possible future development of quantum game theory and its
impact on information processing and the emerging information society. Two of
the authors have recently proposed a quantum description of financial market in
terms of quantum game theory. These "new games" cannot by themselves create
extraordinary profits or multiplication of goods, but they may cause the
dynamism of transaction which would result in more effective markets and
capital flow into hands of the most efficient traders. We focus upon the
problem of universality of measurement in quantum market games. Quantum-like
approach to market description proves to be an important theoretical tool for
investigation of computability problems in economics or game theory even if
never implemented in real markets.


title:
Semiclassical propagation of coherent states using complex and real
  trajectories

abstract:
  We study the semiclassical propagation of coherent states in $d$ dimensions,
which in general involves complex classical dynamics. Several simple
approximations are derived that depend only on real classical trajectories,
among them the thawed Gaussian approximation (TGA). Apart from the TGA, all
other possibilities are able to reproduce interference and tunnelling effects,
and involve propagating a set of classical initial conditions compatible with
the quantum uncertainties. The accuracy of the results is verified in two
dimensions for the scattering by an attractive potential, for a bound nonlinear
system, for motion inside a circular billiard and for a system involving
tunnelling.


title: Hydrogen atom in phase space: The Wigner representation

abstract:
  We have found an effective method of calculating the Wigner function, being a
quantum analogue of joint probability distribution of position and momentum,
for bound states of nonrelativistic hydrogen atom. The formal similarity
between the eigenfunctions of nonrelativistic hydrogen atom in the momentum
representation and Klein-Gordon propagators has allowed the calculation of the
Wigner function for an arbitrary bound state of the hydrogen atom. These Wigner
functions for some low lying states are depicted and discussed.


title:
Observing Quantum Vacuum Lensing in Magnetized Neutron Star Binary
  System

abstract:
  In this letter we study the propagation of light in the neighbourhood of
magnetised neutron stars. Thanks to the optical properties of quantum vacuum in
the presence of a magnetic field, light emitted by background astronomical
objects is deviated giving rise to a phenomenon of the same kind as the
gravitational one. We give a quantitative estimation of this effect and we
discuss the possibility of its observation. We show that this effect could be
detected monitoring the evolution of the recently discovered double neutron
star system J0737-3039.


title: Nonlocal Measurements in the Time-Symmetric Quantum Mechanics

abstract:
  Although nondemolition, reliable, and instantaneous quantum measurements of
some nonlocal variables are impossible, demolition reliable instantaneous
measurements are possible for all variables. It is shown that this is correct
also in the framework of the time-symmetric quantum formalism, i.e. nonlocal
variables of composite quantum systems with quantum states evolving both
forward and backward in time are measurable in a demolition way. The result
follows from the possibility to reverse with certainty the time direction of a
backward evolving quantum state. Demolition measurements of nonlocal backward
evolving quantum states require remarkably small resources. This is so because
the combined operation of time reversal and teleportation of a local backward
evolving quantum state requires only a single quantum channel and no
transmission of classical information.


title:
Towards efficient algorithm deciding separability of distributed quantum
  states

abstract:
  It is pointed out that separability problem for arbitrary multi-partite
states can be fully solved by a finite size, elementary recursive algorithm. In
the worse case scenario, the underlying numerical procedure, may grow doubly
exponentially with the state's rank. Nevertheless, we argue that for generic
states, analysis of concurrence matrices essentially reduces the task of
solving separability problem in $m \times n$ dimensions to solving a set of
linear equations in about $\binom{mn+D-1}{D}$ variables, where $D$ decreases
with $mn$ and for large $mn$ it should not exceed 4. Moreover, the same method
is also applicable to multipartite states where it is at least equally
efficient.


title: Entanglement in coined quantum walks on regular graphs

abstract:
  Quantum walks, both discrete (coined) and continuous time, form the basis of
several recent quantum algorithms. Here we use numerical simulations to study
the properties of discrete, coined quantum walks. We investigate the variation
in the entanglement between the coin and the position of the particle by
calculating the entropy of the reduced density matrix of the coin. We consider
both dynamical evolution and asymptotic limits for coins of dimensions from two
to eight on regular graphs. For low coin dimensions, quantum walks which spread
faster (as measured by the mean square deviation of their distribution from
uniform) also exhibit faster convergence towards the asymptotic value of the
entanglement between the coin and particle's position. For high-dimensional
coins, the DFT coin operator is more efficient at spreading than the Grover
coin. We study the entanglement of the coin on regular finite graphs such as
cycles, and also show that on complete bipartite graphs, a quantum walk with a
Grover coin is always periodic with period four. We generalize the 'glued
trees' graph used by Childs et al (2003 Proc. STOC, pp 5968) to higher
branching rate (fan out) and verify that the scaling with branching rate and
with tree depth is polynomial.


title:
Comment on "On the Electric Charge Quantization from the Aharonov-Bohm
  Potential"

abstract:
  In the paper quant-ph/0503212, Barone and Halayel-Neto (BH) claim that charge
quantization in quantum mechanics can be proven without the need for the
existence of magnetic monopoles. In this paper it is argued that their claim is
untrue.


title: Quantum Symmetries and Cartan Decompositions in Arbitrary Dimensions

abstract:
  We investigate the relation between Cartan decompositions of the unitary
group and discrete quantum symmetries. To every Cartan decomposition there
corresponds a quantum symmetry which is the identity when applied twice. As an
application, we describe a new and general method to obtain Cartan
decompositions of the unitary group of evolutions of multipartite systems from
Cartan decompositions on the single subsystems. The resulting decomposition,
which we call of the odd-even type, contains, as a special case, the
concurrence canonical decomposition (CCD) presented in the context of
entanglement theory. The CCD is therefore extended from the case of a
multipartite system of n qubits to the case where the component subsystems have
arbitrary dimension.


title: Slow Light amplification in a non-inverted gain medium

abstract:
  We investigate the propagation of a coherent probe light pulse through a
three-level atomic medium (in the $\Lambda$--configuration) in the presence of
a pump laser under the conditions for gain without inversion. When the carrier
frequency of the probe pulse and the pump laser are in a Raman configuration,
we show that it is possible to amplify a slow propagating pulse. We also
analyze the regime in which the probe pulse is slightly detuned from resonance
where we observe anomalous light propagation.


title: Adiabatic Approximation for weakly open systems

abstract:
  We generalize the adiabatic approximation to the case of open quantum
systems, in the joint limit of slow change and weak open system disturbances.
We show that the approximation is ``physically reasonable'' as under wide
conditions it leads to a completely positive evolution, if the original master
equation can be written on a time-dependent Lindblad form. We demonstrate the
approximation for a non-Abelian holonomic implementation of the Hadamard gate,
disturbed by a decoherence process. We compare the resulting approximate
evolution with numerical simulations of the exact equation.


title: 't Hooft's quantum determinism -- path integral viewpoint

abstract:
  We present a path integral formulation of 't Hooft's derivation of quantum
from classical physics. Our approach is based on two concepts: Faddeev-Jackiw's
treatment of constrained systems and Gozzi's path integral formulation of
classical mechanics. This treatment is compared with our earlier one
[quant-ph/0409021] based on Dirac-Bergmann's method.


title: Minimax quantum state discrimination

abstract:
  We derive the optimal measurement for quantum state discrimination without a
priori probabilities, i.e. in a minimax strategy instead of the usually
considered Bayesian one. We consider both minimal-error and unambiguous
discrimination problems, and provide the relation between the optimal
measurements according to the two schemes. We show that there are instances in
which the minimum risk cannot be achieved by an orthogonal measurement, and
this is a common feature of the minimax estimation strategy.


title: Quantum entanglement in states generated by bilocal group algebras

abstract:
  Given a finite group G with a bilocal representation, we investigate the
bipartite entanglement in the state constructed from the group algebra of G
acting on a separable reference state. We find an upper bound for the von
Neumann entropy for a bipartition (A,B) of a quantum system and conditions to
saturate it. We show that these states can be interpreted as ground states of
generic Hamiltonians or as the physical states in a quantum gauge theory and
that under specific conditions their geometric entropy satisfies the entropic
area law. If G is a group of spin flips acting on a set of qubits, these states
are locally equivalent to 2-colorable (i.e., bipartite) graph states and they
include GHZ, cluster states etc. Examples include an application to qudits and
a calculation of the n-tangle for 2-colorable graph states.


title:
The complexity of quantum spin systems on a two-dimensional square
  lattice

abstract:
  The problem 2-LOCAL HAMILTONIAN has been shown to be complete for the quantum
computational class QMA, see quant-ph/0406180. In this paper we show that this
important problem remains QMA-complete when the interactions of the 2-local
Hamiltonian are between qubits on a two-dimensional (2-D) square lattice. Our
results are partially derived with novel perturbation gadgets that employ
mediator qubits which allow us to manipulate k-local interactions. As a side
result, we obtain that quantum adiabatic computation using 2-local interactions
restricted to a 2-D square lattice is equivalent to the circuit model of
quantum computation. Our perturbation method also shows how any stabilizer
space associated with a k-local stabilizer (for constant k) can be generated as
an approximate ground-space of a 2-local Hamiltonian.


title:
Dynamics of Two Qubits: Decoherence and an Entanglement Optimization
  Protocol

abstract:
  The evolution of two qubits coupled by a general nonlocal interaction is
studied in two distinct regimes. In the first regime the purity of the
individual qubits is interchanged through the entanglement shared by the two.
We illustrate how this can be a mechanism for decoherence. In the second
regime, the interaction entangles two initially pure qubits. The dynamical maps
for the reduced unitary evolution of both initially simply separable and
not-simply-separable states are found. We outline a protocol for optimizing the
entanglement generation subject to constraints.


title: Entangling power of quantum chaotic evolutions via operator entanglement

abstract:
  We study operator entanglement of the quantum chaotic evolutions. This study
shows that properties of the operator entanglement production are qualitatively
similar to the properties reported in literature about the pure state
entanglement production. This similarity establishes that the operator
entanglement quantifies {\it intrinsic} entangling power of an operator. The
term `intrinsic' suggests that this measure is independent of any specific
choice of initial states.


title:
Strong-field approximation for intense-laser atom processes: the choice
  of gauge

abstract:
  The strong-field approximation can be and has been applied in both length
gauge and velocity gauge with quantitatively conflicting answers. For
ionization of negative ions with a ground state of odd parity, the predictions
of the two gauges differ qualitatively: in the envelope of the angular-resolved
energy spectrum, dips in one gauge correspond to humps in the other. We show
that the length-gauge SFA matches the exact numerical solution of the
time-dependent Schr\"odinger equation.


title:
Error tolerance in an NMR Implementation of Grover's Fixed-Point Quantum
  Search Algorithm

abstract:
  We describe an implementation of Grover's fixed-point quantum search
algorithm on a nuclear magnetic resonance (NMR) quantum computer, searching for
either one or two matching items in an unsorted database of four items. In this
new algorithm the target state (an equally weighted superposition of the
matching states) is a fixed point of the recursive search operator, and so the
algorithm always moves towards the desired state. The effects of systematic
errors in the implementation are briefly explored.


title:
On the upper bound of the electronic kinetic energy in terms of density
  functionals

abstract:
  We propose a simple density functional expression for the upper bound of the
kinetic energy for electronic systems. Such a functional is valid in the limit
of slowly varying density, its validity outside this regime is discussed by
making a comparison with upper bounds obtained in previous work. The advantages
of the functional proposed for applications to realistic systems is briefly
discussed.


title:
Quantum transducers: Integrating Transmission Lines and Nanomechanical
  Resonators via Charge Qubits

abstract:
  We propose a mechanism to interface a transmission line resonator (TLR) with
a nano-mechanical resonator (NAMR) by commonly coupling them to a charge qubit,
a Cooper pair box with a controllable gate voltage. Integrated in this quantum
transducer or simple quantum network, the charge qubit plays the role of a
controllable quantum node coherently exchanging quantum information between the
TLR and NAMR. With such an interface, a maser-like process is predicted to
create a quasi-classical state of the NAMR by controlling a single-mode
classical current in the TLR. Alternatively, a "Cooper pair" coherent output
through the transmission line can be driven by a single-mode classical
oscillation of the NAMR.


title:
Identifying two-photon high-dimensional entanglement in transverse
  patterns

abstract:
  We propose a scheme to explore two-photon high-dimensional entanglement
associated with a transverse pattern by means of two-photon interference in a
beamsplitter. We find that the topological symmetry of the angular spectrum of
the two-photon state governs the nature of the two-photon interference. We
prove that the anti-coalescence interference is the signature of two-photon
entanglement. On the basis of this feature, we propose a special Mach-Zehnder
interferometer incorporated with two spiral phase plates which can change the
interference from a coalescence to an anti-coalescence type only for a
two-photon entangled state. The scheme is simple and straightforward compared
with the test for a Bell inequality.


title:
On the uncertainty relations and quantum measurements:
  conventionalities, shortcomings, reconsiderations

abstract:
  Unsolved controversies about uncertainty relations and quantum measurements
still persists nowadays. They originate around the shortcomings regarding the
conventional interpretation of uncertainty relations. Here we show that the
respective shortcomings disclose veridic and unavoidable facts which require
the abandonment of the mentioned interpretation. So the primitive uncertainty
relations appear as being either thought fictions or fluctuations formulae.
Subsequently we reveal that the conventional approaches of quantum measurements
are grounded on incorrect premises. We propose a new approach in which : (i)
the quantum observables are considered as generalized stochastic variables,
(ii) the view is focused only on the pre-existent state of the measured system,
without any interest for the collapse of the respective state, (iii) a
measurement is described as an input-output transformation which modify the
probability density and current but preserve the expressions of the operators.
The measuring uncertainties are evaluated as changes in the probabilistic
estimators of observables. Related to different observables we do not find
reasons of principle neither for uncertainties-connections nor for measuring
compatibility/incompatibility.


title:
Quantum Key Ditribution Based on Quantum Intensity Correlation of Twin
  Beams

abstract:
  A new and simple quantum key distribution scheme based on the quantum
intensity correlation of optical twin beams and the directly local measurements
of intensity noise of single optical beam is presented and experimentally
demonstrated. Using the twin beams with the quantum intensity correlation of
5dB the effective bit rate of $2\times 10^7bits/s$ is completed. The noncloning
of quantum systems and the sensitivity of the existing correlations to losses
provide the physical mechamism for the security against eavesdropping. In the
presented scheme the signal modulation and homodyne detection are not needed.


title:
On relations between stable and Zeno dynamics in a leaky graph decay
  model

abstract:
  We use a caricature model of a system consisting of a quantum wire and a
finite number of quantum dots, to discuss relation between the Zeno dynamics
and the stable one which governs time evolution of the dot states in the
absence of the wire. We analyze the weak coupling case and argue that the two
time evolutions can differ significantly only at times comparable with the
lifetime of the unstable system undisturbed by perpetual measurement.


title:
Exact solutions for a universal set of quantum gates on a family of
  iso-spectral spin chains

abstract:
  We find exact solutions for a universal set of quantum gates on a scalable
candidate for quantum computers, namely an array of two level systems. The
gates are constructed by a combination of dynamical and geometrical
(non-Abelian) phases. Previously these gates have been constructed mostly on
non-scalable systems and by numerical searches among the loops in the manifold
of control parameters of the Hamiltonian.


title:
Pure-state single-photon wave-packet generation by parametric down
  conversion in a distributed microcavity

abstract:
  We propose an optical parametric down conversion (PDC) scheme that does not
suffer a trade-off between the state-purity of single-photon wave-packets and
the rate of packet production. This is accomplished by modifying the PDC
process by using a microcavity to engineer the density of states of the optical
field at the PDC frequencies. The high-finesse cavity mode occupies a spectral
interval much narrower than the bandwidth of the pulsed pump laser field,
suppressing the spectral correlation, or entanglement, between signal and idler
photons. Spectral filtering of the field occurs prior to photon creation rather
than afterward as in most other schemes. Operator-Maxwell equations are solved
to find the Schmidt-mode decomposition of the two-photon states produced.
Greater than 99% pure-state packet production is predicted to be achievable.


title: Geometric Effects and Computation in Spin Networks

abstract:
  When initially introduced, a Hamiltonian that realises perfect transfer of a
quantum state was found to be analogous to an x-rotation of a large spin. In
this paper we extend the analogy further to demonstrate geometric effects by
performing rotations on the spin. Such effects can be used to determine
properties of the chain, such as its length, in a robust manner. Alternatively,
they can form the basis of a spin network quantum computer. We demonstrate a
universal set of gates in such a system by both dynamical and geometrical
means.


title: Solvable Quantum Two-Body Problem:Entanglement

abstract:
  A simple one dimensional model is introduced describing a two particle "atom"
approaching a point at which the interaction between the particles is lost. The
wave function is obtained analytically and analyzed to display the entangled
nature of the subsequent state.


title: Quadratic pseudosupersymmetry in two-level systems

abstract:
  Using the intertwining relation we construct a pseudosuperpartner for a
(non-Hermitian) Dirac-like Hamiltonian describing a two-level system
interacting in the rotating wave approximation with the electric component of
an electromagnetic field. The two pseudosuperpartners and pseudosupersymmetry
generators close a quadratic pseudosuperalgebra. A class of time dependent
electric fields for which the equation of motion for a two level system placed
in this field can be solved exactly is obtained. New interesting phenomenon is
observed. There exists such a time-dependent detuning of the field frequency
from the resonance value that the probability to populate the excited level
ceases to oscillate and becomes a monotonically growing function of time
tending to 3/4. It is shown that near this fixed excitation regime the
probability exhibits two kinds of oscillations. The oscillations with a small
amplitude and a frequency close to the Rabi frequency (fast oscillations) take
place at the background of the ones with a big amplitude and a small frequency
(slow oscillations). During the period of slow oscillations the minimal value
of the probability to populate the excited level may exceed 1/2 suggesting for
an ensemble of such two-level atoms the possibility to acquire the inverse
population and exhibit lasing properties.


title: Quantum and Fisher Information from the Husimi and Related Distributions

abstract:
  The two principal/immediate influences -- which we seek to interrelate here
-- upon the undertaking of this study are papers of Zyczkowski and
Slomczy\'nski (J. Phys. A 34, 6689 [2001]) and of Petz and Sudar (J. Math.
Phys. 37, 2262 [1996]). In the former work, a metric (the Monge one,
specifically) over generalized Husimi distributions was employed to define a
distance between two arbitrary density matrices. In the Petz-Sudar work
(completing a program of Chentsov), the quantum analogue of the (classically
unique) Fisher information (montone) metric of a probability simplex was
extended to define an uncountable infinitude of Riemannian (also monotone)
metrics on the set of positive definite density matrices. We pose here the
questions of what is the specific/unique Fisher information metric for the
(classically-defined) Husimi distributions and how does it relate to the
infinitude of (quantum) metrics over the density matrices of Petz and Sudar? We
find a highly proximate (small relative entropy) relationship between the
probability distribution (the quantum Jeffreys' prior) that yields quantum
universal data compression, and that which (following Clarke and Barron) gives
its classical counterpart. We also investigate the Fisher information metrics
corresponding to the escort Husimi, positive-P and certain Gaussian probability
distributions, as well as, in some sense, the discrete Wigner
pseudoprobability. The comparative noninformativity of prior probability
distributions -- recently studied by Srednicki (Phys. Rev. A 71, 052107 [2005])
-- formed by normalizing the volume elements of the various information
metrics, is also discussed in our context.


title: Explicit Multiregister Measurements for Hidden Subgroup Problems

abstract:
  We present an explicit measurement in the Fourier basis that solves an
important case of the Hidden Subgroup Problem, including the case to which
Graph Isomorphism reduces. This entangled measurement uses $k=\log_2 |G|$
registers, and each of the $2^k$ subsets of the registers contributes some
information. While this does not, in general, yield an efficient algorithm, it
generalizes the relationship between Subset Sum and the HSP in the dihedral
group, and sheds some light on how quantum algorithms for Graph Isomorphism
might work.


title:
Spin as the Basis for Quantum Mechanics: A New Semiclassical Model for
  Electron Spin

abstract:
  A simple real-space model for the free-electron wavefunction with spin is
proposed, based on coherent vortices on the scale of h/mc, rotating at mc^2/h.
This reproduces the proper values for electron spin and magnetic moment.
Transformation to a moving reference frame turns this into a wave with the de
Broglie wavelength. The mapping of the real two-dimensional vector phasor to
the complex plane satisfies the Schrodinger equation. This suggests a
fundamental role for spin in quantum mechanics.


title:
Outcoupling from a Bose-Einstein condensate with squeezed light to
  produce entangled atom laser beams

abstract:
  We examine the properties of an atom laser produced by outcoupling from a
Bose-Einstein condensate with squeezed light. We model the multimode dynamics
of the output field and show that a significant amount of squeezing can be
transfered from an optical mode to a propagating atom laser beam. We use this
to demonstrate that two-mode squeezing can be used to produce twin atom laser
beams with continuous variable entanglement in amplitude and phase.


title: Preserving Quantum States : A Super-Zeno Effect

abstract:
  We construct an algorithm for suppressing the transitions of a quantum
mechanical system, initially prepared in a subspace P of the full Hilbert space
of the system, to outside this subspace by subjecting it to a sequence of
unequally spaced short-duration pulses. Each pulse multiplies the amplitude of
the vectors in the subspace by -1. The number of pulses required by the
algorithm to limit the leakage probability to $\epsilon$ in time $T$ increases
as $T \exp[ \sqrt{\log(T^2/\epsilon)}]$, compared to $T^2 \epsilon^{-1}$ in the
standard quantum Zeno effect.


title:
There is Neither Classical Bug with a Superluminal Shadow Nor Quantum
  Absolute Collapse Nor (Subquantum) Superluminal Hidden Variable

abstract:
  In this work we analyse critically Griffiths's example of the classical
superluminal motion of a bug shadow. Griffiths considers that this example is
conceptually very close to quantum nonlocality or superluminality,i.e. quantum
breaking of the famous Bell inequality. Or, generally, he suggests implicitly
an absolute asymmetric duality (subluminality vs. superluminality) principle in
any fundamental physical theory.It, he hopes, can be used for a natural
interpretation of the quantum mechanics too. But we explain that such
Griffiths's interpretation retires implicitly but significantly from usual,
Copenhagen interpretation of the standard quantum mechanical formalism. Within
Copenhagen interpretation basic complementarity principle represents, in fact,
a dynamical symmetry principle (including its spontaneous breaking, i.e.
effective hiding by measurement). Similarly, in other fundamental physical
theories instead of Griffiths's absolute asymmetric duality principle there is
a dynamical symmetry (including its spontaneous breaking, i.e. effective hiding
in some of these theories) principle. Finally, we show that Griffiths's example
of the bug shadow superluminal motion is definitely incorrect (it sharply
contradicts the remarkable Roemer's determination of the speed of light by
coming late of Jupiter's first moon shadow).


title: Multi-Partite Entanglement Inequalities via Spin Vector Geometry

abstract:
  We introduce inequalities for multi-partite entanglement, derived from the
geometry of spin vectors. The criteria are constructed iteratively from cross
and dot products between the spins of individual subsystems, each of which may
have arbitrary dimension. For qubit ensembles the maximum violation for our
inequalities is larger than that for the Mermin-Klyshko Bell inequalities, and
the maximally violating states are different from Greenberger-Horne-Zeilinger
states. Our inequalities are violated by certain bound entangled states for
which no Bell-type violation has yet been found.


title: Distinguishability, classical information of quantum operations

abstract:
  A basic property of distinguishability is that it is non-increasing under
further quantum operations. Following this, we generalize two measures of
distinguishability of pure states--fidelity and von Neumann entropy, to mixed
states as self-consistent measures. Then we extend these two measures to
quantum operations. The information-theoretic point of the generalized Holevo
quantity of an ensemble of quantum operations is constructed. Preferably it is
an additive measure. The exact formula for SU(2) ensemble is presented. With
the aid of the formula, we show Jozsa-Schlienz paradox that states as a whole
are less distinguishable while all pairwise are more distinguishable in an
ensemble of quantum states, also occurs in an ensemble of quantum operations,
even in the minimal dimensional case SU(2) ensemble.


title: On the quantum spectrum of isochronous potentials

abstract:
  In this paper, the quantum spectrum of isochronous potentials is
investigated. Given that the frequency of the classical motion in such
potentials is energy-independent, it is natural to expect their quantum spectra
to be equispaced. However, as it has already been shown in some specific
examples, this property is not always true. To gain some general insight into
this problem, a WKB analysis of the spectrum, valid for any analytic potential,
is performed and the first semiclassical corrections to its regular spacing are
calculated. We illustrate the results on the two-parameter family of
isochronous potentials derived in [1], which includes the harmonic oscillator,
the asymmetric parabolic well, the radial harmonic oscillator and Urabe's
potential as special limiting cases. In addition, some new analytical
expressions for families of isochronous potentials and their corresponding
spectra are derived by means of the above-mentioned method.


title: Quantum Information and the PCP Theorem

abstract:
  We show how to encode $2^n$ (classical) bits $a_1,...,a_{2^n}$ by a single
quantum state $|\Psi>$ of size O(n) qubits, such that: for any constant $k$ and
any $i_1,...,i_k \in \{1,...,2^n\}$, the values of the bits
$a_{i_1},...,a_{i_k}$ can be retrieved from $|\Psi>$ by a one-round
Arthur-Merlin interactive protocol of size polynomial in $n$. This shows how to
go around Holevo-Nayak's Theorem, using Arthur-Merlin proofs.
  We use the new representation to prove the following results:
  1) Interactive proofs with quantum advice: We show that the class $QIP/qpoly$
contains ALL languages. That is, for any language $L$ (even non-recursive), the
membership $x \in L$ (for $x$ of length $n$) can be proved by a polynomial-size
quantum interactive proof, where the verifier is a polynomial-size quantum
circuit with working space initiated with some quantum state $|\Psi_{L,n} >$
(depending only on $L$ and $n$). Moreover, the interactive proof that we give
is of only one round, and the messages communicated are classical.
  2) PCP with only one query: We show that the membership $x \in SAT$ (for $x$
of length $n$) can be proved by a logarithmic-size quantum state $|\Psi >$,
together with a polynomial-size classical proof consisting of blocks of length
$polylog(n)$ bits each, such that after measuring the state $|\Psi >$ the
verifier only needs to read {\bf one} block of the classical proof.
  While the first result is a straight forward consequence of the new
representation, the second requires an additional machinery of quantum
low-degree-test that may be interesting in its own right.


title: Long-lived qubit memory using atomic ions

abstract:
  We demonstrate experimentally a robust quantum memory using a
magnetic-field-independent hyperfine transition in 9Be+ atomic ion qubits at a
magnetic field B ~= 0.01194 T. We observe that the single physical qubit memory
coherence time is greater than 10 seconds, an improvement of approximately five
orders of magnitude from previous experiments with 9Be+. We also observe long
coherence times of decoherence-free subspace logical qubits comprising two
entangled physical qubits and discuss the merits of each type of qubit.


title:
Theoretical study of polarization tracking in satellite quantum key
  distribution

abstract:
  The BB84 and B92 protocols based on polarization coding are usually used in
free-space quantum key distribution. Polarization tracking technique is one of
the key techniques in the satellite quantum key distribution. Because the
photon polarization state will be changed as a result of the satellite
movement, both the transmitter and receiver need to have the ability to track
the polarization orientation variation to accomplish the quantum cryptography
protocols. In this paper, the polarization tracking principles are analyzed
based on Faraday effect and the half-wave plate. The transforms of six photon
polarization states in three conjugative bases are given and the quantum key
coding principles based on the polarization tracking are analyzed for the BB84
and B92 protocols.


title:
Possibility, Impossibility and Cheat-Sensitivity of Quantum Bit String
  Commitment

abstract:
  Unconditionally secure non-relativistic bit commitment is known to be
impossible in both the classical and the quantum worlds. But when committing to
a string of n bits at once, how far can we stretch the quantum limits? In this
paper, we introduce a framework for quantum schemes where Alice commits a
string of n bits to Bob in such a way that she can only cheat on a bits and Bob
can learn at most b bits of information before the reveal phase. Our results
are two-fold: we show by an explicit construction that in the traditional
approach, where the reveal and guess probabilities form the security criteria,
no good schemes can exist: a+b is at least n. If, however, we use a more
liberal criterion of security, the accessible information, we construct schemes
where a=4log n+O(1) and b=4, which is impossible classically. We furthermore
present a cheat-sensitive quantum bit string commitment protocol for which we
give an explicit tradeoff between Bob's ability to gain information about the
committed string, and the probability of him being detected cheating.


title: Relations between Entanglement Witnesses and Bell Inequalities

abstract:
  Bell inequalities, considered within quantum mechanics, can be regarded as
non-optimal witness operators. We discuss the relationship between such Bell
witnesses and general entanglement witnesses in detail for the Bell inequality
derived by Clauser, Horne, Shimony, and Holt (CHSH). We derive bounds on how
much an optimal witness has to be shifted by adding the identity operator to
make it positive on all states admitting a local hidden variable model. In the
opposite direction, we obtain tight bounds for the maximal proportion of the
identity operator that can be subtracted from such a CHSH witness, while
preserving the witness properties. Finally, we investigate the structure of
CHSH witnesses directly by relating their diagonalized form to optimal
witnesses of two different classes.


title:
Mode transformations and entanglement relativity in bipartite gaussian
  states

abstract:
  A proper choice of subsystems for a system of identical particles e.g.,
bosons, is provided by second-quantized modes i.e.,creation/annihilation
operators. Here we investigate how the entanglement properties of bipartite
gaussian states of bosons change when modes are changed by means of unitary,
number conserving, Bogolioubov transformations. This set of "virtual"
bi-partitions is then finite-dimensionally parametrized and one can
quantitatively address relevant questions such as the determination of the
minimal and maximal available entanglement. In particular, we show that in the
class of bipartite gaussian states there are states which remain separable for
every possible modes redefinition, while do not exist states which remain
entangled for every possible modes redefinition


title: Comment on "Entangled-Photon Imaging of a Pure Phase Object"

abstract:
  Comment on A.F. Abouraddy, P.R. Stone, A.V. Sergienko, B.E.A. Saleh, and M.C.
Teich, ``Entangled-Photon Imaging of a Pure Phase Object,'' Phys. Rev. Lett.
93, 213903 (2004). Unpublished (rejected by Physical Review Letters), but for a
publication holding main points see A. Gatti, M. Bache, D. Magatti, E.
Brambilla, F. Ferri, and L.A. Lugiato "Coherent imaging with pseudo-thermal
incoherent light", Journal of Modern Optics 53, 739-760 (2006),
quant-ph/0504082.


title: Coherent imaging with pseudo-thermal incoherent light

abstract:
  We investigate experimentally fundamental properties of coherent ghost
imaging using spatially incoherent beams generated from a pseudo-thermal
source. A complementarity between the coherence of the beams and the
correlation between them is demonstrated by showing a complementarity between
ghost diffraction and ordinary diffraction patterns. In order for the ghost
imaging scheme to work it is therefore crucial to have incoherent beams. The
visibility of the information is shown for the ghost image to become better as
the object size relative to the speckle size is decreased, and therefore a
remarkable tradeoff between resolution and visibility exists. The experimental
conclusions are backed up by both theory and numerical simulations.


title:
From optimal measurement to efficient quantum algorithms for the hidden
  subgroup problem over semidirect product groups

abstract:
  We approach the hidden subgroup problem by performing the so-called pretty
good measurement on hidden subgroup states. For various groups that can be
expressed as the semidirect product of an abelian group and a cyclic group, we
show that the pretty good measurement is optimal and that its probability of
success and unitary implementation are closely related to an average-case
algebraic problem. By solving this problem, we find efficient quantum
algorithms for a number of nonabelian hidden subgroup problems, including some
for which no efficient algorithm was previously known: certain metacyclic
groups as well as all groups of the form (Z_p)^r X| Z_p for fixed r (including
the Heisenberg group, r=2). In particular, our results show that entangled
measurements across multiple copies of hidden subgroup states can be useful for
efficiently solving the nonabelian HSP.


title: Generating optimal states for a homodyne Bell test

abstract:
  We present a protocol that produces a conditionally prepared state that can
be used for a Bell test based on homodyne detection. Based on the results of
Munro [PRA 1999], the state is near-optimal for Bell-inequality violations
based on quadrature-phase homodyne measurements that use correlated
photon-number states. The scheme utilizes the Gaussian entanglement
distillation protocol of Eisert et. al. [Annals of Phys. 2004] and uses only
beam splitters and photodetection to conditionally prepare a non-Gaussian state
from a source of two-mode squeezed states with low squeezing parameter,
permitting a loophole-free test of Bell inequalities.


title:
(Almost) tight bounds for randomized and quantum Local Search on
  hypercubes and grids

abstract:
  The Local Search problem, which finds a local minimum of a black-box function
on a given graph, is of both practical and theoretical importance to many areas
in computer science and natural sciences. In this paper, we show that for the
Boolean hypercube $\B^n$, the randomized query complexity of Local Search is
$\Theta(2^{n/2}n^{1/2})$ and the quantum query complexity is
$\Theta(2^{n/3}n^{1/6})$. We also show that for the constant dimensional grid
$[N^{1/d}]^d$, the randomized query complexity is $\Theta(N^{1/2})$ for $d \geq
4$ and the quantum query complexity is $\Theta(N^{1/3})$ for $d \geq 6$. New
lower bounds for lower dimensional grids are also given. These improve the
previous results by Aaronson [STOC'04], and Santha and Szegedy [STOC'04].
Finally we show for $[N^{1/2}]^2$ a new upper bound of $O(N^{1/4}(\log\log
N)^{3/2})$ on the quantum query complexity, which implies that Local Search on
grids exhibits different properties at low dimensions.


title:
Detection of Macroscopic Entanglement by Correlation of Local
  Observables

abstract:
  We propose a correlation of local observables on many sites in macroscopic
quantum systems. By measuring the correlation one can detect, if any,
superposition of macroscopically distinct states, which we call macroscopic
entanglement, in arbitrary quantum states that are (effectively) homogeneous.
Using this property, we also propose an index of macroscopic entanglement.


title: Quantum multiparty communication complexity and circuit lower bounds

abstract:
  We define a quantum model for multiparty communication complexity and prove a
simulation theorem between the classical and quantum models. As a result of our
simulation, we show that if the quantum k-party communication complexity of a
function f is $\Omega(n/2^k)$, then its classical k-party communication is
$\Omega(n/2^{k/2})$. Finding such an f would allow us to prove strong classical
lower bounds for (k>log n) players and hence resolve a main open question about
symmetric circuits. Furthermore, we prove that for the Generalized Inner
Product (GIP) function, the quantum model is exponentially more efficient than
the classical one. This provides the first exponential separation for a total
function between any quantum and public coin randomized communication model.


title: Conversational (dialogue) model of quantum transitions

abstract:
  We introduce an original model of quantum phenomena, a model that provides a
picture of a "deep structure", an "underlying pattern" of quantum dynamics. We
propose that the source of a particle and all of that particle's possible
detectors "talk" before the particle is finally observed by just one detector.
These talks do not take place in physical time. They occur in what we call
"hidden time". Talks are spatially organized in such a way that the model
reproduces standard quantum probability amplitudes. This is most obviously seen
if one uses R. Feynman's formulation of quantum theory. We prefer the "physical
level" of mathematical strictness in describing our model. The model was
initially designed without any background except R. Feynman's many - paths
approach. But it later became apparent that the suggested mechanism is highly
generalizable, and may apply to a wide spectrum of self - organized systems,
including living systems. Stories about such systems are attached in
appendices.


title: Hidden variables and hidden time in quantum theory

abstract:
  Bell's theorem proves only that hidden variables evolving in true physical
time can't exist; still the theorem's meaning is usually interpreted
intolerably wide. The concept of hidden time (and, in general, hidden
space-time) is introduced. Such concept provides a whole new class of physical
theories, fully compatible with current knowledge, but giving new tremendous
possibilities. Those theories do not violate Bell's theorem.


title:
Generation of Werner states and preservation of entnglement in a noisy
  environment

abstract:
  We study the influence of noisy environment on the evolution of two-atomic
system in the presence of collective damping. Generation of Werner states as
asymptotic states of evolution is described. We also show that for some initial
states the amount of entanglement is preserved during the evolution.


title: On the Matrix Representation of Quantum Operations

abstract:
  This paper considers two frequently used matrix representations -- what we
call the $\chi$- and $\mathcal{S}$-matrices -- of a quantum operation and their
applications. The matrices defined with respect to an arbitrary operator basis,
that is, the orthonormal basis for the space of linear operators on the state
space are considered for a general operation acting on a single or two
\textit{d}-level quantum system (qudit). We show that the two matrices are
given by the expansion coefficients of the Liouville superoperator as well as
the associated bijective, positive operator on the doubled-space defined with
respect to two types of induced operator basis having different tensor product
structures, i.e., Kronecker products of the relevant operator basis and dyadic
products of the associated bipartite state basis. The explicit conversion
formulas between the two matrices are established as a computable matrix
multiplication. Extention to more qudits case is trivial. Several applications
of these matrices and the conversion formulas in quantum information science
and technology are presented.


title: "Measurement" by neuronal tunneling: Implications of Born's rule

abstract:
  A non-collapse scenario for ``conscious'' selection of a term from a
superposition was proposed in quant-ph/0309166: thermally assisted tunneling of
neuronal pore molecules. But ``observers'' consisting of only two neurons
appear to be at odds with Born's rule. In the present paper, an observer is
assumed to possess a large number of auxilliary properties irrelevant for the
result of the measurement. Born's rule then reduces to postulating that, prior
to the result becoming conscious, irrelevant properties are in an entangled
state with maximum likelihood, in the sense that phase-equivalent entanglements
cover a maximal fraction of the unit sphere (leading to equal-amplitude
superpositions).


title: Codes for Key Generation in Quantum Cryptography

abstract:
  As an alternative to the usual key generation by two-way communication in
schemes for quantum cryptography, we consider codes for key generation by
one-way communication. We study codes that could be applied to the raw key
sequences that are ideally obtained in recently proposed scenarios for quantum
key distribution, which can be regarded as communication through symmetric
four-letter channels.


title: Theory of a single-atom laser including light forces

abstract:
  We study a single incoherently pumped atom moving within an optical high-Q
resonator in the strong coupling regime. Using a semiclassical description for
the atom and field dynamics, we derive a closed system of differential
equations to describe this coupled atom-field dynamics. For sufficiently strong
pumping the system starts lasing when the atom gets close to a field antinode,
and the associated light forces provide for self-trapping of the atom. For a
cavity mode blue detuned with respect to the atomic transition frequency this
is combined with cavity induced motional cooling allowing for long term
steady-state operation of such a laser. The analytical results for temperature
and field statistics agree well with our earlier predictions based on Quantum
Monte Carlo simulations. We find sub-Doppler temperatures that decrease with
gain and coupling strength and can even go beyond the limit of passive cavity
cooling. Besides demonstrating the importance of light forces in single-atom
lasers, this result also gives strong evidence to enhance laser cooling through
stimulated emission in resonators.


title: Infinite number of conditions for local mixed state manipulations

abstract:
  It is shown that a finite number of conditions are {\em not} sufficient to
determine the locality of transformations between two probability distributions
of pure states as well as the locality of transformations between two $d\times
d$ mixed states with $d\geq 4$. As an example, an infinite, but minimal, set of
necessary and sufficient conditions for the existence of a local procedure that
converts one probability distribution of two pure pair of qubits into another
one is found.


title: Theory of slow-light solitons

abstract:
  In the framework of the nonlinear $\Lambda$-model we investigate propagation
of solitons in atomic vapors and Bose-Einstein condensates. We show how the
complicated nonlinear interplay between fast solitons and slow-light solitons
in the $\Lambda$-type media points to the possibility to create optical gates
and, thus, to control the optical transparency of the $\Lambda$-type media. We
provide an exact analytic description of decelerating, stopping and
re-accelerating of slow-light solitons in atomic media in the nonadiabatic
regime. Dynamical control over slow-light solitons is realized via a
controlling field generated by an auxiliary laser. For a rather general time
dependence of the field; we find the dynamics of the slow-light soliton inside
the medium. We provide an analytical description for the nonlinear dependence
of the velocity of the signal on the controlling field. If the background field
is turned off at some moment of time, the signal stops. We find the location
and shape of the spatially localized memory bit imprinted into the medium. We
discuss physically interesting features of our solution, which are in a good
agreement with recent experiments.


title: Cluster-state quantum computation

abstract:
  This article is a short introduction to and review of the cluster-state model
of quantum computation, in which coherent quantum information processing is
accomplished via a sequence of single-qubit measurements applied to a fixed
quantum state known as a cluster state. We also discuss a few novel properties
of the model, including a proof that the cluster state cannot occur as the
exact ground state of any naturally occurring physical system, and a proof that
measurements on any quantum state which is linearly prepared in one dimension
can be efficiently simulated on a classical computer, and thus are not
candidates for use as a substrate for quantum computation.


title: A Subtlety of the Schr\"{o}dinger Picture Dynamics

abstract:
  We address a mathematical and physical status of exotic (like e.g. fractal)
wave packets and their quantum dynamics. To this end, we extend the formal
meaning of the Schr\"{o}dinger equation beyond the domain of the Hamiltonian.
The dynamical importance of the finite mean energy condition is elucidated.


title: Optimal Quantum Feedback Control for Canonical Observables

abstract:
  We show that the stochastic Schrodinger equation for the filtered state of a
system, with linear free dynamics, undergoing continual non-demolition
measurement or either position or momentum, or both together, can be solved
explicitly within a class of Gaussian states which we call extended coherent
states. The asymptotic limit yields a class of relaxed states which we describe
explicitly. Bellman's principle is then applied directly to optimal feedback
control of such dynamical systems and the Hamilton Jacobi Bellman equation for
the minimum cost is derived. The situation of quadratic performance criteria is
treated as the important special case and solved exactly for the class of
relaxed states.


title: Decompositions of general quantum gates

abstract:
  Quantum algorithms may be described by sequences of unitary transformations
called quantum gates and measurements applied to the quantum register of n
quantum bits, qubits. A collection of quantum gates is called universal if it
can be used to construct any n-qubit gate. In 1995, the universality of the set
of one-qubit gates and controlled NOT gate was shown by Barenco et al. using QR
decomposition of unitary matrices. Almost ten years later the decomposition was
improved to include essentially fewer elementary gates. In addition, the
cosine-sine matrix decomposition was applied to efficiently implement
decompositions of general quantum gates. In this chapter, we review the
different types of general gate decompositions and slightly improve the best
known gate count for the controlled NOT gates to (23/48)4^n in the leading
order. In physical realizations, the interaction strength between the qubits
can decrease strongly as a function of their distance. Therefore, we also
discuss decompositions with the restriction to nearest-neighbor interactions in
a linear chain of qubits.


title:
Hypercomputability of quantum adiabatic processes: Fact versus
  Prejudices

abstract:
  We give an overview of a quantum adiabatic algorithm for Hilbert's tenth
problem, including some discussions on its fundamental aspects and the emphasis
on the probabilistic correctness of its findings. For the purpose of
illustration, the numerical simulation results of some simple Diophantine
equations are presented. We also discuss some prejudicial misunderstandings as
well as some plausible difficulties faced by the algorithm in its physical
implementation.


title:
Complex numbers and symmetries in quantum mechanics, and a nonlinear
  superposition principle for Wigner functions

abstract:
  Complex numbers appear in the Hilbert space formulation of quantum mechanics,
but not in the formulation in phase space. Quantum symmetries are described by
complex, unitary or antiunitary operators defining ray representations in
Hilbert space, whereas in phase space they are described by real, true
representations. Equivalence of the formulations requires that the former
representations can be obtained from the latter and vice versa. Examples are
given. Equivalence of the two formulations also requires that complex
superpositions of state vectors can be described in the phase space
formulation, and it is shown that this leads to a nonlinear superposition
principle for orthogonal, pure-state Wigner functions. It is concluded that the
use of complex numbers in quantum mechanics can be regarded as a computational
device to simplify calculations, as in all other applications of mathematics to
physical phenomena.


title: Electron-nuclear entanglement in the cold lithium gas

abstract:
  We study the ground-state entanglement and thermal entanglement in the
hyperfine interaction of the lithium atom. We give the relationship between the
entanglement and both temperature and external magnetic fields.


title: Statistical Properties of a Quantum Cellular Automaton

abstract:
  We study a quantum cellular automaton (QCA) whose time-evolution is defined
from global transition function of classical cellular automata (CA). In order
to investigate natural transformations from CA to QCA, the present QCA includes
CA with Wolfram's rule 150 and 105 as special cases. We firstly compute the
time-evolution of the QCA and examine its statistical properties. As a basic
statistical value, the probability of finding an active cell averaged over a
spatial-temporal space is introduced, and the difference between CA and QCA is
considered. In addition, it is shown that statistical properties in QCA are
related to the classical trajectory in the configuration space.


title: Wave function collapse implies divergence of average displacement

abstract:
  We show that propagating a truncated discontinuous wave function by
Schr\"odinger's equation, as asserted by the collapse axiom, gives rise to
non-existence of the average displacement of the particle on the line. It also
implies that there is no Zeno effect. On the other hand, if the truncation is
done so that the reduced wave function is continuous, the average coordinate is
finite and there is a Zeno effect. Therefore the collapse axiom of measurement
needs to be revised.


title: Levy Flights over Quantum Paths

abstract:
  An impact of integration over the paths of the Levy flights on the quantum
mechanical kernel has been studied. Analytical expression for a free particle
kernel has been obtained in terms of the Fox H-function. A new equation for the
kernel of a partical in the box has been found. New general results include the
well known quantum formulae for a free particle kernel and particle in box
kernel.


title:
Extended Cahill and Glauber formalism for finite dimensional spaces II.
  Applications in quantum tomography and quantum teleportation

abstract:
  By means of a new mod(N)-invariant operator basis, s-parametrized phase-space
functions associated with bounded operators in a finite-dimensional Hilbert
space are introduced in the context of the extended Cahill-Glauber formalism,
and their properties are discussed in details. The discrete Glauber-Sudarshan,
Wigner, and Husimi functions emerge from this formalism as specific cases of
s-parametrized phase-space functions where, in particular, a hierarchical
process among them is promptly established. In addition, a phase-space
description of quantum tomography and quantum teleportation is presented and
new results are obtained.


title:
An Algebraic Approach to Linear-Optical Schemes for Deterministic
  Quantum Computing

abstract:
  Linear-Optical Passive (LOP) devices and photon counters are sufficient to
implement universal quantum computation with single photons, and particular
schemes have already been proposed. In this paper we discuss the link between
the algebraic structure of LOP transformations and quantum computing. We first
show how to decompose the Fock space of N optical modes in finite-dimensional
subspaces that are suitable for encoding strings of qubits and invariant under
LOP transformations (these subspaces are related to the spaces of irreducible
unitary representations of U(N)). Next we show how to design in algorithmic
fashion
  LOP circuits which implement any quantum circuit deterministically. We also
present some simple examples, such as the circuits implementing a CNOT gate and
a Bell-State Generator/Analyzer.


title:
Foundations of Probability and Physics-3: Preface of Proceedings and
  Round Table on Quantum Foundations and Computing

abstract:
  This preprint contains a detailed Preface to Proceedinngs of the
International Conference ``Foundations of Probability and Physics-3'' held in
V\"axj\"o, Sweden, 7-12 June 2004; table of contents and round table. The main
theme of the round table was {\it ``Fundamental problems in quantum mechanics,
probabilistic description of reality, and quantum information.''} The topics
that were specifically discussed were that of Quantum Cryptography, Quantum
computing, and Quantum Macroscopic Structures. For each of these topics, the
participants were asked to discuss which are the crucial Quantum features
required among the following : violation of Bell's inequality, Entanglement,
Complementarity, and Interference of Probabilities. Finally, the connection
between Mental states and Quantum states was discussed.


title: On a Density-of-States Approach to Bohmian Mechanics

abstract:
  We propose the idea that in Bohmian mechanics the wavefunction is related to
a density of states and explore some of its consequences. Specifically, it
allows a maximum-entropy interpretation of quantum probabilities, which creates
a stronger link between it and statistical mechanics. The proposed approach
also allows a range of extensions of the guidance condition in Bohmian
mechanics.


title: Efficient Graph State Construction Under the Barrett and Kok Scheme

abstract:
  Recently Barrett and Kok (BK) proposed an elegant method for entangling
separated matter qubits. They outlined a strategy for using their entangling
operation (EO) to build graph states, the resource for one-way quantum
computing. However by viewing their EO as a graph fusion event, one perceives
that each successful event introduces an ideal redundant graph edge, which
growth strategies should exploit. For example, if each EO succeeds with
probability p=0.4 then a highly connected graph can be formed with an overhead
of only about ten EO attempts per graph edge. The BK scheme then becomes
competitive with the more elaborate entanglement procedures designed to permit
p to approach unity.


title: Entanglement distribution by an arbitrarily inept delivery service

abstract:
  We consider the scenario where a company C manufactures in bulk pure
entangled pairs of particles, each pair intended for a distinct pair of distant
customers. Unfortunately, its delivery service is inept - the probability that
any given customer pair receives its intended particles is S, and the customers
cannot detect whether an error has occurred. Remarkably, no matter how small S
is, it is still possible for C to distribute entanglement by starting with
non-maximally entangled pairs. We determine the maximum entanglement
distributable for a given S, and also determine the ability of the parties to
perform nonlocal tasks with the qubits they receive.


title: A relation between fidelity and quantum adiabatic evolution

abstract:
  Recently, some quantum algorithms have been implemented by quantum adiabatic
evolutions. In this paper, we discuss the accurate relation between the running
time and the distance of the initial state and the final state of a kind of
quantum adiabatic evolutions. We show that this relation can be generalized to
the case of mixed states.


title:
On the Original Proof by Reductio ad Absurdum of the Hohenberg-Kohn
  Theorem for Many-Electron Coulomb Systems

abstract:
  It is shown that, for isolated many-electron Coulomb systems with Coulombic
external potentials, the usual reductio ad absurdum proof of the Hohenberg-Kohn
theorem is unsatisfactory since the to-be-refuted assumption made about the
one-electron densities and the assumption about the external potentials are not
compatible with the Kato cusp condition. The theorem is, however, provable by
more sophisticated means and it is shown here that the Kato cusp condition
actually leads to a satisfactory proof.

categories: quant-ph cond-mat.other nucl-th physics.chem-ph


title:
Logical analysis of the Bohr Complementarity Principle in Afshar's
  experiment under the NAFL interpretation

abstract:
  The NAFL (non-Aristotelian finitary logic) interpretation of quantum
mechanics requires that no `physical' reality can be ascribed to the wave
nature of the photon. The NAFL theory QM, formalizing quantum mechanics, treats
the superposed state ($S$) of a single photon taking two or more different
paths at the same time as a logical contradiction that is formally unprovable
in QM. Nevertheless, in a nonclassical NAFL model for QM in which the law of
noncontradiction fails, $S$ has a meaningful metamathematical interpretation
that the classical path information for the photon is not available. It is
argued that the existence of an interference pattern does not logically amount
to a proof of the self-interference of a single photon. This fact, when coupled
with the temporal nature of NAFL truth, implies the logical validity of the
retroactive assertion of the path information (and the logical superfluousness
of the grid) in Afshar's experiment. The Bohr complementarity principle, when
properly interpreted with the time dependence of logical truth taken into
account, holds in Afshar's experiment. NAFL supports, but not demands, a
metalogical reality for the particle nature of the photon even when the
semantics of QM requires the state $S$.


title: Quantum walks on directed graphs

abstract:
  We consider the definition of quantum walks on directed graphs. Call a
directed graph reversible if, for each pair of vertices (i, j), if i is
connected to j then there is a path from j to i. We show that reversibility is
a necessary and sufficient condition for a directed graph to allow the notion
of a discrete-time quantum walk, and discuss some implications of this
condition. We present a method for defining a "partially quantum" walk on
directed graphs that are not reversible.


title:
Fast simulation of stabilizer circuits using a graph state
  representation

abstract:
  According to the Gottesman-Knill theorem, a class of quantum circuits, namely
the so-called stabilizer circuits, can be simulated efficiently on a classical
computer. We introduce a new algorithm for this task, which is based on the
graph-state formalism. It shows significant improvement in comparison to an
existing algorithm, given by Gottesman and Aaronson, in terms of speed and of
the number of qubits the simulator can handle. We also present an
implementation.


title: Quantum Heat Engine With Multi-Level Quantum Systems

abstract:
  By reformulating the first law of thermodynamics in the fashion of
quantum-mechanical operators on the parameter manifold, we propose a universal
class of quantum heat engines (QHE) using the multi-level quantum system as the
working substance. We obtain a general expression of work for the thermodynamic
cycle with two thermodynamic adiabatic processes, which are microscopically
quantum adiabatic processes. We also classify the conditions for a 3-level QHE
to extract positive work from a heat bath. Our result is counter-intuitively
different from that of a 2-level system. As a more realistic illustration, a
3-level atom system with dark state configuration manipulated by classical
light is used to demonstrate our central idea.


title:
Bidirectional quantum secret sharing and secret splitting with polarized
  single photons

abstract:
  In this Letter, we present quantum secret sharing and secret splitting
protocols with single photons running forth and back between the participating
parties. The protocol has a high intrinsic efficiency, namely all photons
except those chosen for eavesdropping check could be used for sharing secret.
The participants need not to announce the measuring bases at most of the time
and this reduces the classical information exchanged largely.


title:
An efficient quantum secret sharing scheme with Einstein-Podolsky-Rosen
  Pairs

abstract:
  An efficient quantum secret sharing scheme is proposed. In this scheme, the
particles in an entangled pair group form two particle sequences. One sequence
is sent to Bob and the other is sent to Charlie after rearranging the particle
orders. Bob and Charlie make coding unitary operations and send the particles
back. Alice makes Bell-basis measurement to read their coding operations.


title: Common Cause and Contextual Realization of Bell Correlation

abstract:
  Considering the common cause principle, we construct a local-contextual
hidden-variable model for the Bohm version of EPR experiment. Our proposed
model can reproduce the predictions of quantum mechanics. It can be also
extended to classical examples in which similar correlations may be revealed.


title:
Comment on "A linear optics implementation of weak values in Hardy's
  paradox"

abstract:
  A recent experimental proposal by Ahnert and Payne [S.E. Ahnert and M.C.
Payne, Phys. Rev. A 70, 042102 (2004)] outlines a method to measure the weak
value predictions of Aharonov in Hardy's paradox. This proposal contains flaws
such as the state preparation method and the procedure for carrying out the
requisite weak measurements. We identify previously published solutions to some
of the flaws.


title:
Irrotational Momentum Fluctuations Conditioning the Quantum Nature of
  Physical Processes

abstract:
  Starting from a simple classical framework and employing some stochastic
concepts, the basic ingredients of the quantum formalism are recovered. It has
been shown that the traditional axiomatic structure of quantum mechanics can be
rebuilt, so that the quantum mechanical framework resembles to a large extent
that of the classical statistical mechanics. The main assumption used here is
the existence of a random irrotational component in the classical momentum.
Various basic elements of the quantum formalism (calculation of expectation
values, the Heisenberg uncertainty principle, the correspondence principle) are
recovered by applying traditional techniques, borrowed from classical
statistical mechanics.


title: Quantum-classical correspondence via a deformed kinetic operator

abstract:
  We propose an approach to the quantum-classical correspondence based on a
deformation of the momentum and kinetic operators of quantum mechanics. Making
use of the factorization method, we construct classical versions of the
momentum and kinetic operators which, in addition to the standard quantum
expressions, contain terms that are functionals of the N-particle density. We
show that this implementation of the quantum-classical correspondence is
related to Witten's deformation of the exterior derivative and Laplacian,
introduced in the context of supersymmetric quantum mechanics. The
corresponding deformed action is also shown to be related to the Fisher
information. Finally, we briefly consider the possible relevance of our
approach to the construction of kinetic-energy density functionals.


title: The Discontinuous Spatiality of Quantum Mechanical Objects

abstract:
  The quantum mechanical wave-particle dualism is analyzed and criticized, in
the framework of Reichenbach's concepts of phenomenon and interphenomenon. It
is suggested that the dual pictures be de-emphasized in the study of quantum
theory, and that a qualitative picture of atomic processes need not make use of
them. In this connection we stress a view of the electron and other such
particles as having discontinuous spatiality in time: they only have a place or
a shape when they participate in a phenomenon.


title:
Faithful and deterministic teleportation of an arbitrary $N$-qubit state
  using and identifying only Bell states

abstract:
  First, I show explicitly a scheme to {\it faithfully} and {\it
deterministically} teleport an arbitrary 2-qubit state from Alice to Bob. In
this scheme two same Bell states are sufficient for use. Bob can recover the
2-qubit state by performing at most 4 single-qubit unitary operations
conditioned on Alice's 4-bit classical public message corresponding to her two
Bell-state measurement outcomes. Then I generalize the 2-qubit teleportation
scheme to an aribitrary $N(N\ge 3)$-qubit state teleportation case by using $N$
same Bell states. In the generalized scheme, Alice only needs to identify $N$
Bell states after quantum swapping and then publish her measurement outcomes
($2N$-bit classical message). Conditioned on Alice's $2N$-bit classical
message, Bob only needs to perform at most $2N$ single-qubit unitary operations
to {\it fully} recover the arbitrary state. By comparing with the newest
relevant work [Phys. Rev. A{\bf 71}, 032303(2005)], the advantages of the
present schemes are revealed, respectively.


title:
"Local Instruction-Set Model for the Experiment of Pan et al" of
  Aschwanden, Philipp, Hess, and Barraza-Lopez Cannot Beat Quantum Models

abstract:
  We show the critique of the Pan et al experiment, given in quant-ph/0503108,
is unfounded.


title: Wath Time an Incident Wave Packet is Reflected?

abstract:
  We study the one dimensional time dependent Schr\"{o}dinger equation for a
potential step with $E < V_0$. We obtain the wave is not instantaneously
reflected, but for a few moment of time the wave packet penetrate into
inaccessible classically region and then reflected. So it is shown that one can
write the peneterated wave paket as superposition of incident and reflected
wave packets like.


title: Distributivity breaking and macroscopic quantum games

abstract:
  Examples of games between two partners with mixed strategies, calculated by
the use of the probability amplitude as some vector in Hilbert space are given.
The games are macroscopic, no microscopic quantum agent is supposed. The reason
for the use of the quantum formalism is in breaking of the distributivity
property for the lattice of yes-no questions arising due to the special rules
of games. The rules of the games suppose two parts: the preparation and
measurement. In the first part due to use of the quantum logical
orthocomplemented non-distributive lattice the partners freely choose the wave
functions as descriptions of their strategies. The second part consists of
classical games described by Boolean sublattices of the initial non-Boolean
lattice with same strategies which were chosen in the first part. Examples of
games for spin one half are given. New Nash equilibria are found for some
cases. Heisenberg uncertainty relations without the Planck constant are written
for the "spin one half game".


title:
The Vortex Phase Qubit: Generating Arbitrary, Counter-Rotating, Coherent
  Superpositions in Bose-Einstein Condensates via Optical Angular Momentum
  Beams

abstract:
  We propose a scheme for generation of arbitrary coherent superposition of
vortex states in Bose-Einstein condensates (BEC) using the orbital angular
momentum (OAM) states of light. We devise a scheme to generate coherent
superpositions of two counter-rotating OAM states of light using known
experimental techniques. We show that a specially designed Raman scheme allows
transfer of the optical vortex superposition state onto an initially
non-rotating BEC. This creates an arbitrary and coherent superposition of a
vortex and anti-vortex pair in the BEC. The ideas presented here could be
extended to generate entangled vortex states, design memories for the OAM
states of light, and perform other quantum information tasks. Applications to
inertial sensing are also discussed.


title: Compression Bases in Unital Groups

abstract:
  We study unital groups with a distinguished family of compressions called a
compression base. A motivating example is the partially ordered additive group
of a von Neumann algebra with all Naimark compressions as the compression base.


title: Limitations on the Utility of Exact Master Equations

abstract:
  The low temperature solution of the exact master equation for an oscillator
coupled to a linear passive heat bath is known to give rise to serious
divergences. We now show that, even in the high temperature regime, problems
also exist, notably the fact that the density matrix is not necessarily
positive.


title: Implications of Superstrong Nonlocality for Cryptography

abstract:
  Non-local boxes are hypothetical ``machines'' that give rise to superstrong
non-local correlations, leading to a stronger violation of Bell/CHSH
inequalities than is possible within the framework of quantum mechanics. We
show how non-local boxes can be used to perform any two-party secure
computation. We first construct a protocol for bit commitment and then show how
to achieve oblivious transfer using non-local boxes. Both have been shown to be
impossible using quantum mechanics alone.


title:
The physics of no-bit-commitment : Generalized quantum non-locality
  versus oblivious transfer

abstract:
  We show here that the recent work of Wolf and Wullschleger (quant-ph/0502030)
on oblivious transfer apparently opens the possibility that non-local
correlations which are stronger than those in quantum mechanics could be used
for bit-commitment. This is surprising, because it is the very existence of
non-local correlations which in quantum mechanics prevents bit-commitment. We
resolve this apparent paradox by stressing the difference between non-local
correlations and oblivious transfer, based on the time-ordering of their inputs
and outputs, which prevents bit-commitment.


title: Quantum random walk of the field in an externally driven cavity

abstract:
  Using resonant interaction between atoms and the field in a high quality
cavity, we show how to realize quantum random walks as proposed by Aharonov et
al [Phys. Rev. A {\bf48}, 1687 (1993)]. The atoms are driven strongly by a
classical field. Under conditions of strong driving we could realize an
effective interaction of the form $ iS^{x}(a-a^{\dag})$ in terms of the spin
operator associated with the two level atom and the field operators. This
effective interaction generates displacement in the field's wavefunction
depending on the state of the two level atom. Measurements of the state of the
two level atom would then generate effective state of the field. Using a
homodyne technique, the state of the quantum random walker can be monitored.


title: On the power of non-local boxes

abstract:
  A non-local box is a virtual device that has the following property: given
that Alice inputs a bit at her end of the device and that Bob does likewise, it
produces two bits, one at Alice's end and one at Bob's end, such that the XOR
of the outputs is equal to the AND of the inputs. This box, inspired from the
CHSH inequality, was first proposed by Popescu and Rohrlich to examine the
question: given that a maximally entangled pair of qubits is non-local, why is
it not maximally non-local? We believe that understanding the power of this box
will yield insight into the non-locality of quantum mechanics. It was shown
recently by Cerf, Gisin, Massar and Popescu, that this imaginary device is able
to simulate correlations from any measurement on a singlet state. Here, we show
that the non-local box can in fact do much more: through the simulation of the
magic square pseudo-telepathy game and the Mermin-GHZ pseudo-telepathy game, we
show that the non-local box can simulate quantum correlations that no entangled
pair of qubits can in a bipartite scenario and even in a multi-party scenario.
Finally we show that a single non-local box cannot simulate all quantum
correlations and propose a generalization for a multi-party non-local box. In
particular, we show quantum correlations whose simulation requires an
exponential amount of non-local boxes, in the number of maximally entangled
qubit pairs.


title:
Optimal generation of single-qubit operation from an always-on
  interaction by algebraic decoupling

abstract:
  We present a direct algebraic decoupling approach to generate arbitrary
single-qubit operations in the presence of a constant interaction by applying
local control signals. To overcome the difficulty of undesirable entanglement
generated by the untunable interaction, we derive local control fields that are
designed to both drive the qubit systems back to unentangled states at the end
of the time interval over which the desired single-qubit operation is
completed. This approach is seen to be particularly relevant for the physical
implementation of solid-state quantum computation and for the design of
low-power pulses in NMR.


title:
Optimal unambiguous filtering of a quantum state: An instance in mixed
  state discrimination

abstract:
  Deterministic discrimination of nonorthogonal states is forbidden by quantum
measurement theory. However, if we do not want to succeed all the time, i.e.
allow for inconclusive outcomes to occur, then unambiguous discrimination
becomes possible with a certain probability of success. A variant of the
problem is set discrimination: the states are grouped in sets and we want to
determine to which particular set a given pure input state belongs. We consider
here the simplest case, termed quantum state filtering, when the $N$ given
non-orthogonal states, $\{|\psi_{1} >,..., |\psi_{N} > \}$, are divided into
two sets and the first set consists of one state only while the second consists
of all of the remaining states. We present the derivation of the optimal
measurement strategy, in terms of a generalized measurement (POVM), to
distinguish $|\psi_1>$ from the set $\{|\psi_2 >,...,|\psi_N > \}$ and the
corresponding optimal success and failure probabilities. The results, but not
the complete derivation, were presented previously [\prl {\bf 90}, 257901
(2003)] as the emphasis there was on appplication of the results to novel
probabilistic quantum algorithms. We also show that the problem is equivalent
to the discrimination of a pure state and an arbitrary mixed state.


title: Geometric Phase for entangled Mixed state

abstract: This paper has been withdrawn by the author


title: Coherent population trapping in quantized light field

abstract:
  A full quantum treatment of coherent population trapping (CPT) is given for a
system of resonantly coupled atoms and electromagnetic field. We develop a
regular analytical method of the construction of generalized dark states (GDS).
It turns out that GDS do exist for all optical transitions $F_g\to F_e$,
including bright transitions $F\to F+1$ and $F''\to F''$ with $F''$ a
half-integer, for which the CPT effect is absent in a classical field. We
propose an idea to use an optically thick medium with a transition $F''\to F''$
with $F'' \ge 3/2$ a half-integer as a ''quantum filter'', which transmits only
a quantum light.


title:
Quantum dephasing and decay of classical correlation functions in
  chaotic systems

abstract:
  We discuss the dephasing induced by the internal classical chaotic motion in
the absence of any external environment. To this end we consider a suitable
extension of fidelity for mixed states which is measurable in a Ramsey
interferometry experiment. We then relate the dephasing to the decay of this
quantity which, in the semiclassical limit, is expressed in terms of an
appropriate classical correlation function. Our results are derived
analytically for the example of a nonlinear driven oscillator and then
numerically confirmed for the kicked rotor model.


title: Bound states in continuum in an electron waveguide

abstract:
  It is shown that in a double-cavity, two-dimensional electron waveguide, the
interplay between quasi-bound states of each cavity leads to the appearance of
bound states in continuum for certain distances between the cavities. These
bound states may be used to trap electrons in de-localized states distributed
in both cavities.


title: The Electromagnetic Field Stress Tensor between Dielectric Half-Spaces

abstract:
  The stress tensor for the quantized electromagnetic field is calculated in
the region between a pair of dispersive, dielectric half-spaces. This
generalizes the stress tensor for the Casimir energy to the case where the
boundaries have finite reflectivity. We also include the effects of finite
temperature. This allows us to discuss the circumstances under which the weak
energy condition and the null energy condition can be violated in the presence
of finite reflectivity and finite temperature.


title:
Multipartite entangled state representation and its squeezing
  transformation

abstract:
  The multipartite entangled state $|p,\xi_2,\xi_2,...,\xi_n>$ for the total
momentum and relative coordinates of n particles is constructed. The
corresponding quantum mechanical operator with respect to the classical
transformation $p\to e^{\lambda_1} p$, $\xi_i\to e^{\lambda_i} \xi_i$,
$i=1,...,n$, in the state $|p,\xi_2,\xi_2,...,\xi_n>$ is investigated.