title: Notes on the Fidelity of Symplectic Quantum Error-Correcting Codes

abstract:
  Two observations are given on the fidelity of schemes for quantum information
processing. In the first one, we show that the fidelity of a symplectic
(stabilizer) code, if properly defined, exactly equals the `probability' of the
correctable errors for general quantum channels. The second observation states
that for any coding rate below the quantum capacity, exponential convergence of
the fidelity of some codes to unity is possible.


title: Entanglement and Time

abstract:
  It is argued that recent experiments testing Multisimultaneity prove that
quantum entanglement occurs without the flow of time. Bohm's theory cannot be
considered a real temporal description.


title: Orthogonality of Biphoton Polarization States

abstract:
  Orthogonality of two-photon polarization states belonging to a single
frequency and spatial mode is demonstrated experimentally, in a generalization
of the well-known anti-correlation 'dip' experiment.


title:
Continuous-variable quantum cryptography is secure against non-gaussian
  attacks

abstract:
  A general study of arbitrary finite-size coherent attacks against
continuous-variable quantum cryptographic schemes is presented. It is shown
that, if the size of the blocks that can be coherently attacked by an
eavesdropper is fixed and much smaller than the key size, then the optimal
attack for a given signal-to-noise ratio in the transmission line is an
individual gaussian attack. Consequently, non-gaussian coherent attacks do not
need to be considered in the security analysis of such quantum cryptosystems.


title: Average case quantum lower bounds for computing the boolean mean

abstract:
  We study the average case approximation of the Boolean mean by quantum
algorithms. We prove general query lower bounds for classes of probability
measures on the set of inputs. We pay special attention to two probabilities,
where we show specific query and error lower bounds and the algorithms that
achieve them. We also study the worst expected error and the average expected
error of quantum algorithms and show the respective query lower bounds. Our
results extend the optimality of the algorithm of Brassard et al.


title: Compiling Quantum Circuits using the Palindrome Transform

abstract:
  The design and optimization of quantum circuits is central to quantum
computation. This paper presents new algorithms for compiling arbitrary 2^n x
2^n unitary matrices into efficient circuits of (n-1)-controlled single-qubit
and (n-1)-controlled-NOT gates. We first present a general algebraic
optimization technique, which we call the Palindrome Transform, that can be
used to minimize the number of self-inverting gates in quantum circuits
consisting of concatenations of palindromic subcircuits. For a fixed column
ordering of two-level decomposition, we then give an numerative algorithm for
minimal (n-1)-controlled-NOT circuit construction, which we call the
Palindromic Optimization Algorithm. Our work dramatically reduces the number of
gates generated by the conventional two-level decomposition method for
constructing quantum circuits of (n-1)-controlled single-qubit and
(n-1)-controlled-NOT gates.


title: Quantum random walks with history dependence

abstract:
  We introduce a multi-coin discrete quantum random walk where the amplitude
for a coin flip depends upon previous tosses. Although the corresponding
classical random walk is unbiased, a bias can be introduced into the quantum
walk by varying the history dependence. By mixing the biased random walk with
an unbiased one, the direction of the bias can be reversed leading to a new
quantum version of Parrondo's paradox.


title:
Experimental demonstration of an efficient quantum phase-covariant
  cloning and its possible applications to simulating eavesdropping in quantum
  cryptography

abstract:
  We describe a nuclear magnetic resonance (NMR) experiment which implements an
efficient one-to-two qubit phase-covariant cloning machine(QPCCM). In the
experiment we have achieved remarkably high fidelities of cloning, 0.848 and
0.844 respectively for the original and the blank qubit. This experimental
value is close to the optimal theoretical value of 0.854. We have also
demonstrated how to use our phase-covariant cloning machine for quantum
simulations of bit by bit eavesdropping in the four-state quantum key
distribution protocol.


title: Quantum Theory of Two-Photon Wavepacket Interference in a Beam Splitter

abstract:
  We study a general theory on the interference of a two-photon wavepacket in a
beam splitter. The theory is carried out in the Schr\"{o}dinger picture so that
the quantum nature of the two-photon interference is explicitly presented. We
find that the topological symmetry of the probability-amplitude spectrum of the
two-photon wavepacket dominates the manners of two-photon interference which
are distinguished according to increasing and decreasing the coincidence
probability for the absence of interference. However, two-photon entanglement
can be witnessed by the interference manner. We demonstrate the necessary and
sufficient conditions for the perfect two-photon interference. For a two-photon
entangled state with an anti-symmetric spectrum, it passes a 50/50 beam
splitter with the perfect transparency. The theory contributes an unified
understanding to a variety of the two-photon interference effects.


title: Collective Atomic Recoil Lasing Including Friction and Diffusion Effects

abstract:
  We extend the Collective Atomic Recoil Lasing (CARL) model including the
effects of friction and diffusion forces acting on the atoms due to the
presence of optical molasses fields. The results from this model are consistent
with those from a recent experiment by Kruse et al. [Phys. Rev. Lett. 91,
183601 (2003)]. In particular, we obtain a threshold condition above which
collective backscattering occurs. Using a nonlinear analysis we show that the
backscattered field and the bunching evolve to a steady-state, in contrast to
the non-stationary behaviour of the standard CARL model. For a proper choice of
the parameters, this steady-state can be superfluorescent.


title:
Generalized protocol for distribution and concentration of Quantum
  information

abstract:
  Alice can distribute a quantum state $|\phi>$ to $N$ spatially separated
parties(say Bobs) by telecloning. It is possible for Charlie to reconstruct the
quantum state to him if he shares same kind of telecloning quantum channel with
Bobs using only LOCC. For N=3 reconstruction can be done faithfully using
Smolin's 4 party unlockable bound entangled state as shared channel. In this
note we investigate, in multiparty setting, the general structure of quantum
channel and protocol by which faithful distribution and concentration of
quantum information can be done.


title: Fault-Tolerant Logical Gate Networks for CSS Codes

abstract:
  Fault-tolerant logical operations for qubits encoded by CSS codes are
discussed, with emphasis on methods that apply to codes of high rate, encoding
k qubits per block with k>1. It is shown that the logical qubits within a given
block can be prepared by a single recovery operation in any state whose
stabilizer generator separates into X and Z parts. Optimized methods to move
logical qubits around and to achieve controlled-not and Toffoli gates are
discussed. It is found that the number of time-steps required to complete a
fault-tolerant quantum computation is the same when k>1 as when k=1.


title: Tripartite Quantum State Sharing

abstract:
  We demonstrate a multipartite protocol to securely distribute and reconstruct
a quantum state. A secret quantum state is encoded into a tripartite entangled
state and distributed to three players. Any two of the three players are able
to reconstruct the state, whilst individual players obtain nothing. We
characterize this (2,3) threshold quantum state sharing scheme in terms of
fidelity, signal transfer and reconstruction noise. We demonstrate a fidelity
averaged over all reconstruction permutations of 0.73, which is achievable only
using quantum resources.


title: Moving Picture and Hamilton-Jacobi Theory in Quantum Mechanics

abstract:
  We propose a new picture, which we call the {\it moving picture}, in quantum
mechanics. The Schr\"{o}dinger equation in this picture is derived and its
solution is examined. We also investigate the close relationship between the
moving picture and the Hamilton-Jacobi theory in classical mechanics.


title: Universality of Entanglement and Quantum Computation Complexity

abstract:
  We study the universality of scaling of entanglement in Shor's factoring
algorithm and in adiabatic quantum algorithms across a quantum phase transition
for both the NP-complete Exact Cover problem as well as the Grover's problem.
The analytic result for Shor's algorithm shows a linear scaling of the entropy
in terms of the number of qubits, therefore difficulting the possibility of an
efficient classical simulation protocol. A similar result is obtained
numerically for the quantum adiabatic evolution Exact Cover algorithm, which
also shows universality of the quantum phase transition the system evolves
nearby. On the other hand, entanglement in Grover's adiabatic algorithm remains
a bounded quantity even at the critical point. A classification of scaling of
entanglement appears as a natural grading of the computational complexity of
simulating quantum phase transitions.


title: Let us play with qubits

abstract:
  Quantum game theory offers a lot of interesting questions, and it is relevant
to use the quantum information theory to resolve or improve games with lack of
information : how to use the power of quantum entanglement to show the
superiority of a quantum player that is allowed to use quantum mechanics versus
a classical player, how to use quantum communication properties in cooperative
games ... But games are also useful to make notions easier to understand, and
permit to apprehend easier new ways of reasoning. The objective of this work is
to formalize and to study a simple game with qubits using quantum notions of
measurement and superposition but keeping a simple formalism so that knowing
quantum mechanics is not necessary to play the game. We solve a quantum
combinatorial game by giving a winning strategy for it. We also propose a
quantisation of a family of combinatorial games.


title: Decoherence at zero temperature

abstract:
  Most discussions of decoherence in the literature consider the
high-temperature regime but it is also known that, in the presence of
dissipation, decoherence can occur even at zero temperature. Whereas most
previous investigations all assumed initial decoupling of the quantum system
and bath, we consider that the system and environment are entangled at all
times. Here, we discuss decoherence for a free particle in an initial
Schr\"{o}dinger cat state. Memory effects are incorporated by use of the single
relaxation time model (since the oft-used Ohmic model does not give physically
correct results).


title: Effect of an External Field on Decoherence

abstract:
  "Decoherence of quantum superpositions through coupling to engineered
reservoirs" is the topic of a recent article by Myatt et al. [Nature
{\underline{403}}, 269 (2000)] which has attracted much interest because of its
relevance to current research in fundamental quantum theory, quantum
computation, teleportation, entanglement and the quantum-classical interface.
However, the preponderance of theoretical work on decoherence does not consider
the effect of an {\underline{external field}}. Here, we present an analysis of
such an effect in the case of the random delta-correlated force discussed by
Myatt et al.


title: The Equation of Motion of an Electron

abstract:
  The claim by Rohrlich that the Abraham-Lorentz-Dirac equation is not the
correct equation for a classical point charge is shown to be incorrect and it
is pointed out that the equation which he proposes is the equation
{\underline{derived}} by Ford and O'Connell for a charge with structure. The
quantum-mechanical case is also discussed.


title:
Exact decoherence to pointer states in free open quantum systems is
  universal

abstract:
  In this paper it is shown that exact decoherence to minimal uncertainty
Gaussian pointer states is generic for free quantum particles coupled to a heat
bath. More specifically, the paper is concerned with damped free particles
linearly coupled under product initial conditions to a heat bath at arbitrary
temperature, with arbitrary coupling strength and spectral densities covering
the Ohmic, subohmic, and supraohmic regime. Then it is true that there exists a
time t_c such that for times t>t_c the state can always be exactly represented
as a mixture (convex combination) of particular minimal uncertainty Gaussian
states, regardless of and independent from the initial state. This exact
`localisation' is hence not a feature specific to high temperatures and weak
damping limit, but is rather a generic property of damped free particles.


title: Forces between a single atom and its distant mirror image

abstract:
  An excited-state atom whose emitted light is back-reflected by a distant
mirror can experience trapping forces, because the presence of the mirror
modifies both the electromagnetic vacuum field and the atom's own radiation
reaction field. We demonstrate this mechanical action using a single trapped
barium ion. We observe the trapping conditions to be notably altered when the
distant mirror is shifted by an optical wavelength. The well-localised barium
ion enables the spatial dependence of the forces to be measured explicitly. The
experiment has implications for quantum information processing and may be
regarded as the most elementary optical tweezers.


title: HYPER and gravitational decoherence

abstract:
  We study the decoherence process associated with the scattering of stochastic
backgrounds of gravitational waves. We show that it has a negligible influence
on HYPER-like atomic interferometers although it may dominate decoherence of
macroscopic motions, such as the planetary motion of the Moon around the Earth.


title: Two-color interference stabilization of atoms

abstract:
  The effect of interference stabilization is shown to exist in a system of two
atomic levels coupled by a strong two-color laser field, the two frequencies of
which are close to a two-photon Raman-type resonance between the chosen levels,
with open channels of one-photon ionization from both of them. We suggest an
experiment, in which a rather significant (up to 90%) suppression of ionization
can take place and which demonstrates explicitly the interference origin of
stabilization. Specific calculations are made for H and He atoms and optimal
parameters of a two-color field are found. The physics of the effect and its
relation with such well-known phenomena as LICS and population trapping in a
three-level system are discussed.


title: Distinguishability and indistinguishability by LOCC

abstract:
  We show that a set of linearly independent quantum states $\{(U_{m,n}\otimes
I)\rho ^{AB}(U_{m,n}^{\dagger}\otimes I)\}_{m,n=0}^{d-1}$, where $U_{m,n}$ are
generalized Pauli matrices, cannot be discriminated deterministically or
probabilistically by local operations and classical communications (LOCC). On
the other hand, any $l$ maximally entangled states from this set are locally
distinguishable if $l(l-1)\le 2d$. The explicit projecting measurements are
obtained to locally discriminate these states. As an example, we show that four
Werner states are locally indistinguishable.


title: Arbitrary rotation and entanglement of flux SQUID qubits

abstract:
  We propose a new approach for the arbitrary rotation of a three-level SQUID
qubit and describe a new strategy for the creation of coherence transfer and
entangled states between two three-level SQUID qubits. The former is succeeded
by exploring the coupled-uncoupled states of the system when irradiated with
two microwave pulses, and the latter is succeeded by placing the SQUID qubits
into a microwave cavity and used adiabatic passage methods for their
manipulation.


title: Entanglement of identical particles and reference phase uncertainty

abstract:
  We have recently introduced a measure of the bipartite entanglement of
identical particles, E_P, based on the principle that entanglement should be
accessible for use as a resource in quantum information processing. We show
here that particle entanglement is limited by the lack of a reference phase
shared by the two parties, and that the entanglement is constrained to
reference-phase invariant subspaces. The super-additivity of E_P results from
the fact that this constraint is weaker for combined systems. A shared
reference phase can only be established by transferring particles between the
parties, that is, with additional nonlocal resources. We show how this nonlocal
operation can increase the particle entanglement.


title: Generalized Intelligent States for an Arbitrary Quantum System

abstract:
  Generalized Intelligent States (coherent and squeezed states) are derived for
an arbitrary quantum system by using the minimization of the so-called
Robertson-Schr\"odinger uncertainty relation. The Fock-Bargmann representation
is also considered. As a direct illustration of our construction, the
P\"oschl-Teller potentials of trigonometric type will be shosen. We will show
the advantage of the Fock-Bargmann representation in obtaining the generalized
intelligent states in an analytical way. Many properties of these states are
studied.


title:
Coherent states \`a la Klauder-Perelomov for the P\"oschl-Teller
  potentials

abstract:
  In this paper we present a scheme for constructing the coherent states of
Klauder-Perelomov's type for a particle which is trapped in P\"oschl-Teller
potentials.


title:
Quantifying entanglement in "Experimental entanglement of four
  particles"

abstract:
  We quantify various possible entanglement measures for the four particles GHZ
entangled state that has been produced experimentally [C. Sackett et al, Nature
404, 256-259 (2000)].


title: Casimir-Polder interaction in the presence of parallel walls

abstract:
  Making use of the quantum correlators associated with the Maxwell field
vacuum distorted by the presence of plane parallel material surfaces we derive
the Casimir-Polder interaction in the presence of plane parallel conducting
walls and in the presence of a conducting wall and a magnetically permeable
one.


title: Combinatorial coherent states via normal ordering of bosons

abstract:
  We construct and analyze a family of coherent states built on sequences of
integers originating from the solution of the boson normal ordering problem.
These sequences generalize the conventional combinatorial Bell numbers and are
shown to be moments of positive functions. Consequently, the resulting coherent
states automatically satisfy the resolution of unity condition. In addition
they display such non-classical fluctuation properties as super-Poissonian
statistics and squeezing.


title: Quantum control in infinite dimensions

abstract:
  Accurate control of quantum evolution is an essential requirement for quantum
state engineering, laser chemistry, quantum information and quantum computing.
Conditions of controllability for systems with a finite number of energy levels
have been extensively studied. By contrast, results for controllability in
infinite dimensions have been mostly negative, stating that full control cannot
be achieved with a finite dimensional control Lie algebra. Here we show that by
adding a discrete operation to a Lie algebra it is possible to obtain full
control in infinite dimensions with a small number of control operators.


title:
A field theoretic causal model of a Mach-Zehnder Wheeler delayed-choice
  experiment

abstract:
  We consider a Wheeler delayed-choice experiment based on the Mach-Zehnder
Interferometer. Since the development of the causal interpretation of
relativistic boson fields there have not been any applications for which the
equations of motion for the field have been solved explicitly. Here, we provide
perhaps the first application of the causal interpretation of boson fields for
which the equations of motion are solved. Specifically, we consider the
electromagnetic field. Solving the equations of motion allows us to develop a
relativistic causal model of the Wheeler delayed-choice Mach-Zehnder
Interferometer. We show explicitly that a photon splits at a beam splitter. We
also demonstrate the inherent nonlocal nature of a relativistic quantum field.
This is particularly revealed in a which-path measurement where a quantum is
nonlocally absorbed from both arms of the interferometer. This feature explains
how when a photon is split by a beam splitter it nevertheless registers on a
detector in one arm of the interferometer. Bohm et al \cite{BDH85} have argued
that a causal model of a Wheeler delayed-choice experiment avoids the paradox
of creating or changing history, but they did not provide the details of such a
model. The relativistic causal model we develop here serves as a detailed
example which demonstrates this point, though our model is in terms of a field
picture rather than the particle picture of the Bohm-de Broglie nonrelativistic
causal interpretation.


title: Quantum Boolean Summation with Repetitions in the Worst-Average Setting

abstract:
  We study the quantum summation QS algorithm of Brassard,
  Hoyer, Mosca and Tapp, which approximates the arithmetic mean of a Boolean
function defined on $N$ elements. We present sharp error bounds of the QS
algorithm in the worst-average setting with the average performance measured in
the $L_q$ norm, $q \in [1,\infty]$. We prove that the QS algorithm with $M$
quantum queries, $M<N$, has the worst-average error bounds of the form
$\Theta(\ln M/M)$ for $q=1$, $\Theta(M^{-1/q})$ for $q\in (1,\infty)$, and is
equal to 1 for $q=\infty$. We also discuss the asymptotic constants of these
estimates. We improve the error bounds by using the QS algorithm with
repetitions. Using the number of repetitions which is independent of $M$ and
linearly dependent on $q$, we get the error bound of order $M^{-1}$ for any $q
\in [1,\infty)$. Since $\Omega(M^{-1})$ is a lower bound on the worst-average
error of any quantum algorithm with $M$ queries, the QS algorithm with
repetitions is optimal in the worst-average setting.


title: Tema Con Variazioni: Quantum Channel Capacity

abstract:
  Channel capacity describes the size of the nearly ideal channels, which can
be obtained from many uses of a given channel, using an optimal error
correcting code. In this paper we collect and compare minor and major
variations in the mathematically precise statements of this idea which have
been put forward in the literature. We show that all the variations considered
lead to equivalent capacity definitions. In particular, it makes no difference
whether one requires mean or maximal errors to go to zero, and it makes no
difference whether errors are required to vanish for any sequence of block
sizes compatible with the rate, or only for one infinite sequence.


title: Quantum algorithms for subset finding

abstract:
  Recently, Ambainis gave an O(N^(2/3))-query quantum walk algorithm for
element distinctness, and more generally, an O(N^(L/(L+1)))-query algorithm for
finding L equal numbers. We point out that this algorithm actually solves a
much more general problem, the problem of finding a subset of size L that
satisfies any given property. We review the algorithm and give a considerably
simplified analysis of its query complexity. We present several applications,
including two algorithms for the problem of finding an L-clique in an N-vertex
graph. One of these algorithms uses O(N^(2L/(L+1))) edge queries, and the other
uses \tilde{O}(N^((5L-2)/(2L+4))), which is an improvement for L <= 5. The
latter algorithm generalizes a recent result of Magniez, Santha, and Szegedy,
who considered the case L=3 (finding a triangle). We also pose two open
problems regarding continuous time quantum walk and lower bounds.


title: Multilinear Formulas and Skepticism of Quantum Computing

abstract:
  Several researchers, including Leonid Levin, Gerard 't Hooft, and Stephen
Wolfram, have argued that quantum mechanics will break down before the
factoring of large numbers becomes possible. If this is true, then there should
be a natural set of quantum states that can account for all experiments
performed to date, but not for Shor's factoring algorithm. We investigate as a
candidate the set of states expressible by a polynomial number of additions and
tensor products. Using a recent lower bound on multilinear formula size due to
Raz, we then show that states arising in quantum error-correction require
n^{Omega(log n)} additions and tensor products even to approximate, which
incidentally yields the first superpolynomial gap between general and
multilinear formula size of functions. More broadly, we introduce a complexity
classification of pure quantum states, and prove many basic facts about this
classification. Our goal is to refine vague ideas about a breakdown of quantum
mechanics into specific hypotheses that might be experimentally testable in the
near future.


title:
Simultaneous non-disturbing detection of incompatible properties in
  double-slit experiment

abstract:
  We exploit the notion of which-slit detector introduced by Englert, Scully
and Walther (ESW), to show that two incompatible properties can be detected
together for each particle hitting the screen, without disturbing the
center-of-mass motion of the particle.


title:
Electron wavepacket propagation and entanglement in a chain of coupled
  quantum dots

abstract:
  We study the coherent dynamics of one- and two-electron transport in a linear
array of tunnel-coupled quantum dots. We find that this system exhibits a rich
variety of coherent phenomena, ranging from electron wavepacket propagation and
interference to two-particle bonding and entanglement. Our studies, apart from
their relevance to the exploration of quantum dynamics and transport in
periodic structures, are also aimed at possible applications in future quantum
computation schemes.


title: Inferring linear quantum dynamics without no-signaling

abstract:
  It is shown that the no-signaling condition is not needed in order to argue a
linear quantum dynamics from standard quantum statics and the usual
interpretation of quantum measurement outcomes as probabilistic mixtures.


title: Robust String Matching in O(\sqrt{N}+M) Quantum Queries

abstract: This paper was withdrawn by the author due to a fatal error.


title: Non-Hermitian time-dependent quantum systems with real energies

abstract:
  In this work we intend to study a class of time-dependent quantum systems
with non-Hermitian Hamiltonians, particularly those whose Hermitian counterpart
are important for the comprehension of posed problems in quantum optics and
quantum chemistry, which consists of an oscillator with time-dependent mass and
frequency under the action of a time-dependent imaginary potential. The
propagator for a general time-dependence of the parameters and the
wave-functions are obtained explicitly for constant frequency and mass and a
linear time-dependence in the potential. The wave-functions are used to obtain
the expectation value of the Hamiltonian. Although it is neither Hermitian nor
PT symmetric, the case under study exhibits real values of energy.


title:
The su(n) Lie algebraic structures in the Pegg-Barnett quantization
  formulation

abstract:
  We investigate the oscillator algebra of the Pegg-Barnett oscillator with a
finite-dimensional number-state space and show that it possesses the su($n$)
Lie algebraic structure. In addition, a so-called supersymmetric Pegg-Barnett
oscillator is suggested, and the related topics such as the algebraic structure
and particle occupation number of the Pegg-Barnett oscillator are briefly
discussed.


title:
Robust high-fidelity teleportation of an atomic state through the
  detection of cavity decay

abstract:
  We propose a scheme for quantum teleportation of an atomic state based on the
detection of cavity decay. The internal state of an atom trapped in a cavity
can be disembodiedly transferred to another atom trapped in a distant cavity by
measuring interference of polarized photons through single-photon detectors. In
comparison with the original proposal by S. Bose, P.L. Knight, M.B. Plenio, and
V. Vedral [Phys. Rev. Lett. 83, 5158 (1999)], our protocol of teleportation has
a high fidelity of almost unity, and inherent robustness, such as the
insensitivity of fidelity to randomness in the atom's position, and to
detection inefficiency. All these favorable features make the scheme feasible
with the current experimental technology.


title:
Cavity-induced damping and level shifts in a wide aperture spherical
  resonator

abstract:
  We calculate explicitly the space dependence of the radiative relaxation
rates and associated level shifts for a dipole placed in the vicinity of the
center of a spherical cavity with a large numerical aperture and a relatively
low finesse. In particular, we give simple and useful analytic formulas for
these quantities, that can be used with arbitrary mirrors transmissions. The
vacuum field in the vicinity of the center of the cavity is actually equivalent
to the one obtained in a microcavity, and this scheme allows one to predict
significant cavity QED effects.


title: Vacuum-field atom trapping in a wide aperture spherical resonator

abstract:
  We consider the situation where a two-level atom is placed in the vicinity of
the center of a spherical cavity with a large numerical aperture. The vacuum
field at the center of the cavity is actually equivalent to the one obtained in
a microcavity, and both the dissipative and the reactive parts of the atom's
spontaneous emission are significantly modified. Using an explicit calculation
of the spatial dependence of the radiative relaxation rate and of the
associated level shift, we show that for a weakly excitating light field, the
atom can be attracted to the center of the cavity by vacuum-induced light
shifts.


title: Black holes and information theory

abstract:
  During the past three decades investigators have unveiled a number of deep
connections between physical information and black holes whose consequences for
ordinary systems go beyond what has been deduced purely from the axioms of
information theory. After a self-contained introduction to black hole
thermodynamics, we review from its vantage point topics such as the information
conundrum that emerges from the ability of incipient black holes to radiate,
the various entropy bounds for non-black hole systems (holographic bound,
universal entropy bound, etc) which are most easily derived from black hole
thermodynamics, Bousso's covariant entropy bound, the holographic principle of
particle physics, and the subject of channel capacity of quantum communication
channels.


title: Quantum Limitations on the Storage and Transmission of Information

abstract:
  Information must take up space, must weigh, and its flux must be limited.
Quantum limits on communication and information storage leading to these
conclusions are here described. Quantum channel capacity theory is reviewed for
both steady state and burst communication. An analytic approximation is given
for the maximum signal information possible with occupation number signal
states as a function of mean signal energy. A theorem guaranteeing that these
states are optimal for communication is proved. A heuristic "proof" of the
linear bound on communication is given, followed by rigorous proofs for signals
with specified mean energy, and for signals with given energy budget. And
systems of many parallel quantum channels are shown to obey the linear bound
for a natural channel architecture. The time--energy uncertainty principle is
reformulated in information language by means of the linear bound. The quantum
bound on information storage capacity of quantum mechanical and quantum field
devices is reviewed. A simplified version of the analytic proof for the bound
is given for the latter case. Solitons as information caches are discussed, as
is information storage in one dimensional systems. The influence of signal
self--gravitation on communication is considerd. Finally, it is shown that
acceleration of a receiver acts to block information transfer.


title: Entanglement and Frustration in Ordered Systems

abstract:
  This article reviews and extends recent results concerning entanglement and
frustration in multipartite systems which have some symmetry with respect to
the ordering of the particles. Starting point of the discussion are Bell
inequalities: their relation to frustration in classical systems and their
satisfaction for quantum states which have a symmetric extension. It is then
discussed how more general global symmetries of multipartite systems constrain
the entanglement between two neighboring particles. We prove that maximal
entanglement (measured in terms of the entanglement of formation) is always
attained for the ground state of a certain nearest neighbor interaction
Hamiltonian having the considered symmetry with the achievable amount of
entanglement being a function of the ground state energy. Systems of Gaussian
states, i.e. quantum harmonic oscillators, are investigated in more detail and
the results are compared to what is known about ordered qubit systems.


title: Geometric Quantum Information Storage Based on Atomic Ensemble

abstract:
  Quantum information storage (QIS) is a physical process to write quantum
states into a quantum memory (QM). We observe that in some general cases the
quantum state can be retrieved up to a unitary transformation depicted by the
non-Abelian Berry's geometric phase factor (holonomy). The QIS of photon with
this geometric character can be implemented with the symmetric collective
excitations of a $\Lambda$-atom ensemble, which is adiabatically controlled by
a classical light with a small detuning $\delta$. The cyclic change of the
controlled Rabi frequency $\Omega(t)$ with period $T=\frac{2n\pi}{\delta}$
accumulates additional geometric phases in different components of the final
photon state. Then, in a purely geometric way the stored state can be decoded
from the final state.


title: Quantum Magnetic Algebra and Magnetic Curvature

abstract:
  The symplectic geometry of the phase space associated with a charged particle
is determined by the addition of the Faraday 2-form to the standard structure
on the Euclidean phase space. In this paper we describe the corresponding
algebra of Weyl-symmetrized functions in coordinate and momentum operators
satisfying nonlinear commutation relations. The multiplication in this algebra
generates an associative product of functions on the phase space. This product
is given by an integral kernel whose phase is the symplectic area of a
groupoid-consistent membrane. A symplectic phase space connection with
non-trivial curvature is extracted from the magnetic reflections associated
with the Stratonovich quantizer. Zero and constant curvature cases are
considered as examples. The quantization with both static and time dependent
electromagnetic fields is obtained. The expansion of the product by the
deformation parameter, written in the covariant form, is compared with the
known deformation quantization formulas.


title: Cavity Assisted Nondestructive Laser Cooling of Atomic Qubits

abstract:
  We analyze two configurations for laser cooling of neutral atoms whose
internal states store qubits. The atoms are trapped in an optical lattice which
is placed inside a cavity. We show that the coupling of the atoms to the damped
cavity mode can provide a mechanism which leads to cooling of the motion
without destroying the quantum information.


title:
Secure direct communication using step-split Einstein-Podolsky-Rosen
  pair

abstract:
  We presen a secure direct communication protocol by using step-split
Einstein-Podolsky-Rosen (EPR) pair. In this communication protocol, Alice first
sends one qubit of an EPR pair to Bob. Bob sends a receipt signal to Alice
through public channel when he receives Alice's first qubit. Alice performs her
encoding operations on the second qubit and sends this qubit to Bob. Bob
performs a Bell-basis measurement to draw Alice's information. The security of
this protocol is based on `High fidelity implies low entropy'. If Eve want to
eavesdrop Alice's information, she has to attack both qubits of the EPR pair,
which results in that any effective eavesdropping attack can be detected. Bob's
receipt signal can protect this protocol against the eavesdropping hiding in
the quantum channel losses. And this protocol is strictly secure to perform a
quantum key distribution by using Calderbank-Shor-Steane codes.


title: Experimental demonstration of quantum teleportation of a squeezed state

abstract:
  Quantum teleportation of a squeezed state is demonstrated experimentally. Due
to some inevitable losses in experiments, a squeezed vacuum necessarily becomes
a mixed state which is no longer a minimum uncertainty state. We establish an
operational method of evaluation for quantum teleportation of such a state
using fidelity, and discuss the classical limit for the state. The measured
fidelity for the input state is 0.85$\pm$ 0.05 which is higher than the
classical case of 0.73$\pm$0.04. We also verify that the teleportation process
operates properly for the nonclassical state input and its squeezed variance is
certainly transferred through the process. We observe the smaller variance of
the teleported squeezed state than that for the vacuum state input.


title:
The Relativistic Quantum Stationary Hamilton Jacobi Equation for
  Particle with Spin 1/2

abstract:
  For one dimensional motions, we derive from the Dirac Spinors Equation (DSE)
the Quantum Stationary Hamilton-Jacobi Equation for particles with spin 1/2.
Then, We give its solution. We demonstrate that the $QSHJES_{1\over2}$ have two
explicit forms, which represent the two possible projection of the Spin 1/2.


title: Ground-State Entanglement in Interacting Bosonic Graphs

abstract:
  We consider a collection of bosonic modes corresponding to the vertices of a
graph $\Gamma.$ Quantum tunneling can occur only along the edges of $\Gamma$
and a local self-interaction term is present. Quantum entanglement of one
vertex with respect the rest of the graph is analyzed in the ground-state of
the system as a function of the tunneling amplitude $\tau.$ The topology of
$\Gamma$ plays a major role in determining the tunneling amplitude $\tau^*$
which leads to the maximum ground-state entanglement. Whereas in most of the
cases one finds the intuitively expected result $\tau^*=\infty$ we show that it
there exists a family of graphs for which the optimal value of$\tau$ is pushed
down to a finite value. We also show that, for complete graphs, our bi-partite
entanglement provides useful insights in the analysis of the cross-over between
insulating and superfluid ground states


title: The Relativistic Quantum Law of motion for a Particle with Spin 1/2

abstract:
  In this paper, we introduce a deterministic approach of quantum mechanics for
particles with spin 1 2 moving in one dimension. We present a Lagrangian of a
spinning particle ($s ={1 \over 2} $), and deduce the expression of the
conjugate momentum related to the velocity of the particle.


title: On the power of Ambainis's lower bounds

abstract:
  The polynomial method and the Ambainis's lower bound (or \emph{Alb}, for
short) method are two main quantum lower bound techniques. While recently
Ambainis showed that the polynomial method is not tight, the present paper aims
at studying the power and limitation of \emph{Alb}'s. We first use known
\emph{Alb}'s to derive $\Omega(n^{1.5})$ lower bounds for
\textsc{Bipartiteness}, \textsc{Bipartiteness Matching} and \textsc{Graph
Matching}, in which the lower bound for \textsc{Bipartiteness} improves the
previous $\Omega(n)$ one. We then show that all the three known Ambainis's
lower bounds have a limitation $\sqrt{N\cdot \min\{C_0(f), C_1(f)\}}$, where
$C_0(f)$ and $C_1(f)$ are the 0- and 1-certificate complexity, respectively.
This implies that for some problems such as \textsc{Triangle},
$k$-\textsc{Clique}, and \textsc{Bipartite/Graph Matching} which draw wide
interest and whose quantum query complexities are still open, the best known
lower bounds cannot be further improved by using Ambainis's techniques. Another
consequence is that all the Ambainis's lower bounds are not tight. For total
functions, this upper bound for \emph{Alb}'s can be further improved to $\min
\{\sqrt{C_0(f)C_1(f)}, \sqrt{N\cdot CI(f)}\}$, where $CI(f)$ is the size of max
intersection of a 0-and a 1-certificate set. Again this implies that $Alb$'s
cannot improve the best known lower bound for some specific problems such as
\textsc{And-Or Tree}, whose precise quantum query complexity is still open.
Finally, we generalize the three known \emph{Alb}'s and give a new \emph{Alb}
style lower bound method, which may be easier to use for some problems.


title:
KCQ: A New Approach to Quantum Cryptography I. General Principles and
  Key Generation

abstract:
  A new approach to quantum cryptography to be called KCQ, keyed communication
in quantum noise, is developed on the basis of quantum detection and
communication theory for classical information transmission. By the use of a
shared secret key that determines the quantum states generated for different
data bit sequences, the users may employ the corresponding optimum quantum
measurement to decode the data. This gives them a better error performance than
an attacker who does not know the key when she makes her quantum measurement,
and an overall generation of a fresh key may be obtained from the resulting
advantage. This principle is illustrated in the operation of a concrete qubit
system A general information-theoretic description of the overall approach will
be presented, and contrasted with the detection/coding description necessary
for specific protocols.


title: Local cloning of Bell states and distillable entanglement

abstract:
  The necessary and sufficient amount of entanglement required for cloning of
orthogonal Bell states by local operation and classical communication is
derived, and using this result, we provide here some additional examples of
reversible, as well as irreversible states.


title: Time-delay, energy-continuum, and systematics of particles

abstract:
  Finding systematics in the mass-lifetime data for all the hadrons has been an
outstanding problem. In this work, we show that the product of mass and
lifetime for unstable particles is very well-approximated by \hbar 2^n/n where
n is an integer specific for a particle. In doing so, we have employed a
relation between time-delay and resonances. The energy-continuum has been
treated in a way to take advantage of Cantor's mathematical work on continuum.
Thus, even though the resonances are designated by complex energy variables
where ordering is not possible, in terms of stability, the index n labels these
resonances; larger the n, more stable a resonance is.


title: Multipartite Bound Information exists and can be activated

abstract:
  We prove the conjectured existence of Bound Information, a classical analog
of bound entanglement, in the multipartite scenario. We give examples of
tripartite probability distributions from which it is impossible to extract any
kind of secret key, even in the asymptotic regime, although they cannot be
created by local operations and public communication. Moreover, we show that
bound information can be activated: three honest parties can distill a common
secret key from different distributions having bound information. Our results
demonstrate that quantum information theory can provide useful insight for
solving open problems in classical information theory.


title: Can quantum cryptography imply quantum mechanics? Reply to Smolin

abstract:
  Clifton, Bub, and Halvorson (CBH) have argued that quantum mechanics can be
derived from three cryptographic, or broadly information-theoretic, axioms. But
Smolin disagrees, and he has given a toy theory that he claims is a
counterexample. Here we show that Smolin's toy theory violates an independence
condition for spacelike separated systems that was assumed in the CBH argument.
We then argue that any acceptable physical theory should satisfy this
independence condition.


title:
Practical quantum key distribution: On the security evaluation with
  inefficient single-photon detectors

abstract:
  Quantum Key Distribution with the BB84 protocol has been shown to be
unconditionally secure even using weak coherent pulses instead of single-photon
signals. The distances that can be covered by these methods are limited due to
the loss in the quantum channel (e.g. loss in the optical fiber) and in the
single-photon counters of the receivers. One can argue that the loss in the
detectors cannot be changed by an eavesdropper in order to increase the covered
distance. Here we show that the security analysis of this scenario is not as
easy as is commonly assumed, since already two-photon processes allow
eavesdropping strategies that outperform the known photon-number splitting
attack. For this reason there is, so far, no satisfactory security analysis
available in the framework of individual attacks.


title:
Concatenating dynamical decoupling with decoherence-free subspaces for
  quantum computation

abstract:
  A scheme to implement a quantum computer subjected to decoherence and
governed by an untunable qubit-qubit interaction is presented. By concatenating
dynamical decoupling through bang-bang (BB) pulse with decoherence-free
subspaces (DFSs) encoding, we protect the quantum computer from
environment-induced decoherence that results in quantum information dissipating
into the environment. For the inherent qubit-qubit interaction that is
untunable in the quantum system, BB control plus DFSs encoding will eliminate
its undesired effect which spoils quantum information in qubits. We show how
this quantum system can be used to implement universal quantum computation.


title: Filling of a cavity with zero-point electromagnetic radiation

abstract:
  In the present contribution we analyse a simple thought process at T = 0 in
an idealized heat engine having partitions made of a material with an upper
frequency cut-off and bathed in zero-point (ZP) electromagnetic radiation. As a
result, a possible mechanism of filling real cavities with ZP radiation based
on Doppler's effect has been suggested and corresponding entropy changes are
discussed.


title: Controlling bi-partite entanglement in multi-qubit systems

abstract:
  Bi-partite entanglement in multi-qubit systems cannot be shared freely. The
rules of quantum mechanics impose bounds on how multi-qubit systems can be
correlated. In this paper we utilize a concept of entangled graphs with
weighted edges in order to analyze pure quantum states of multi-qubit systems.
Here qubits are represented by vertexes of the graph while the presence of
bi-partite entanglement is represented by an edge between corresponding
vertexes. The weight of each edge is defined to be the entanglement between the
two qubits connected by the edge, as measured by the concurrence. We prove that
each entangled graph with entanglement bounded by a specific value of the
concurrence can be represented by a pure multi-qubit state. In addition we
present a logic network with O(N2) elementary gates that can be used for
preparation of the weighted entangled graphs of N qubits.


title: An Extension of Gleason's Theorem for Quantum Computation

abstract:
  We develop a synthesis of Turing's paradigm of computation and von Neumann's
quantum logic to serve as a model for quantum computation with recursion, such
that potentially non-terminating computation can take place, as in a quantum
Turing machine. This model is based on the extension of von Neumann's quantum
logic to partial states, defined here as sub-probability measures on the
Hilbert space, equipped with the natural pointwise partial ordering. The
sub-probability measures allow a certain probability for the non-termination of
the computation. We then derive an extension of Gleason's theorem and show
that, for Hilbert spaces of dimension greater than two, the partial order of
sub-probability measures is order isomorphic with the collection of partial
density operators, i.e., trace class positive operators with trace between zero
and one, equipped with the usual partial ordering induced from positive
operators. We show that the expected value of a bounded observable with respect
to a partial state can be defined as a closed bounded interval, which extends
the classical definition of expected value.


title:
Effective Action for a Statistical System with a Field dependent Wave
  Function

abstract:
  We compute the first order correction in $\hbar $ to the field dependent wave
function in Statistical Field Theory. These corrections are evaluated by
several usual methods. We limit ourselves to a one dimensional model in order
to avoid the usual difficulties with the UV divergences that are not relevant
for our purposes. The main result of the paper is that the various methods
yield different corrections to the wave function. Moreover, we give arguments
to show that the perturbative integration of the exact renormalization group
provides the right result.


title: Action at a distance and the no-mediator theorem

abstract:
  It is known that outcomes of space-like separated measurements of entangled
particles are interdependent. As in the classical physics no one saw
action-at-a-distance, not mediated by some real communication using a carrier,
people look for some mediator that makes possible an influence-passing between
the distant particles. The wave function does not comprise such a kind of
object. The present text tries to incorporate the mediator in the formalism of
the quantum mechanics. The result is a contradiction.


title: Components for Optical Qubits in the Radio Frequency Basis

abstract:
  We describe a scheme for the encoding and manipulation of single photon
qubits in radio frequency sideband modes using standard optical elements.


title: Samaritan's Dilemma: Classical and quantum strategies in Welfare Game

abstract:
  Effects of classical/quantum correlations and operations in game theory are
analyzed using Samaritan's Dilemma. We observe that introducing either quantum
or classical correlations to the game results in the emergence of a unique or
multiple Nash equilibria (NE) which do not exist in the original classical
game. It is shown that the strategies creating the NE and the amount of payoffs
the players receive at these NE's depend on the type of the correlation. We
also discuss whether the Samaritan can resolve the dilemma acting unilaterally.


title:
Distinguishing genuine entangled two-photon-polarization states from
  independently generated pairs of entangled photons

abstract:
  A scheme to distinguish entangled two-photon-polarization states (ETP) from
two independent entangled one-photon-polarization states (EOP) is proposed.
Using this scheme, the experimental generation of ETP by parametric
down-conversion is confirmed through the anti-correlations between three
orthogonal two-photon-polarization states. The estimated fraction of ETP among
the correlated photon pairs is 37% in the present experimental setup.


title:
Enhancement of field generation via maximal atomic coherence prepared by
  fast adiabatic passage in Rb vapor

abstract:
  We have experimentally demonstrated the enhancement of coherent Raman
scattering in Rb atomic vapor by exciting atomic coherence with fractional
stimulated Raman adiabatic passage. Experimental results are in good agreement
with numerical simulations. The results support the possibility of increasing
the sensitivity of CARS by preparing atomic or molecular coherence using short
pulses.


title: Is the dynamics of open quantum systems always linear?

abstract:
  We study the influence of the preparation of an open quantum system on its
reduced time evolution. In contrast to the frequently considered case of an
initial preparation where the total density matrix factorizes into a product of
a system density matrix and a bath density matrix the time evolution generally
is no longer governed by a linear map nor is this map affine. Put differently,
the evolution is truly nonlinear and cannot be cast into the form of a linear
map plus a term that is independent of the initial density matrix of the open
quantum system. As a consequence, the inhomogeneity that emerges in formally
exact generalized master equations is in fact a nonlinear term that vanishes
for a factorizing initial state. The general results are elucidated with the
example of two interacting spins prepared at thermal equilibrium with one spin
subjected to an external field. The second spin represents the environment. The
field allows the preparation of mixed density matrices of the first spin that
can be represented as a convex combination of two limiting pure states, i.e.
the preparable reduced density matrices make up a convex set. Moreover, the map
from these reduced density matrices onto the corresponding density matrices of
the total system is affine only for vanishing coupling between the spins. In
general, the set of the accessible total density matrices is nonconvex.


title: Spin, statistics, and the spinor ambiguity

abstract: Flaw in the treatment of different spin components


title: Collapsing the Wavefunction of a Baseball

abstract:
  The transition from microscopic to macroscopic in quantum mechanics can be
seen from various points of view. It is often not merely a transition from
quantum to classical mechanics in the sense of the Correspondence Principle.
The fact that real macroscopic objects like baseballs are composites of an
extremely large number of microscopic particles (electrons, protons etc.) is a
complicating factor. Here such composite objects are studied in some detail and
the Copenhagen interpretation is applied to them. A computer game model for a
simplified composite object is used to illustrate some of the issues.


title: Algebras of infinite qubit systems

abstract:
  The input and output algebras of an infinite qubit system and their
representations are described.


title:
Simultaneous Measurement of Non-commuting Observables and Quantum
  Fractals on Complex Projective Spaces

abstract:
  Simultaneous measurement of several noncommuting observables is modeled by
using semigroups of completely positive maps on an algebra with a non-trivial
center. The resulting piecewise-deterministic dynamics leads to chaos and to
nonlinear iterated function systems (quantum fractals) on complex projective
spaces.


title: The 3D Quantum Law of motion

abstract:
  In this paper, we give the solution of the three dimensional quantum
stationary Hamilton-Jacobi Equation (3D-QSHJE) for a general form of the
potential. We present the quantum coordinates transformation with which the
3D-QSHJE takes its classical form. Then, we derived the 3D quantum law of
motion.


title: Thermodynamical Detection of Entanglement by Maxwell's Demons

abstract:
  Quantum correlation, or entanglement, is now believed to be an indispensable
physical resource for certain tasks in quantum information processing, for
which classically correlated states cannot be useful. Besides information
processing, what kind of physical processes can exploit entanglement? In this
paper, we show that there is indeed a more basic relationship between
entanglement and its usefulness in thermodynamics. We derive an inequality
showing that we can extract more work out of a heat bath via entangled systems
than via classically correlated ones. We also analyze the work balance of the
process as a heat engine, in connection with the Second Law of thermodynamics.


title:
Wigner Distribution Function Approach to Dissipative Problems in Quantum
  Mechanics with emphasis on Decoherence and Measurement Theory

abstract:
  We first review the usefulness of the Wigner distribution functions (WDF),
associated with Lindblad and pre-master equations, for analyzing a host of
problems in Quantum Optics where dissipation plays a major role, an arena where
weak coupling and long-time approximations are valid. However, we also show
their limitations for the discussion of decoherence, which is generally a
short-time phenomenon with decay rates typically much smaller than typical
dissipative decay rates. We discuss two approaches to the problem both of which
use a quantum Langevin equation (QLE) as a starting-point: (a) use of a reduced
WDF but in the context of an exact master equation (b) use of a WDF for the
complete system corresponding to entanglement at all times.


title: A Quantum Cryptographic Protocol with Detection of Compromised Server

abstract:
  This paper presents a hybrid cryptographic protocol, using quantum and
classical resources, to generate a key for authentication and optionally for
encryption in a network. One or more trusted servers distribute streams of
entangled photons to individual resources that seek to communicate. An
important class of cheating by a compromised server will be detected.


title: Generation of atomic entangled states using linear optics

abstract:
  In this paper, we propose a novel scheme that can generate two-atom maximally
entangled states from pure product states and mixed states using linear optics.
Because the scheme can generate pure maximally entangled states from mixed
states, we denote it as purification-like generation scheme.


title: Diverging Entanglement Length in Gapped Quantum Spin Systems

abstract:
  We prove the existence of gapped quantum Hamiltonians whose ground states
exhibit an infinite entanglement length, as opposed to their finite correlation
length. Using the concept of entanglement swapping, the localizable
entanglement is calculated exactly for valence bond and finitely correlated
states, and the existence of the so--called string-order parameter is
discussed. We also report on evidence that the ground state of an
antiferromagnetic chain can be used as a perfect quantum channel if local
measurements on the individual spins can be implemented.


title:
Quantum fluctuations and correlations of spatial scalar or multimode
  vector solitons in Kerr media

abstract:
  We apply the Green's function method to determine the global degree of
squeezing and the transverse spatial distribution of quantum fluctuations of
solitons in Kerr media. We show that both scalar bright solitons and multimode
vector solitons experience strong squeezing on the optimal quadrature. For
vector solitons, this squeezing is shown to result from an almost perfect
anti-correlation between the fluctuations on the two incoherently-coupled
circular polarisations.


title: Microscopic Origin of Spatial Coherence and Wolf Shifts

abstract:
  We show that the vacuum of electromagnetic field has intrinsic partial
spatial coherence in frequency domain which effectively extends over regions of
the order of wavelength $\lambda$. This spatial coherence leads to a dynamical
coupling between atoms and is the cause of source correlations and Wolf shifts.
We show how the source spatial correlations can lead to tailor made coherent
emissions. We discuss the universality of source correlation effects and
presents several application.


title:
Wave functions and tunneling times for one-dimensional transmission and
  reflection

abstract:
  It is shown that in the case of the one-particle one-dimensional scattering
problem for a given time-independent potential, for each state of the whole
quantum ensemble of identically prepared particles, there is an unique pair of
(subensemble's) solutions to the Schr\"odinger equation, which, as we
postulate, describe separately transmission and reflection: in the case of
nonstationary states, for any instant of time, these functions are orthogonal
and their sum describes the state of all particles; evolving with constant
norms, one of them approaches at late times the transmitted wave packet and
another approaches the reflected packet. Both for transmission and reflection,
1) well before and after the scattering event, the average kinetic energy of
particles is the same, 2) the average starting point differs, in the general
case, from that for all particles. It is shown that for reflection, in the case
of symmetric potential barriers, the domain of the motion of particles is
bounded by the midpoint of the barrier region. We define (exact and asymptotic)
transmission and reflection times and show that the basic results of our
formalism can be, in principle, checked experimentally.


title: Kraus representation for density operator of arbitrary open qubit system

abstract:
  We show that the time evolution of density operator of open qubit system can
always be described in terms of the Kraus representation. A general scheme on
how to construct the Kraus operators for an open qubit system is proposed,
which can be generalized to open higher dimensional quantum systems.


title: Stationary pulses of light in an atomic medium

abstract:
  Physical processes that could facilitate coherent control of light
propagation are now actively explored. In addition to fundamental interest,
these efforts are stimulated by possibilities to develop, for example, a
quantum memory for photonic states. At the same time, controlled localization
and storage of photonic pulses may allow novel approaches to manipulate light
via enhanced nonlinear optical processes. Recently, Electromagnetically Induced
Transparency (EIT) was used to reduce the group velocity of propagating light
pulses and to reversibly map propagating light pulses into stationary spin
excitations in atomic media. Here we describe and experimentally demonstrate a
novel technique in which light propagating in a medium of Rb atoms is converted
into an excitation with localized, stationary electromagnetic energy, which can
be held and released after a controllable interval. Our method creates pulses
of light with stationary envelopes bound to an atomic spin coherence, raising
new possibilities for photon state manipulation and non-linear optical
processes at low light levels.


title: Transmission Of Optical Coherent State Qubits

abstract:
  We discuss the long distance transmission of qubits encoded in optical
coherent states. Through absorption these qubits suffer from two main types of
errors, the reduction of the amplitude of the coherent states and accidental
application of the Pauli Z operator. We show how these errors can be fixed
using techniques of teleportation and error correcting codes.


title: Temperature Dependence of the Casimir Force for Metals

abstract:
  Starting from the Lifshitz formula for the Casimir force between parallel
plates we calculate the difference between the forces at two different
settings, one in which the temperature is $T_1=350$ K, the other when $T_2=300$
K. As material we choose gold, and make use of the Drude dispersion relation.
Our results, which are shown graphically, should be directly comparable to
experiment. As an analogous calculation based upon the plasma dispersion
relation leads to a different theoretical force difference, an experiment of
this kind would be a decisive test. We also present an analogous calculation
for the case when the two plates are replaced with a sphere-plate system, still
with gold as material in both bodies. The sphere is assumed so large that the
proximity theorem holds. Discussion of the consistency with the third law of
thermodynamics and the validity of the surface impedance approach is provided.


title:
Distilling multipartite pure states from a finite number of copies of
  multipartite mixed states

abstract:
  This paper will address the question of the distillation of entanglement from
a finite number of multi-partite mixed states. It is shown that if one can
distill a pure entangled state from n copies of a mixed state $\sigma
_{ABC...}$ there must be at least a subspace in whole Hilbert space of the all
copies such that the projection of $\sigma_{ABC...}^{\otimes n}$ onto the
subspace is a pure entangled state. We also show that the purification of
entanglement or distillation of entanglement can be carried out by local joint
projective measurements with the help of classical communication and local
general positive operator valued measurements on a single particle, in
principle. Finally we discuss experimental realizability of the entanglement
purification.


title: Teleportation in a non-inertial frame

abstract:
  In this work, we describe the process of teleportation between Alice in an
inertial frame, and Rob who is in uniform acceleration with respect to Alice.
The fidelity of the teleportation is reduced due to Davies-Unruh radiation in
Rob's frame. In so far as teleportation is a measure of entanglement, our
results suggest that quantum entanglement is degraded in non-inertial frames.
We discuss this reduction in fidelity for both bosonic and fermionic resources.


title:
Iterative maximum-likelihood reconstruction in quantum homodyne
  tomography

abstract:
  I propose an iterative expectation maximization algorithm for reconstructing
a quantum optical ensemble from a set of balanced homodyne measurements
performed on an optical state. The algorithm applies directly to the acquired
data, bypassing the intermediate step of calculating marginal distributions.
The advantages of the new method are made manifest by comparing it with the
traditional inverse Radon transformation technique.


title: On the uniqueness of paths for spin-0 and spin-1 quantum mechanics

abstract:
  The uniqueness of the Bohmian particle interpretation of the Kemmer equation,
which describes massive spin-0 and spin-1 particles, is discussed. Recently the
same problem for spin-1/2 was dealt with by Holland. It appears that the
uniqueness of boson paths can be enforced under well determined conditions.
This in turn fixes the nonrelativistic particle equations of the
nonrelativistic Schrodinger equation, which appear to correspond with the
original definitions given by de Broglie and Bohm only in the spin-0 case.
Similar to the spin-1/2 case, there appears an additional spin-dependent term
in the guidance equation in the spin-1 case. We also discuss the ambiguity
associated with the introduction of an electromagnetic coupling in the Kemmer
theory. We argue that when the minimal coupling is correctly introduced, then
the current constructed from the energy-momentum tensor is no longer conserved.
Hence this current can not serve as a particle probability four-vector.


title: Coupling Efficiencies in Single Photon On-Demand Sources

abstract:
  Many quantum computation and communication schemes require, or would
significantly benefit from, true sources of single photon on-demand (SPOD).
Unfortunately, such sources do not exist. It is becoming increasingly clear
that coupling photons out of a SPOD source will be a limiting factor in many
SPOD implementations. In particular, coupling these source outputs into optical
fibers (usually single mode fibers) is often the preferred method for handling
this light. We investigate the practical limits to this coupling as relates to
parametric downconversion, an important starting point for many SPOD schemes.
We also explored whether it is possible to optimize the engineering of the
downconversion sources to improve on this coupling. We present our latest
results in this area.


title: Distinguishing maximally entangled states locally

abstract:
  We demonstrate that one maximally entangled state is sufficient and necessary
to distinguish a complete basis of maximally entangled states by local
operation and classical communication.


title: Quantum Relays for Long Distance Quantum Cryptography

abstract:
  Quantum Cryptography is on the verge of commercial application. One of its
greatest limitations is over long distance - secret key rates are low and the
longest fibre over which any key has been exchanged is currently 100 km. We
investigate the quantum relay, which can increase the maximum distance at which
quantum cryptography is possible. The relay splits the channel into sections,
and sends a different photon across each section, increasing the signal to
noise ratio. The photons are linked as in teleportation, with entangled photon
pairs and Bell measurements. We show that such a scheme could allow
cryptography over hundreds of kilometers with today's detectors. It could not,
however, improve the rate of key exchange over distances where the standard
single section scheme already works. We also show that reverse key
reconciliation, previously used in continuous variable quantum cryptography,
gives a secure key over longer distances than forward key reconciliation.


title:
A Modern Introduction to Cardano and Ferrari Formulas in the Algebraic
  Equations

abstract:
  We give a modern approach to the famous Cardano and Ferrari formulas in the
algebraic equations with three and four degrees. Namely, we reconstruct these
formulas from the point of view of superposition principle in quantum
computation based on three and four level systems which are being developed by
the author. We also present a problem on some relation between Galois theory
and Qudit theory.


title:
Implementation of Conditional Phase Shift gate for Quantum Information
  Processing by NMR, using Transition-selective pulses

abstract:
  Experimental realization of quantum information processing in the field of
nuclear magnetic resonance (NMR) has been well established. Implementation of
conditional phase shift gate has been a significant step, which has lead to
realization of important algorithms such as Grover's search algorithm and
quantum Fourier transform. This gate has so far been implemented in NMR by
using coupling evolution method. We demonstrate here the implementation of the
conditional phase shift gate using transition selective pulses. As an
application of the gate, we demonstrate Grover's search algorithm and quantum
Fourier transform by simulations and experiments using transition selective
pulses.


title: Quantum and classical correlations between players in game theory

abstract:
  Effects of quantum and classical correlations on game theory are studied to
clarify the new aspects brought into game theory by the quantum mechanical
toolbox. In this study, we compare quantum correlation represented by a
maximally entangled state and classical correlation that is generated through
phase damping processes on the maximally entangled state. Thus, this also sheds
light on the behavior of games under the influence of noisy sources. It is
observed that the quantum correlation can always resolve the dilemmas in
non-zero sum games and attain the maximum sum of both players' payoffs, while
the classical correlation cannot necessarily resolve the dilemmas.


title:
Relation between entanglement measures and Bell inequalities for three
  qubits

abstract:
  For two qubits in a pure state there exists a one-to-one relation between the
entanglement measure (the concurrence ${\cal C}$) and the maximal violation
${\cal M}$ of a Bell inequality. No such relation exists for the three-qubit
analogue of ${\cal C}$ (the tangle $\tau$), but we have found that numerical
data is consistent with a simple set of upper and lower bounds for $\tau$ given
${\cal M}$. The bounds on $\tau$ become tighter with increasing ${\cal M}$, so
they are of practical use. The Svetlichny form of the Bell inequality gives
tighter bounds than the Mermin form. We show that the bounds can be tightened
further if the tangle is replaced by an entanglement monotone that can identify
both the W state and the Greenberger-Horne-Zeilinger state.


title: Quantum Key Distribution Using Equiangular Spherical Codes

abstract:
  Mutually unbiased bases have been extensively studied in the literature and
are simple and effective in quantum key distribution protocols, but they are
not optimal. Here equiangular spherical codes are introduced as a more
efficient and robust resource for key distribution. Such codes are sets of
states that are as evenly spaced throughout the vector space as possible. In
the case the two parties use qubits and face the intercept/resend eavesdropping
strategy, they can make use of three equally-spaced states, called a
\emph{trine}, to outperform the original four-state BB84 protocol in both speed
and reliability. This points toward the optimality of spherical codes in
arbitrary dimensions.


title:
Operator normalized quantum arrival times in the presence of
  interactions

abstract:
  We model ideal arrival-time measurements for free quantum particles and for
particles subject to an external interaction by means of a narrow and weak
absorbing potential. This approach is related to the operational approach of
measuring the first photon emitted from a two-level atom illuminated by a
laser. By operator-normalizing the resulting time-of-arrival distribution, a
distribution is obtained which for freely moving particles not only recovers
the axiomatically derived distribution of Kijowski for states with purely
positive momenta but is also applicable to general momentum components. For
particles interacting with a square barrier the mean arrival time and
corresponding ``tunneling time'' obtained at the transmission side of the
barrier becomes independent of the barrier width (Hartman effect) for
arbitrarily wide barriers, i.e., without the transition to the ultra-opaque,
classical-like regime dominated by wave packet components above the barrier.


title: How can one find nonlocality in Bohmian mechanics?

abstract:
  We perform the probabilistic analysis of the pilot wave formalism. From the
probabilistic point of view it is not so natural to follow D. Bohm and to
consider nonlocal interactions between parts of (e.g.) a two-particle system.
It is more natural to consider dependence of corresponding preparation
procedures and the propagation of the initial correlations between preparation
procedures. In the pilot wave formalism it is more natural to speak about
correlations of the initial pilot waves which propagate with time.


title:
From Classical Hamiltonian Flow to Quantum Theory: Derivation of the
  Schroedinger Equation

abstract:
  It is shown how the essentials of quantum theory, i.e., the Schroedinger
equation and the Heisenberg uncertainty relations, can be derived from
classical physics. Next to the empirically grounded quantisation of energy and
momentum, the only input is given by the assumption of fluctuations in energy
and momentum to be added to the classical motion. Extending into the
relativistic regime for spinless particles, this procedure leads also to a
derivation of the Klein-Gordon equation. Comparing classical Hamiltonian flow
with quantum theory, then, the essential difference is given by a vanishing
divergence of the velocity of the probability current in the former, whereas
the latter results from a much less stringent requirement, i.e., that only the
average over fluctuations and positions of the average divergence be identical
to zero.


title: Geometroneurodynamics

abstract:
  Hilbert space structure is assumed as a valid geometric description for
neurodynamics, i.e., for applying any kind of quantum formalism in brain
dynamics. The orientation selectivity of the neurons is used as a justification
to construct a type of statistical distance function which is proportional to
the usual distance (or angle) between orientations of the neurons. The
equivalence between the statistical distance and the Hilbert-space distance is
discussed within this framework. It gives rise to the possibility of
reanalysing the issue of measurement and information processing in the brain
function


title:
Ultrafast deterministic generation of entanglement in a time-dependent
  asymmetric two-qubit-cavity system

abstract:
  We present an efficient scheme for the controlled generation of pure
two-qubit states possessing {\em any} desired degree of entanglement and a {\em
prescribed} symmetry in two cavity QED based systems, namely, cold trapped ions
and flying atoms. This is achieved via on-resonance ion/atom-cavity couplings
which are time-dependent and asymmetric, leading to a trapping vacuum state
condition which does not arise for identical couplings. A duality in the role
of the coupling ratio yields states with a given concurrence but opposing
symmetries. The experimental feasibility of the proposed scheme is also
discussed.


title:
A high-performance integrated single-photon detector for telecom
  wavelengths

abstract:
  We have integrated a commercial avalanche photodiode (APD) and the circuitry
needed to operate it as a single-photon detector (SPD) onto a single PC-board.
At temperatures accessible with Peltier coolers (~200-240K), the PCB-SPD
achieves high detection efficiency (DE) at 1308 and 1545 nm with low dark count
probability (e.g. ~10-6/bias pulse at DE=20%, 220 K), making it useful for
quantum key distribution (QKD). The board generates fast bias pulses, cancels
noise transients, amplifies the signals, and sends them to an on-board
discriminator. A digital blanking circuit suppresses afterpulsing.


title: Towards mechanical entanglement in nano-electromechanical devices

abstract:
  We study arrays of mechanical oscillators in the quantum domain and
demonstrate how the motions of distant oscillators can be entangled without the
need for control of individual oscillators and without a direct interaction
between them. These oscillators are thought of as being members of an array of
nano-electromechanical resonators with a voltage being applicable between
neighboring resonators. Sudden non-adiabatic switching of the interaction
results in a squeezing of the states of the mechanical oscillators, leading to
an entanglement transport in chains of mechanical oscillators. We discuss
spatial dimensions, Q-factors, temperatures and decoherence sources in some
detail, and find a distinct robustness of the entanglement in the canonical
coordinates in such a scheme. We also briefly discuss the challenging aspect of
detection of the generated entanglement.


title: Optimal cloning for finite distributions of coherent states

abstract:
  We derive optimal cloning limits for finite Gaussian distributions of
coherent states, and describe techniques for achieving them. We discuss the
relation of these limits to state estimation and the no-cloning limit in
teleportation. A qualitatively different cloning limit is derived for a
single-quadrature Gaussian quantum cloner.


title:
Decoherence from Internal Dynamics in Macroscopic Matter-Wave
  Interferometry

abstract:
  Usually, decoherence is generated from the coupling with an outer
environment. However, a macroscopic object generically possesses its own
environment in itself, namely the complicated dynamics of internal degrees of
freedom. We address a question: when and how the internal dynamics decohere
interference of the center of mass motion of a macroscopic object. We will also
show that weak localization of a macroscopic object in disordered potentials
can be destroyed by such decoherence.


title: Quantum Error Correction on Linear Nearest Neighbor Qubit Arrays

abstract:
  A minimal depth quantum circuit implementing 5-qubit quantum error correction
in a manner optimized for a linear nearest neighbor architecture is described.
The canonical decomposition is used to construct fast and simple gates that
incorporate the necessary swap operations. Simulations of the circuit's
performance when subjected to discrete and continuous errors are presented. The
relationship between the error rate of a physical qubit and that of a logical
qubit is investigated with emphasis on determining the concatenated error
correction threshold.


title: Average fidelity between random quantum states

abstract:
  We analyze mean fidelity between random density matrices of size N, generated
with respect to various probability measures in the space of mixed quantum
states: Hilbert-Schmidt measure, Bures (statistical) measure, the measures
induced by partial trace and the natural measure on the space of pure states.
In certain cases explicit probability distributions for fidelity are derived.
Results obtained may be used to gauge the quality of quantum information
processing schemes.


title: Localization of Two-Dimensional Quantum Walks

abstract:
  The Grover walk, which is related to the Grover's search algorithm on a
quantum computer, is one of the typical discrete time quantum walks. However, a
localization of the two-dimensional Grover walk starting from a fixed point is
striking different from other types of quantum walks. The present paper
explains the reason why the walker who moves according to the degree-four
Grover's operator can remain at the starting point with a high probability. It
is shown that the key factor for the localization is due to the degeneration of
eigenvalues of the time evolution operator. In fact, the global time evolution
of the quantum walk on a large lattice is mainly determined by the degree of
degeneration. The dependence of the localization on the initial state is also
considered by calculating the wave function analytically.


title:
How to measure squeezing and entanglement of Gaussian states without
  homodyning

abstract:
  We propose a scheme for measuring the squeezing, purity, and entanglement of
Gaussian states of light that does not require homodyne detection. The
suggested setup only needs beam splitters and single-photon detectors. Two-mode
entanglement can be detected from coincidences between photodetectors placed on
the two beams.


title:
Shifting the boundaries: pulse-shape effects in the atom-optics kicked
  rotor

abstract:
  We present the results of experiments performed on cold caesium in a pulsed
sinusoidal optical potential created by counter-propagating laser beams having
a small frequency difference in the laboratory frame. Since the atoms, which
have average velocity close to zero in the laboratory frame, have non-zero
average velocity in the co-moving frame of the optical potential, we are able
to centre the initial velocity distribution of the cloud at an arbitrary point
in phase-space. In particular, we demonstrate the use of this technique to
place the initial velocity distribution in a region of phase-space not
accessible to previous experiments, namely beyond the momentum boundaries
arising from the finite pulse duration of the potential. We further use the
technique to explore the kicked rotor dynamics starting from a region of
phase-space where there is a strong velocity dependence of the diffusion
constant and quantum break time and demonstrate that this results in a marked
asymmetry in the chaotic evolution of the atomic momentum distribution.


title:
Violation of a Bell-like Inequality in Neutron Optical Experiments:
  Quantum contextuality

abstract:
  We report a single-neutron optical experiment to demonstrate the violation of
a Bell-like inequality. Entanglement is achieved not between particles, but
between the degrees of freedom, in this case, for a single-particle. The
spin-{\small 1/2} property of neutrons are utilized. The total wave function of
the neutron is described in a tensor product Hilbert space. A Bell-like
inequality is derived not by a non-locality but by a contextuality. Joint
measurements of the spinor and the path properties lead to the violation of a
Bell-like inequality. Manipulation of the wavefunction in one Hilbert space
influences the result of the measurement in the other Hilbert space. A
discussion is given on the quantum contextuality and an entanglement-induced
correlation in our experiment.


title: Nano-displacement measurements using spatially multimode squeezed light

abstract:
  We demonstrate the possibility of surpassing the quantum noise limit for
simultaneous multi-axis spatial displacement measurements that have zero mean
values. The requisite resources for these measurements are squeezed light beams
with exotic transverse mode profiles. We show that, in principle, lossless
combination of these modes can be achieved using the non-degenerate Gouy phase
shift of optical resonators. When the combined squeezed beams are measured with
quadrant detectors, we experimentally demonstrate a simultaneous reduction in
the transverse x- and y- displacement fluctuations of 2.2 dB and 3.1 dB below
the quantum noise limit.


title:
Non-linear and quantum optics of a type II OPO containing a birefringent
  element Part 2 : bright entangled beams generation

abstract:
  We describe theoretically the quantum properties of atype-II Optical
Parametric Oscillator containing a birefringent plate which induces a linear
coupling between the orthogonally polarized signal and idler beams and results
in phase locking between these two beams. As in a classical OPO, the signal and
idler waves show large quantum correlations which can be measured
experimentally due to the phase locking between the two beams. We study the
influence of the waveplate on the various criteria characterizing quantum
correlations. We show in particular that the quantum correlations can be
maximized by using optimized quadratures.


title: The Helmholtz Theorem and Superluminal Signals

abstract:
  The conventional decomposition of a vector field into longitudinal
(potential) and transverse (vortex) components (Helmholtz's theorem) is claimed
in [1] to be inapplicable to the time-dependent vector fields and, in
particular, to the retarded solutions of Maxwell's equations. Because of this,
according to [1], a number of conclusions drawn in [2] on the basis of the
Helmholtz theorem turns out to be erroneous. The Helmholtz theorem is proved in
this letter to hold for arbitrary vector field, both static and time-dependent.
Therefore, the conclusions of the paper [2] questioned in [1] are true. The
validity of Helmholtz's theorem in the general case is due to the fact that the
decomposition above of vector field does not influence the field time
coordinate, which plays, thus, a passive role in the decomposition procedure.
An analysis is given of the mistakes made in [1]. It is noted that for point
particle the longitudinal and transverse components of electric field, taken
separately, are characterized by the infinitely great velocity of propagation.
However, superluminal contributions to the expression for the total electric
field cancel each other.


title: Maximal Bell's Inequality Violation for Non Maximal Entanglement

abstract:
  Bell's inequality violation (BIQV) for correlations of polarization is
studied for a {\it product} state of two two-mode squeezed vacuum (TMSV)
states. The violation allowed is shown to attain its maximal limit for all
values of the squeezing parameter, $\zeta$. We show via an explicit example
that a state whose entanglement is not maximal allow maximal BIQV. The Wigner
function of the state is non negative and the average value of either
polarization is nil.


title: Noise enhancing the classical information capacity of a quantum channel

abstract:
  We present a simple model of quantum communication where a noisy quantum
channel may benefit from the addition of further noise at the decoding stage.
We demonstrate enhancement of the classical information capacity of an
amplitude damping channel, with a predetermined detection threshold, by the
addition of noise in the decoding measurement.


title: On the Role of Density Matrices in Bohmian Mechanics

abstract:
  It is well known that density matrices can be used in quantum mechanics to
represent the information available to an observer about either a system with a
random wave function (``statistical mixture'') or a system that is entangled
with another system (``reduced density matrix''). We point out another role,
previously unnoticed in the literature, that a density matrix can play: it can
be the ``conditional density matrix,'' conditional on the configuration of the
environment. A precise definition can be given in the context of Bohmian
mechanics, whereas orthodox quantum mechanics is too vague to allow a sharp
definition, except perhaps in special cases. In contrast to statistical and
reduced density matrices, forming the conditional density matrix involves no
averaging. In Bohmian mechanics with spin, the conditional density matrix
replaces the notion of conditional wave function, as the object with the same
dynamical significance as the wave function of a Bohmian system.


title:
About evolution of particle transitions from one well to another in
  double-well potential

abstract:
  The Poincare's period of particle oscillations between wells is obtained in
double-well potential. The dependencies of oscillation period on transmission
coefficient on distance between levels are obtained. The cases of squared
potentials and some potentials having rounded off forms are considered.


title: A scheme for dense coding in the non-symmetric quantum channel

abstract:
  We investigate the dense coding in the case of non-symmetric Hilbert spaces
of the sender and receiver's particles sharing the quantum maximally entangled
state. The efficiency of classical information gain is also considered. We
conclude that when a more level particle is with the sender, she can get a
non-symmetric quantum channel from a symmetric one by entanglement transfer.
Thus the efficiency of information transmission is improved.


title: Valence Bond Solids for Quantum Computation

abstract:
  Cluster states are entangled multipartite states which enable to do universal
quantum computation with local measurements only. We show that these states
have a very simple interpretation in terms of valence bond solids, which allows
to understand their entanglement properties in a transparent way. This allows
to bridge the gap between the differences of the measurement-based proposals
for quantum computing, and we will discuss several features and possible
extensions.


title:
The capacity of a quantum channel for simultaneous transmission of
  classical and quantum information

abstract:
  An expression is derived characterizing the set of admissible rate pairs for
simultaneous transmission of classical and quantum information over a given
quantum channel, generalizing both the classical and quantum capacities of the
channel. Although our formula involves regularization, i.e. taking a limit over
many copies of the channel, it reduces to a single-letter expression in the
case of generalized dephasing channels. Analogous formulae are conjectured for
the simultaneous public-private capacity of a quantum channel and for the
simultaneously 1-way distillable common randomness and entanglement of a
bipartite quantum state.


title:
Secure direct communication using Einstein-Podolsky-Rosen pairs and
  teleportation

abstract:
  A novel scheme for secure direct communication between Alice and Bob is
proposed, where there is no need for establishing a shared secret key. The
communication is based on Einstein-Podolsky-Rosen pairs and teleportation
between Alice and Bob. After insuring the security of the quantum channel (EPR
pairs), Bob encodes the secret message directly on a sequence of particle
states and transmits them to Alice by teleportation. In this scheme
teleportation transmits Bob's message without revealing any information to a
potential eavesdropper. Alice can read out the encoded messages directly by the
measurement on her qubits. Because there is not a transmission of the qubit
which carry the secret message between Alice and Bob, it is completely secure
for direct secret communication if perfect quantum channel is used.


title: The Existence of Quantum Entanglement Catalysts

abstract:
  Without additional resources, it is often impossible to transform one
entangled quantum state into another with local quantum operations and
classical communication. Jonathan and Plenio [Phys. Rev. Lett. 83, 3566(1999)]
presented an interesting example showing that the presence of another state,
called a catalyst, enables such a transformation without changing the catalyst.
They also pointed out that in general it is very hard to find an analytical
condition under which a catalyst exists. In this paper we study the existence
of catalysts for two incomparable quantum states. For the simplest case of
$2\times 2$ catalysts for transformations from one $4\times 4$ state to
another, a necessary and sufficient condition for existence is found. For the
general case, we give an efficient polynomial time algorithm to decide whether
a $k\times k$ catalyst exists for two $n\times n$ incomparable states, where
$k$ is treated as a constant.


title:
Quantum Computing Discrete Logarithms with the Help of a Preprocessed
  State

abstract:
  An alternative quantum algorithm for the discrete logarithm problem is
presented. The algorithm uses two quantum registers and two Fourier transforms
whereas Shor's algorithm requires three registers and four Fourier transforms.
A crucial ingredient of the algorithm is a quantum state that needs to be
constructed before we can perform the computation. After one copy of this state
is created, the algorithm can be executed arbitrarily many times.


title: Entanglement generated between a single atom and a laser pulse

abstract:
  We quantify the entanglement generated between an atom and a laser pulse in
free space. We find that the entanglement calculated using a simple
closed-system Jaynes-Cummings Hamiltonian is in remarkable agreement with a
full open-system calculation, even though the free-space geometry is far from
the strong coupling regime of cavity QED. We explain this result using a simple
model in which the atom couples weakly to the laser while coupling strongly to
the vacuum. Additionally we place an upper bound on the total entanglement
between the atom and all paraxial modes using a quantum trajectories
unravelling. This upper bound provides a benchmark for atom-laser coupling.


title:
A Quantum Information Theoretical Model for Quantum Secret Sharing
  Schemes

abstract:
  In this paper we introduce a quantum information theoretical model for
quantum secret sharing schemes. We show that quantum information theory
provides a unifying framework for the study of these schemes. We prove that the
information theoretical requirements for a class of quantum secret sharing
schemes reduce to only one requirement (the recoverability condition) as a
consequence of the no-cloning principle. We give also a shorter proof of the
fact that the size of the shares in a quantum secret sharing scheme must be at
least as large as the secret itself.


title: Preparation of W, GHZ, and two-qutrit states using bimodal cavities

abstract:
  We show how one can prepare three-qubit entangled states like W states,
Greenberger-Horne-Zeilinger states as well as two-qutrit entangled states using
the multiatom two-mode entanglement. We propose a technique of preparing such a
multi-particle entanglement using stimulated Raman adiabatic passage. We
consider a collection of three-level atoms in $\Lambda$ configuration
simultaneously interacting with a resonant two-mode cavity for this purpose.
Our approach permits a variety of multiparticle extensions.


title:
Toward Quantum-Limited Position Measurements Using Optically Levitated
  Microspheres

abstract:
  We describe the use of optically levitated microspheres as test masses in
experiments aimed at reaching and potentially exceeding the standard quantum
limit for position measurements. Optically levitated microspheres have low mass
and are essentially free of suspension thermal noise, making them well suited
for reaching the quantum regime. Table-top experiments using microspheres can
bridge the gap between quantum-limited position measurements of single atoms
and measurements with multi-kg test masses like those being used in
interferometric gravitational wave detectors.


title:
New solvable quantum mechanical potentials by iteration of the free V=0
  potential

abstract:
  A huge family of solvable potentials can be generated by systematically
exploiting the factorization (Darboux) method. Starting from the free case, a
large class of the known solvable families is thus reproduced, together with
new ones. We explicitly find and solve several new singular potentials obtained
by iteration from the V=0 case; some of them have an E=0 bound state and
constant phase shift without being explicitly scale invariant. The new
potentials are rational functions, and can be related to rational solutions of
the KdV family.


title:
An approach to the time-dependent Jaynes-Cummings model without the
  rotating wave approximation

abstract:
  This report presents an approach to the exact solutions of the time-dependent
Jaynes-Cummings (J-C) model without the rotating wave approximation (RWA). It
is shown that there is a squeezing-operator unitary transformation for relating
the J-C model without RWA and the one with RWA. Thus by using an appropriate
squeezing unitary transformation, the time-dependent J-C model without RWA can
be transformed into the one with RWA that has been exactly solved previously,
and based on this one can readily obtain the exact solutions of the
time-dependent Jaynes-Cummings (J-C) model without RWA. The approach presented
here also shows that we can treat these two kinds of time-dependent J-C models
(both with and without RWA) in a unified way.


title:
Quantum Logic Networks for Probabilistic Teleportation of Many Particle
  State of General Form

abstract:
  The scheme for probabilistic teleportation of an N-particle state of general
form is proposed. As the special cases we construct efficient quantum logic
networks for implementing probabilistic teleportation of a two-particle state,
a three-particle state and a four-particle state of general form, built from
single qubit gates, two-qubit controlled-not gates, Von Neumann measurement and
classically controlled operations.


title: Non-Probabilistic Termination of Measurement-based Quantum Computation

abstract:
  Nielsen [quant-ph/0108020] introduced a model of quantum computation by
measurement-based simulation of unitary computations. In this model, a
consequence of the non-determinism of quantum measurement is the probabilistic
termination of simulations. This means that the time when simulation terminates
for a given computation is probabilistic, and this simulation may even never
end.
  We introduce (section 3) a measurement-based model with non probabilistic
termination, which permits, unlike existing models, to predict the time of
termination. This new scheme is a modification of Nielsen's. After an
introduction to Nielsen's scheme (section 1), an analysis of different temporal
organisations of elementary simulations within Nielsen's scheme (section 2)
leads to the non probabilistic model.