title: On v^2/c^2 expansion of the Dirac equation with external potentials

abstract:
  The v^2/c^2 expansion of the Dirac equation with external potentials is
reexamined. A complete, gauge invariant form of the expansion to order (1/c)^2
is established which contains two additional terms, as compared to various
versions existing in the literature. It is shown that the additional terms
describe relativistic decrease of the electron spin magnetic moment with
increasing electron energy.


title: Radiative corrections and quantum gates in molecular systems

abstract:
  We propose a method for quantum information processing using molecules
coupled to an external laser field. This utilizes molecular interactions,
control of the external field and an effective energy shift of the
doubly-excited state of two coupled molecules. Such a level shift has been seen
in the two-photon resonance experiments recently reported in Ref. [1]. Here we
show that this can be explained in terms of the QED Lamb shift. We quantify the
performance of the proposed quantum logic gates in the presence of dissipative
mechanisms. The unitary transformations required for performing one- and
two-qubit operations can be implemented with present day technology.


title:
Space-to-ground quantum-communication using an optical ground station: a
  feasibility study

abstract:
  We have tested the experimental prerequisites for a Space-to-Ground quantum
communication link between satellites and an optical ground station. The
feasibility of our ideas is being assessed using the facilities of the ASI
Matera Laser Ranging Observatory (MLRO). Specific emphasis is put on the
necessary technological modifications of the existing infrastructure to achieve
single photon reception from an orbiting satellite.


title: Logical Interpretation of a Reversible Measurement in Quantum Computing

abstract:
  We give the logical description of a new kind of quantum measurement that is
a reversible operation performed by an hypothetical insider observer, or, which
is the same, a quantum measurement made in a quantum space background, like the
fuzzy sphere. The result is that the non-contradiction and the excluded middle
principles are both invalidated, leading to a paraconsistent, symmetric logic.
Our conjecture is that, in this setting, one can develop the adequate logic of
quantum computing. The role of standard quantum logic is then confined to
describe the projective measurement scheme.


title: On Estimating the State of a Finite Level Quantum System

abstract:
  We revisit the problem of mutually unbiased measurements in the context of
estimating the unknown state of a $d$-level quantum system, first studied by W.
K. Wootters and B. D. fields[7] in 1989 and later investigated by S.
Bandyopadhyay et al [3] in 2001 and A. O. Pittenger and M. H. Rubin [6] in
2003. Our approach is based directly on the Weyl operators in the $L^2$-space
over a finite field when $d=p^r$ is the power of a prime. When $d$ is not a
prime power we sacrifice a bit of optimality and construct a recovery operator
for reconstructing the unknown state from the probabilities of elementary
events in different measurements.


title: Quantum games with decoherence

abstract:
  A protocol for considering decoherence in quantum games is presented. Results
for two-player, two-strategy quantum games subject to decoherence are derived
and some specific examples are given. Decoherence in other types of quantum
games is also considered. As expected, the advantage that a quantum player
achieves over a player restricted to classical strategies is diminished for
increasing decoherence but only vanishes in the limit of maximum decoherence.


title:
Wave packet dynamics of the matter wave field of a Bose-Einstein
  condensate

abstract:
  We show in the framework of a tractable model that revivals and fractional
revivals of wave packets afford clear signatures of the extent of departure
from coherence and from Poisson statistics of the matter wave field in a
Bose-Einstein condensate, or of a suitably chosen initial state of the
radiation field propagating in a Kerr-like medium.


title: Greenberger-Horne-Zeilinger Nonlocality in Arbitrary Even Dimensions

abstract:
  We generalize Greenberger-Horne-Zeilinger (GHZ) nonlocality to every
even-dimensional and odd-partite system. For the purpose we employ concurrent
observables that are incompatible and nevertheless have a common eigenstate. It
is remarkable that a tripartite system can exhibit the genuinely
high-dimensional GHZ nonlocality.


title: Spontaneous Relaxation of a Charge Qubit under Electrical Measurement

abstract:
  In this work we first derive a generalized conditional master equation for
quantum measurement by a mesoscopic detector, then study the readout
characteristics of qubit measurement where a number of new features are found.
The work would in particular highlight the qubit spontaneous relaxation effect
induced by the measurement itself rather than an external thermal bath.


title:
Tightening the Theory-Experiment Connection in Physics: R_{n} based
  Space and Time

abstract:
  Some aspects of replacing C based physics by C_{n} based physics are
discussed. Here C_{n} ={R_{n},I_{n}} where R_{n} and I_{n} are the real and
imaginary components of the numbers in C_{n}, and both R_{n} and I_{n}) are
sets of length 2n string numbers in some basis. The discussion here is limited
to describing the experimental basis and choice for the numbers in R_{n}, and a
few basic but interesting properties of R_{n} based space and time.


title: Casimir force acting on magnetodielectric bodies embedded in media

abstract:
  Within the framework of macroscopic quantum electrodynamics, general
expressions for the Casimir force acting on linearly and causally responding
magnetodielectric bodies that can be embedded in another linear and causal
magnetodielectric medium are derived. Consistency with microscopic
harmonic-oscillator models of the matter is shown. The theory is applied to
planar structures and proper generalizations of Casimir's and Lifshitz-type
formulas are given.


title:
Classical simulatability, entanglement breaking, and quantum computation
  thresholds

abstract:
  We investigate the amount of noise required to turn a universal quantum gate
set into one that can be efficiently modelled classically. This question is
useful for providing upper bounds on fault tolerant thresholds, and for
understanding the nature of the quantum/classical computational transition. We
refine some previously known upper bounds using two different strategies. The
first one involves the introduction of bi-entangling operations, a class of
classically simulatable machines that can generate at most bipartite
entanglement. Using this class we show that it is possible to sharpen
previously obtained upper bounds in certain cases. As an example, we show that
under depolarizing noise on the controlled-not gate, the previously known upper
bound of 74% can be sharpened to around 67%. Another interesting consequence is
that measurement based schemes cannot work using only 2-qubit non-degenerate
projections. In the second strand of the work we utilize the Gottesman-Knill
theorem on the classically efficient simulation of Clifford group operations.
The bounds attained for the pi/8 gate using this approach can be as low as 15%
for general single gate noise, and 30% for dephasing noise.


title:
Ground State Entanglement in a Combination of Star And Ring Geometries
  Of Interacting Spins

abstract:
  We compare a star and a ring network of interacting spins in terms of the
entanglement they can provide between the nearest and the next to nearest
neighbor spins in the ground state. We then investigate whether this
entanglement can be optimized by allowing the system to interact through a
weighted combination of the star and the ring geometries. We find that such a
weighted combination is indeed optimal in certain circumstances for providing
the highest entanglement between two chosen spins. The entanglement shows jumps
and counterintuitive behavior as the relative weighting of the star and the
ring interactions is varied. We give an exact mathematical explanation of the
behavior for a five qubit system (four spins in a ring and a central spin) and
an intuitive explanation for larger systems. For the case of four spins in a
ring plus a central spin, we demonstrate how a four qubit GHZ state can be
generated as a simple derivative of the ground state. Our calculations also
demonstrate that some of the multi-particle entangled states derivable from the
ground state of a star network are sufficiently robust to the presence of
nearest neighbor ring interactions.


title: Efficient Decoupling Schemes Based on Hamilton Cycles

abstract:
  Decoupling the interactions in a spin network governed by a pair-interaction
Hamiltonian is a well-studied problem. Combinatorial schemes for decoupling and
for manipulating the couplings of Hamiltonians have been developed which use
selective pulses. In this paper we consider an additional requirement on these
pulse sequences: as few {\em different} control operations as possible should
be used. This requirement is motivated by the fact that optimizing each
individual selective pulse will be expensive, i. e., it is desirable to use as
few different selective pulses as possible. For an arbitrary $d$-dimensional
system we show that the ability to implement only two control operations is
sufficient to turn off the time evolution. In case of a bipartite system with
local control we show that four different control operations are sufficient.
Turning to networks consisting of several $d$-dimensional nodes which are
governed by a pair-interaction Hamiltonian, we show that decoupling can be
achieved if one is able to control a number of different control operations
which is logarithmic in the number of nodes.


title:
Distinctness of ensembles having the same density matrix and the nature
  of liquid NMR quantum computing

abstract:
  We show that differently constructed ensembles having the same density matrix
may be physically distinguished by observing fluctuations of some observables.
An explicit expression for fluctuations of an observable in an ensemble is
given. This result challenges Peres's fundamental postulate and seems to be
contrary to the widely-spread belief that ensembles with the same density
matrix are physically identical. This leads us to suggest that the current
liquid NMR quantum computing is truly quantum-mechanical in nature.


title: Classical Robustness of Quantum Unravellings

abstract:
  We introduce three measures which quantify the degree to which quantum
systems possess the robustness exhibited by classical systems when subjected to
continuous observation. Using these we show that for a fixed environmental
interaction the level of robustness depends on the measurement strategy, or
unravelling, and that no single strategy is maximally robust in all ways.


title: Robustness of Shor's algorithm

abstract:
  Shor's factorisation algorithm is a combination of classical pre- and
post-processing and a quantum period finding (QPF) subroutine which allows an
exponential speed up over classical factoring algorithms. We consider the
stability of this subroutine when exposed to a discrete error model that acts
to perturb the computational trajectory of a quantum computer. Through detailed
state vector simulations of an appropriate quantum circuit, we show that the
error locations within the circuit itself heavily influences the probability of
success of the QPF subroutine. The results also indicate that the naive
estimate of required component precision is too conservative.


title: Wootters' distance revisited: a new distinguishability criterium

abstract:
  The notion of distinguishability between quantum states has shown to be
fundamental in the frame of quantum information theory. In this paper we
present a new distinguishability criterium by using a information theoretic
quantity: the Jensen-Shannon divergence (JSD). This quantity has several
interesting properties, both from a conceptual and a formal point of view.
Previous to define this distinguishability criterium, we review some of the
most frequently used distances defined over quantum mechanics' Hilbert space.
In this point our main claim is that the JSD can be taken as a unifying
distance between quantum states.


title:
Coherence measurements on Rydberg wave packets kicked by a half-cycle
  pulse

abstract:
  A kick from a unipolar half-cycle pulse (HCP) can redistribute population and
shift the relative phase between states in a radial Rydberg wave packet. We
have measured the quantum coherence properties following the kick, and show
that selected coherences can be destroyed by applying an HCP at specific times.
Quantum mechanical simulations show that this is due to redistribution of the
angular momentum in the presence of noise. These results have implications for
the storage and retrieval of quantum information in the wave packet.


title:
Non-Markovian qubit dynamics in a thermal field bath: Relaxation,
  decoherence and entanglement

abstract:
  We study the non-Markovian dynamics of a qubit made up of a two-level atom
interacting with an electromagnetic field (EMF) initially at finite
temperature. Unlike most earlier studies where the bath is assumed to be fixed,
we study the coherent evolution of the combined qubit-EMF system, thus allowing
for the back-action from the bath on the qubit and the qubit on the bath in a
self-consistent manner. In this way we can see the development of quantum
correlations and entanglement between the system and its environment, and how
that affects the decoherence and relaxation of the system. We find
non-exponential decay for both the diagonal and non-diagonal matrix elements of
the qubit's reduced density matrix in the pointer basis. From the diagonal
elements we see the qubit relaxes to thermal equilibrium with the bath. From
the non-diagonal elements, we see the decoherence rate beginning at the usually
predicted thermal rate, but changing to the zero temperature decoherence rate
as the qubit and bath become entangled. These two rates are comparable, as was
shown before in the zero temperature case [C. Anastopoulos and B. L. Hu, Phys.
Rev. A {\bf 62} (2000) 033821]. On the entanglement of a qubit with the EMF
under this type of resonant coupling we calculated, for the qubit reduced
density matrix, the fidelity and the von Neumann entropy, which is a measure of
the purity of the density matrix. The present more accurate non-Markovian
calculations predict lower loss of fidelity and purity as compared with the
Markovian results. Generally speaking, with the inclusion of quantum
correlations between the qubit and its environment, the non-Markovian processes
tend to slow down the drive of the system to equilibrium, prolonging the
decoherence and better preserving the fidelity and purity of the system.


title: Unconditional Security of Three State Quantum Key Distribution Protocols

abstract:
  Quantum key distribution (QKD) protocols are cryptographic techniques with
security based only on the laws of quantum mechanics. Two prominent QKD schemes
are the BB84 and B92 protocols that use four and two quantum states,
respectively. In 2000, Phoenix et al. proposed a new family of three state
protocols that offers advantages over the previous schemes. Until now, an error
rate threshold for security of the symmetric trine spherical code QKD protocol
has only been shown for the trivial intercept/resend eavesdropping strategy. In
this paper, we prove the unconditional security of the trine spherical code QKD
protocol, demonstrating its security up to a bit error rate of 9.81%. We also
discuss on how this proof applies to a version of the trine spherical code QKD
protocol where the error rate is evaluated from the number of inconclusive
events.


title: Energy as an Entanglement Witness for Quantum Many-Body Systems

abstract:
  We investigate quantum many-body systems where all low-energy states are
entangled. As a tool for quantifying such systems, we introduce the concept of
the entanglement gap, which is the difference in energy between the
ground-state energy and the minimum energy that a separable (unentangled) state
may attain. If the energy of the system lies within the entanglement gap, the
state of the system is guaranteed to be entangled. We find Hamiltonians that
have the largest possible entanglement gap; for a system consisting of two
interacting spin-1/2 subsystems, the Heisenberg antiferromagnet is one such
example. We also introduce a related concept, the entanglement-gap temperature:
the temperature below which the thermal state is certainly entangled, as
witnessed by its energy. We give an example of a bipartite Hamiltonian with an
arbitrarily high entanglement-gap temperature for fixed total energy range. For
bipartite spin lattices we prove a theorem demonstrating that the entanglement
gap necessarily decreases as the coordination number is increased. We
investigate frustrated lattices and quantum phase transitions as physical
phenomena that affect the entanglement gap.


title: Decoherence versus Dynamical Casimir Effect

abstract:
  By means of two simple examples: phase and amplitude damping, the impact of
decoherence on the dynamical Casimir effect is investigated. Even without
dissipating energy (i.e., pure phase damping), the amount of created particles
can be diminished significantly via the coupling to the environment (reservoir
theory) inducing decoherence. For a simple microscopic model, it is
demonstrated that spontaneous decays within the medium generate those problems
-- Rabi oscillations are far more advantageous in that respect. These findings
are particularly relevant in view of a recently proposed experimental
verification of the dynamical Casimir effect. PACS: 42.50.Lc, 03.65.Yz,
03.70.+k, 42.50.Dv.


title:
Quantum tomographic cryptography with Bell diagonal states:
  non-equivalence of classical and quantum distillation protocols

abstract:
  We present a generalized tomographic quantum key distribution protocol in
which the two parties share a Bell diagonal mixed state of two qubits. We show
that if an eavesdropper performs a coherent measurement on many quantum ancilla
states simultaneously, classical methods of secure key distillation are less
effective than quantum entanglement distillation protocols. We also show that
certain Bell diagonal states are resistant to any attempt of incoherent
eavesdropping.


title:
Testing Bell's inequality in constantly coupled Josephson circuits by
  effective single-qubit operations

abstract:
  In superconducting circuits with interbit untunable (e.g., capacitive)
couplings, ideal local quantum operations cannot be exactly performed on
individual Josephson qubits. Here we propose an effective dynamical decoupling
approach to overcome the "fixed-interaction" difficulty for effectively
implementing elemental logical gates for quantum computation. The proposed
single-qubit operations and local measurements should allow testing Bell's
inequality with a pair of capacitively-coupled Josephson qubits. This provides
a powerful approach, besides spectral-analysis [Nature \textbf{421}, 823
(2003); Science \textbf{300}, 1548 (2003)], to verify the existence of
macroscopic quantum entanglement between two fixed-coupling Josephson qubits.

categories: quant-ph cond-mat.mes-hall cond-mat.mtrl-sci cond-mat.supr-con


title:
Extended GHZ n-player games with classical probability of winning
  tending to 0

abstract:
  In 1990, Mermin presented a n player game that is won with certainty using n
spin-1/2 particles in a GHZ state whilst no classical strategy (or local
theory) can win with probability higher than ${1/2} + \frac{1}{2^{\lceil n/2
\rceil}}$ (which is larger than 1/2). This article first introduces a class of
arithmetic games containing Mermin's and gives a quantum algorithm based on a
generalized n party GHZ state that wins those games with certainty. It is then
proved for a subclass of those games where each player is given a single bit of
input that no classical strategy can win with a probability that is
asymptotically larger than 1.6 times the inverse of the square root of n, thus
giving a new and stronger Bell inequality.


title: Noise-induced finite-time disentanglement in two-atomic system

abstract:
  We discuss the influence of a noisy environment on entangled states of two
atoms and show that all such states disentangle in finite time.


title: Photon-bunching measurement after 2x25km of standard optical fibers

abstract:
  To show the feasibility of a long distance partial Bell-State measurement, a
Hong-Ou-Mandel experiment with coherent photons is reported. Pairs of
degenerate photons at telecom wavelength are created by parametric down
conversion in a periodically poled lithium niobate waveguide. The photon pairs
are separated in a beam-splitter and transmitted via two fibers of 25km. The
wave-packets are relatively delayed and recombined on a second beam-splitter,
forming a large Mach-Zehnder interferometer. Coincidence counts between the
photons at the two output modes are registered. The main challenge consists in
the trade-off between low count rates due to narrow filtering and length
fluctuations of the 25km long arms during the measurement. For balanced paths a
Hong-Ou-Mandel dip with a visibility of 47.3% is observed, which is close to
the maximal theoretical value of 50% developed here. This proves the
practicability of a long distance Bell state measurement with two independent
sources, as e.g. required in an entanglement swapping configuration in the
scale of tens of km.


title: Heralding Single Photons from Pulsed Parametric Down-Conversion

abstract:
  We describe an experiment in which photon pairs from a pulsed parametric
down-conversion source were coupled into single-mode fibers. Detecting one of
the photons heralded the presence of the other photon in its fiber with a
probability of 83%. The heralded photons were then used in a simple
multi-photon interference experiment to illustrate their potential for quantum
information applications.


title: Measures of entanglement in quantum mechanics

abstract:
  I give an overview of some of the most used measures of entanglement. To make
the presentation self-contained, a number of concepts from quantum information
theory are first explained. Then the structure of bipartite entanglement is
studied qualitatively, before a number of bipartite entanglement measures are
described, both for pure and mixed states. Results from the study of
multipartite systems and continuous variable systems are briefly discussed.


title: Quantum gloves: Physics and Information

abstract:
  The slogan information is physical has been so successful that it led to some
excess. Classical and quantum information can be thought of independently of
any physical implementation. Pure information tasks can be realized using such
abstract c- and qu-bits, but physical tasks require appropriate physical
realizations of c- or qu-bits. As illustration we consider the problem of
communicating chirality.


title: Geometric Quantization, Coherent States and Stochastic Measurements

abstract:
  The geometric quantization problem is considered from the point of view of
the Davies and Lewis approach to quantum mechanics. The influence of the
measuring device is accounted in the classical and quantum case and it is shown
that the conditions of the measurement define the type of quantization (Weyl,
normal, antinormal, etc.). The quantum states and quantum operators are
obtained by means of the projection, defined from the system of generalized
coherent states.


title: Quantum Computing Using Single Photons and the Zeno Effect

abstract:
  We show that the quantum Zeno effect can be used to suppress the failure
events that would otherwise occur in a linear optics approach to quantum
computing. From a practical viewpoint, that would allow the implementation of
deterministic logic gates without the need for ancilla photons or
high-efficiency detectors. We also show that the photons can behave as if they
were fermions instead of bosons in the presence of a strong Zeno effect, which
leads to a new paradigm for quantum computation.


title: Utilizing Encoding in Scalable Linear Optics Quantum Computing

abstract:
  We present a scheme which offers a significant reduction in the resources
required to implement linear optics quantum computing. The scheme is a
variation of the proposal of Knill, Laflamme, and Milburn, and makes use of an
incremental approach to the error encoding to boost probability of success.


title: Optimal Unravellings for Feedback Control in Linear Quantum Systems

abstract:
  For quantum systems with linear dynamics in phase space much of classical
feedback control theory applies. However, there are some questions that are
sensible only for the quantum case, such as: given a fixed interaction between
the system and the environment what is the optimal measurement on the
environment for a particular control problem? We show that for a broad class of
optimal (state-based) control problems (the stationary
Linear-Quadratic-Gaussian class), this question is a semi-definite program.
Moreover, the answer also applies to Markovian (current-based) feedback.


title: Relation between coined quantum walks and quantum cellular automata

abstract:
  Motivated by the recent work of Patel et al., this paper clarifies a
connection between coined quantum walks and quantum cellular automata in a
general setting. As a consequence, their result is naturally derived from the
connection.


title: The ground state entanglement in the $XXZ$ model

abstract:
  In this paper, we investigate spin entanglement in the $XXZ$ model defined on
a $d$-dimensional bipartite lattice. The concurrence, a measure of the
entanglement between two spins, is analyzed. We prove rigorously that the
ground state concurrence reaches maximum at the isotropic point. For
dimensionality $d \ge 2$, the concurrence develops a cusp at the isotropic
point and we attribute it to the existence of magnetic long-range order.


title: Quantum privacy amplification for quantum secure direct communication

abstract:
  Using quantum mechanics, secure direct communication between distant parties
can be performed. Over a noisy quantum channel, quantum privacy amplification
is a necessary step to ensure the security of the message. In this paper, we
present a quantum privacy amplification scheme for quantum secure direct
communication using single photons. The quantum privacy amplification procedure
contains two control-not gates and a Hadamard gate. After the unitary gate
operations, a measurement is performed and one photon is retained. The retained
photon carries the state information of the discarded photon, and hence reduces
the information leakage. The procedure can be performed recursively so that the
information leakage can be reduced to any arbitrarily low level.


title:
Conditions for the multiplicativity of maximal l_p-norms of channels for
  fixed integer p

abstract:
  We introduce a condition for memoryless quantum channels which, when
satisfied guarantees the multiplicativity of the maximal l_p-norm with p a
fixed integer. By applying the condition to qubit channels, it can be shown
that it is not a necessary condition, although some known results for qubits
can be recovered. When applied to the Werner-Holevo channel, which is known to
violate multiplicativity when p is large relative to the dimension d, the
condition suggests that multiplicativity holds when $d \geqslant 2^{p-1}$. This
conjecture is proved explicitly for p=2, 3, 4. Finally, a new class of channels
is considered which generalizes the depolarizing channel to maps which are
combinations of the identity channel and a noisy one whose image is an
arbitrary density matrix. It is shown that these channels are multiplicative
for p = 2.


title:
On a group-theoretical approach to the periodic table of chemical
  elements

abstract:
  This paper is concerned with the application of the group SO(4,2)xSU(2) to
the periodic table of chemical elements. It is shown how the Madelung rule of
the atomic shell model can be used for setting up a periodic table that can be
further rationalized via the group SO(4,2)xSU(2) and some of its subgroups.
Qualitative results are obtained from the table and the general lines of a
programme for a quantitative approach to the properties of chemical elements
are developed on the basis of the group SO(4,2)xSU(2).

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


title: EPR and Bell Locality

abstract:
  A new formulation of the EPR argument is presented, one which uses John
Bell's mathematically precise local causality condition in place of the looser
locality assumption which was used in the original EPR paper and on which Niels
Bohr seems to have based his objection to the EPR argument. The new formulation
of EPR bears a striking resemblance to Bell's derivation of his famous
inequalities. The relation between these two arguments -- in particular, the
role of EPR as part one of Bell's two-part argument for nonlocality -- is also
discussed in detail.


title: Kochen-Specker theorem for von Neumann algebras

abstract:
  The Kochen-Specker theorem has been discussed intensely ever since its
original proof in 1967. It is one of the central no-go theorems of quantum
theory, showing the non-existence of a certain kind of hidden states models. In
this paper, we first offer a new, non-combinatorial proof for quantum systems
with a type $I_{n}$ factor as algebra of observables, including $I_{\infty}$.
Afterwards, we give a proof of the Kochen-Specker theorem for an arbitrary von
Neumann algebra $\mathcal{R}$ without summands of types $I_{1}$ and $I_{2}$,
using a known result on two-valued measures on the projection lattice
$\mathcal{P(R)}$. Some connections with presheaf formulations as proposed by
Isham and Butterfield are made.


title: Monitoring Quantum Oscillations with very small Disturbance

abstract:
  We present a new scheme to detect and visualize oscillations of a single
quantum system in real time. The scheme is based upon a sequence of very weak
generalized measurements, distinguished by their low disturbance and low
information gain. Accumulating the information from the single measurements by
means of an appropriate Bayesian Estimator, the actual oscillations can be
monitored nevertheless with high accuracy and low disturbance. For this purpose
only the minimum and the maximum expected oscillation frequency need to be
known. The accumulation of information is based on a general derivation of the
optimal estimator of the expectation value of a hermitian observable for a
sequence of measurements. At any time it takes into account all the preceding
measurement results.


title: Statistically Secure Quantum Oblivious Transfer

abstract: This paper has been withdrawn.


title: Cramer's Transactional Interpretation and Causal Loop Problems

abstract:
  Tim Maudlin's argument for the inconsistency of Cramer's Transactional
Interpretation (TI) of quantum theory has been considered in some detail by
Joseph Berkovitz, who has provided a possible solution to this challenge at the
cost of a significant empirical lacuna on the part of TI. The present paper
proposes an alternative solution in which Maudlin's charge of inconsistency is
evaded but at no cost of empirical content on the part of TI. However,
Maudlin's argument is taken as ruling out Cramer's heuristic ``pseudotime''
explanation of the realization of one transaction out of many.


title: Squeezing Operator and Squeeze Tomography

abstract:
  Some properties of Plebanski squeezing operator and squeezed states created
with time-dependent quadratic in position and momentum Hamiltonians are
reviewed. New type of tomography of quantum states called squeeze tomography is
discussed.


title:
Superoperator Many-body Theory of Molecular Currents: Non-equilibrium
  Green Functions in Real Time

abstract:
  The electric conductance of a molecular junction is calculated by recasting
the Keldysh formalism in Liouville space. Dyson equations for nonequilibrium
many body Green's functions (NEGF) are derived directly in real (physical)
time. The various NEGFs appear naturally in the theory as time ordered products
of superoperators, while the Keldysh forward/backward time loop is avoided.


title:
Quantum secret key encryption algorithm based on quantum discrete
  logarithm problem

abstract:
  In this paper, we first define the quantum discrete logarithm problem
(QDLP)which is similar to classical discrete logarithm problem. But, this
problem cannot be solved by Shor's quantum algorithm. Based on quantum discrete
logarithm problem, we present a novel quantum secret key encryption algorithm.
The receiver constructs his quantum channel using their secret key. Then, the
sender can use the receiver's quantum channel to encrypt the message. Finally,
the receiver dencrypts the ciphertext by using secret key. In our algorithm,
the quantum system will be broken after transferring messages. But, the secret
key can still be used repeatedly in our algorithm.


title: Understanding Bohmian mechanics: A dialogue

abstract:
  This paper is an introduction to the ideas of Bohmian mechanics, an
interpretation of quantum mechanics in which the observer plays no fundamental
role. Bohmian mechanics describes, instead of probabilities of measurement
results, objective microscopic events. In recent years, Bohmian mechanics has
attracted increasing attention by researchers. The form of a dialogue allows me
to address questions about the Bohmian view that often arise.


title: Transmission spectra of two-dimensional quantum structures

abstract:
  To study the ballistic transport of charge carriers in nano-structured
quantum devices, a highly efficient numerical technique is developed, which
provides continuous transmission spectra for arbitrarily complex potential
geometries in two dimensions. We apply the proposed method to single and double
barrier structures and compare the results with those obtained using standard
techniques for computing transmission coefficients. Excellent numerical
agreement as well as considerable computational saving is demonstrated.


title: Classical randomness in quantum measurements

abstract:
  Similarly to quantum states, also quantum measurements can be "mixed",
corresponding to a random choice within an ensemble of measuring apparatuses.
Such mixing is equivalent to a sort of hidden variable, which produces a noise
of purely classical nature. It is then natural to ask which apparatuses are
"indecomposable", i. e. do not correspond to any random choice of apparatuses.
This problem is interesting not only for foundations, but also for
applications, since most optimization strategies give optimal apparatuses that
are indecomposable.
  Mathematically the problem is posed describing each measuring apparatus by a
positive operator-valued measure (POVM), which gives the statistics of the
outcomes for any input state. The POVM's form a convex set, and in this
language the indecomposable apparatuses are represented by extremal points--the
analogous of "pure states" in the convex set of states. Differently from the
case of states, however, indecomposable POVM's are not necessarily rank-one, e.
g. von Neumann measurements.
  In this paper we give a complete classification of indecomposable apparatuses
(for discrete spectrum), by providing different necessary and sufficient
conditions for extremality of POVM's, along with a simple general algorithm for
the decomposition of a POVM into extremals. As an interesting application,
"informationally complete" measurements are analyzed in this respect. The
convex set of POVM's is fully characterized by determining its border in terms
of simple algebraic properties of the corresponding POVM's.


title: Quantum calibration of measuring apparatuses

abstract:
  By quantum calibration we name an experimental procedure apt to completely
characterize an unknown measurement apparatus by comparing it with other
calibrated apparatuses. Here we show how to achieve the calibration of an
arbitrary measuring apparatus, by using it in conjunction with a
``tomographer'' in a correlation setup with an input bipartite system. The
method is robust to imperfections of the tomographer, and works for practically
any input state of the bipartite system.


title: A symmetry analyser for non-destructive Bell state detection using EIT

abstract:
  We describe a method to project photonic two-qubit states onto the symmetric
and antisymmetric subspaces of their Hilbert space. This device utilizes an
ancillary coherent state, together with a weak cross-Kerr non-linearity,
generated, for example, by electromagnetically induced transparency. The
symmetry analyzer is non-destructive, and works for small values of the
cross-Kerr coupling. Furthermore, this device can be used to construct a
non-destructive Bell state detector.


title: A near deterministic linear optical CNOT gate

abstract:
  We show how to construct a near deterministic CNOT using several single
photons sources, linear optics, photon number resolving quantum non-demolition
detectors and feed-forward. This gate does not require the use of massively
entangled states common to other implementations and is very efficient on
resources with only one ancilla photon required. The key element of this gate
are non-demolition detectors that use a weak cross-Kerr nonlinearity effect to
conditionally generate a phase shift on a coherent probe, if a photon is
present in the signal mode. These potential phase shifts can then be measured
using highly efficient homodyne detection.


title:
Quantum Computing and Hidden Variables II: The Complexity of Sampling
  Histories

abstract:
  This paper shows that, if we could examine the entire history of a hidden
variable, then we could efficiently solve problems that are believed to be
intractable even for quantum computers. In particular, under any
hidden-variable theory satisfying a reasonable axiom called "indifference to
the identity," we could solve the Graph Isomorphism and Approximate Shortest
Vector problems in polynomial time, as well as an oracle problem that is known
to require quantum exponential time. We could also search an N-item database
using O(N^{1/3}) queries, as opposed to O(N^{1/2}) queries with Grover's search
algorithm. On the other hand, the N^{1/3} bound is optimal, meaning that we
could probably not solve NP-complete problems in polynomial time. We thus
obtain the first good example of a model of computation that appears slightly
more powerful than the quantum computing model.


title: Security of Quantum Bit-String Generation

abstract:
  We consider the cryptographic task of bit-string generation. This is a
generalisation of coin tossing in which two mistrustful parties wish to
generate a string of random bits such that an honest party can be sure that the
other cannot have biased the string too much. We consider a quantum protocol
for this task, originally introduced in Phys. Rev. A {\bf 69}, 022322 (2004),
that is feasible with present day technology. We introduce security conditions
based on the average bias of the bits and the Shannon entropy of the string.
For each, we prove rigorous security bounds for this protocol in both noiseless
and noisy conditions under the most general attacks allowed by quantum
mechanics. Roughly speaking, in the absence of noise, a cheater can only bias
significantly a vanishing fraction of the bits, whereas in the presence of
noise, a cheater can bias a constant fraction, with this fraction depending
quantitatively on the level of noise. We also discuss classical protocols for
the same task, deriving upper bounds on how well a classical protocol can
perform. This enables the determination of how much noise the quantum protocol
can tolerate while still outperforming classical protocols. We raise several
conjectures concerning both quantum and classical possibilities for large n
cryptography. An experiment corresponding to the scheme analysed in this paper
has been performed and is reported elsewhere.


title: Provably Secure Experimental Quantum Bit-String Generation

abstract:
  Coin tossing is a cryptographic task in which two parties who do not trust
each other aim to generate a common random bit. Using classical communication
this is impossible, but non trivial coin tossing is possible using quantum
communication. Here we consider the case when the parties do not want to toss a
single coin, but many. This is called bit string generation. We report the
experimental generation of strings of coins which are provably more random than
achievable using classical communication. The experiment is based on the ``plug
and play'' scheme developed for quantum cryptography, and therefore well suited
for long distance quantum communication.


title:
Photon-Number-Splitting versus Cloning Attacks in Practical
  Implementations of the Bennett-Brassard 1984 protocol for Quantum
  Cryptography

abstract:
  In practical quantum cryptography, the source sometimes produces multi-photon
pulses, thus enabling the eavesdropper Eve to perform the powerful
photon-number-splitting (PNS) attack. Recently, it was shown by Curty and
Lutkenhaus [Phys. Rev. A 69, 042321 (2004)] that the PNS attack is not always
the optimal attack when two photons are present: if errors are present in the
correlations Alice-Bob and if Eve cannot modify Bob's detection efficiency, Eve
gains a larger amount of information using another attack based on a 2->3
cloning machine. In this work, we extend this analysis to all distances
Alice-Bob. We identify a new incoherent 2->3 cloning attack which performs
better than those described before. Using it, we confirm that, in the presence
of errors, Eve's better strategy uses 2->3 cloning attacks instead of the PNS.
However, this improvement is very small for the implementations of the
Bennett-Brassard 1984 (BB84) protocol. Thus, the existence of these new attacks
is conceptually interesting but basically does not change the value of the
security parameters of BB84. The main results are valid both for Poissonian and
sub-Poissonian sources.


title: Theoretical investigation of the quantum noise in ghost imaging

abstract:
  Ghost imaging is a method to nonlocally image an object by transmitting pairs
of entangled photons through the object and a reference optical system
respectively. We present a theoretical analysis of the quantum noise in this
imaging technique. The dependence of the noise on the properties of the
apertures in the imaging system are discussed and demonstrated with a numerical
example. For a given source, the resolution and the signal-to-noise ratio
cannot be improved at the same time .


title: Geometry of the Casimir Effect

abstract:
  When the vacuum is partitioned by material boundaries with arbitrary shape,
one can define the zero-point energy and the free energy of the electromagnetic
waves in it: this can be done, independently of the nature of the boundaries,
in the limit that they become perfect conductors, provided their curvature is
finite. The first examples we consider are Casimir's original configuration of
parallel plates, and the experimental situation of a sphere in front of a
plate. For arbitrary geometries, we give an explicit expression for the
zero-point energy and the free energy in terms of an integral kernel acting on
the boundaries; it can be expanded in a convergent series interpreted as a
succession of an even number of scatterings of a wave. The quantum and thermal
fluctuations of vacuum then appear as a purely geometric property. The Casimir
effect thus defined exists only owing to the electromagnetic nature of the
field. It does not exist for thin foils with sharp folds, but Casimir forces
between solid wedges are finite. We work out various applications: low
temperature, high temperature where wrinkling constraints appear, stability of
a plane foil, transfer of energy from one side of a curved boundary to the
other, forces between distant conductors, special shapes (parallel plates,
sphere, cylinder, honeycomb).

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


title:
Environment as a Witness: Selective Proliferation of Information and
  Emergence of Objectivity in a Quantum Universe

abstract:
  We study the role of the information deposited in the environment of an open
quantum system in course of the decoherence process. Redundant spreading of
information -- the fact that some observables of the system can be
independently ``read-off'' from many distinct fragments of the environment --
is investigated as the key to effective objectivity, the essential ingredient
of ``classical reality''. This focus on the environment as a communication
channel through which observers learn about physical systems underscores
importance of quantum Darwinism -- selective proliferation of information about
``the fittest states'' chosen by the dynamics of decoherence at the expense of
their superpositions -- as redundancy imposes the existence of preferred
observables. We demonstrate that the only observables that can leave multiple
imprints in the environment are the familiar pointer observables singled out by
environment-induced superselection (einselection) for their predictability.
Many independent observers monitoring the environment will therefore agree on
properties of the system as they can only learn about preferred observables. In
this operational sense, the selective spreading of information leads to
appearance of an objective ``classical reality'' from within quantum substrate.


title:
Spatial overlap of nonclassical ultrashort light pulses and formation of
  polarization-squeezed light

abstract:
  We investigate the spatial overlap of nonclassical ultrashort light pulses
produced by self-phase modulation effect in electronic Kerr media and its
relevance in the formation of polarization-squeezed states of light. The light
polarization is treated in terms of four quantum Stokes parameters whose
spectra of quantum fluctuations are investigated. We show that the frequency at
which the suppression of quantum fluctuations of Stokes parameters is the
greatest can be controlled by adjusting the linear phase difference between
pulses. By varying the intensity of one pulse one can suppress effectively the
quantum fluctuations of Stokes parameters. We study the overlap of nonclassical
pulses inside of an anisotropic electronic Kerr medium and we show that the
cross-phase modulation effect can be employed to control the
polarization-squeezed state of light. Moreover, we establish that the change of
the intensity or of the nonlinear phase shift per photon for one pulse controls
effectively the squeezing of Stokes parameters. The spatial overlap of a
coherent pulse field with an interference pulse produced by mixing two
quadrature-squeezed pulses on a beam splitter is analyzed. It is found that
squeezing is produced in three of the four Stokes parameters, with the
squeezing in the first two being simultaneous.


title: Lorentz-invariant Bell's inequality

abstract:
  We study Bell's inequality in relation to the Einstein-Podolsky-Rosen paradox
in the relativistic regime. For this purpose, a relativistically invariant
observable is used in the calculation of the Bell's inequality, which results
in the maximally violated Bell's inequality in any reference frames.


title: Fault-Tolerant Quantum Dynamical Decoupling

abstract:
  Dynamical decoupling pulse sequences have been used to extend coherence times
in quantum systems ever since the discovery of the spin-echo effect. Here we
introduce a method of recursively concatenated dynamical decoupling pulses,
designed to overcome both decoherence and operational errors. This is important
for coherent control of quantum systems such as quantum computers. For
bounded-strength, non-Markovian environments, such as for the spin-bath that
arises in electron- and nuclear-spin based solid-state quantum computer
proposals, we show that it is strictly advantageous to use concatenated, as
opposed to standard periodic dynamical decoupling pulse sequences. Namely, the
concatenated scheme is both fault-tolerant and super-polynomially more
efficient, at equal cost. We derive a condition on the pulse noise level below
which concatenated is guaranteed to reduce decoherence.


title: Quantum computing and polynomial equations over the finite field Z_2

abstract:
  What is the computational power of a quantum computer? We show that
determining the output of a quantum computation is equivalent to counting the
number of solutions to an easily computed set of polynomials defined over the
finite field Z_2. This connection allows simple proofs to be given for two
known relationships between quantum and classical complexity classes.


title: A simple proof of the strong subadditivity inequality

abstract:
  Arguably the deepest fact known about the von Neumann entropy, the strong
subadditivity inequality is a potent hammer in the quantum information
theorist's toolkit. This short tutorial describes a simple proof of strong
subadditivity due to Petz [Rep. on Math. Phys. 23 (1), 57--65 (1986)]. It
assumes only knowledge of elementary linear algebra and quantum mechanics.


title: A Note on Entanglement of Formation and Generalized Concurrence

abstract:
  We discuss a kind of generalized concurrence for a class of high dimensional
quantum pure states such that the entanglement of formation is a monotonically
increasing convex function of the generalized concurrence. An analytical
expression of the entanglement of formation for a class of high dimensional
quantum mixed states is obtained.


title:
Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum
  Mechanics

abstract:
  For a non-Hermitian Hamiltonian H possessing a real spectrum, we introduce a
canonical orthonormal basis in which a previously introduced unitary mapping of
H to a Hermitian Hamiltonian h takes a simple form. We use this basis to
construct the observables O of the quantum mechanics based on H. In particular,
we introduce pseudo-Hermitian position and momentum operators and a
pseudo-Hermitian quantization scheme that relates the latter to the ordinary
classical position and momentum observables. These allow us to address the
problem of determining the conserved probability density and the underlying
classical system for pseudo-Hermitian and in particular PT-symmetric quantum
systems. As a concrete example we construct the Hermitian Hamiltonian h, the
physical observables O, the localized states, and the conserved probability
density for the non-Hermitian PT-symmetric square well. We achieve this by
employing an appropriate perturbation scheme. For this system, we conduct a
comprehensive study of both the kinematical and dynamical effects of the
non-Hermiticity of the Hamiltonian on various physical quantities. In
particular, we show that these effects are quantum mechanical in nature and
diminish in the classical limit. Our results provide an objective assessment of
the physical aspects of PT-symmetric quantum mechanics and clarify its
relationship with both the conventional quantum mechanics and the classical
mechanics.


title: An atom diode

abstract:
  An atom diode, i.e., a device that lets the ground state atom pass in one
direction but not in the opposite direction in a velocity range is devised. It
is based on the adiabatic transfer achieved with two lasers and a third laser
potential that reflects the ground state.


title:
Iterative procedure for computing accessible information in quantum
  communication

abstract:
  We present an iterative algorithm that finds the optimal measurement for
extracting the accessible information in any quantum communication scenario.
The maximization is achieved by a steepest-ascent approach toward the extremal
point, following the gradient uphill in sufficiently small steps. We apply it
to a simple ad-hoc example, as well as to a problem with a bearing on the
security of a tomographic protocol for quantum key distribution.


title:
Incoherent Coincidence Imaging and Its Applicability in X-ray
  Diffraction

abstract:
  Entangled-photon coincidence imaging is a method to nonlocally image an
object by transmitting a pair of entangled photons through the object and a
reference optical system, respectively. The image of the object can be
extracted from the coincidence rate of these two photons. From a classical
perspective, the image is proportional to the fourth-order correlation function
of the wave field. Using classical statistical optics, we study a particular
aspect of coincidence imaging with incoherent sources. As an application, we
give a proposal to realize lensless Fourier-transform imaging, and discuss its
applicability in x-ray diffraction.


title:
High quality asynchronous heralded single photon source at telecom
  wavelength

abstract:
  We report on the experimental realization and characterization of an
asynchronous heralded single photon source based on spontaneous parametric down
conversion. Photons at 1550nm are heralded as being inside a single-mode fiber
with more than 60% probability, and the multi-photon emission probability is
reduced by up to a factor 600 compared to poissonian light sources. These
figures of merit, together with the choice of telecom wavelength for the
heralded photons are compatible with practical applications needing very
efficient and robust single photon sources.


title: Eigenvalue Estimation of Differential Operators

abstract:
  We demonstrate how linear differential operators could be emulated by a
quantum processor, should one ever be built, using the Abrams-Lloyd algorithm.
Given a linear differential operator of order 2S, acting on functions
psi(x_1,x_2,...,x_D) with D arguments, the computational cost required to
estimate a low order eigenvalue to accuracy Theta(1/N^2) is
Theta((2(S+1)(1+1/nu)+D)log N) qubits and O(N^{2(S+1)(1+1/nu)} (D log N)^c)
gate operations, where N is the number of points to which each argument is
discretized, nu and c are implementation dependent constants of O(1). Optimal
classical methods require Theta(N^D) bits and Omega(N^D) gate operations to
perform the same eigenvalue estimation. The Abrams-Lloyd algorithm thereby
leads to exponential reduction in memory and polynomial reduction in gate
operations, provided the domain has sufficiently large dimension D >
2(S+1)(1+1/nu). In the case of Schrodinger's equation, ground state energy
estimation of two or more particles can in principle be performed with fewer
quantum mechanical gates than classical gates.


title: Probabilistic Quantum Control Via Indirect Measurement

abstract:
  The most basic scenario of quantum control involves the organized
manipulation of pure dynamical states of the system by means of unitary
transformations. Recently, Vilela Mendes and Mank'o have shown that the
conditions for controllability on the state space become less restrictive if
unitary control operations may be supplemented by projective measurement. The
present work builds on this idea, introducing the additional element of
indirect measurement to achieve a kind of remote control. The target system
that is to be remotely controlled is first entangled with another identical
system, called the control system. The control system is then subjected to
unitary transformations plus projective measurement. As anticipated by
Schrodinger, such control via entanglement is necessarily probabilistic in
nature. On the other hand, under appropriate conditions the remote-control
scenario offers the special advantages of robustness against decoherence and a
greater repertoire of unitary transformations. Simulations carried out for a
two-level system demonstrate that, with optimization of control parameters, a
substantial gain in the population of reachable states can be realized.


title: Control of entanglement with multipulse application

abstract:
  We show that the multipulse application can suppress the degradation of the
quantum entanglement with focusing on the concurrence, the degree of
entanglement. By evaluating the time evolution of concurrence with a linearly
interacting spin-boson model under pulse application, we find that the
effectiveness of the multipulse control depends on the non-Markovian nature of
the reservoir.


title: Limit Theorem for Continuous-Time Quantum Walk on the Line

abstract:
  Concerning a discrete-time quantum walk X^{(d)}_t with a symmetric
distribution on the line, whose evolution is described by the Hadamard
transformation, it was proved by the author that the following weak limit
theorem holds: X^{(d)}_t /t \to dx / \pi (1-x^2) \sqrt{1 - 2 x^2} as t \to
\infty. The present paper shows that a similar type of weak limit theorems is
satisfied for a {\it continuous-time} quantum walk X^{(c)}_t on the line as
follows: X^{(c)}_t /t \to dx / \pi \sqrt{1 - x^2} as t \to \infty. These
results for quantum walks form a striking contrast to the central limit theorem
for symmetric discrete- and continuous-time classical random walks: Y_{t}/
\sqrt{t} \to e^{-x^2/2} dx / \sqrt{2 \pi} as t \to \infty. The work deals also
with issue of the relationship between discrete and continuous-time quantum
walks. This topic, subject of a long debate in the previous literature, is
treated within the formalism of matrix representation and the limit
distributions are exhaustively compared in the two cases.


title: Pseudo-Hermitian approach to energy-dependent Klein-Gordon models

abstract:
  The relativistic Klein-Gordon system is studied as an illustration of Quantum
Mechanics using non-Hermitian operators as observables. A version of the model
is considered containing a generic coordinate- and energy-dependent
phenomenological mass-term $m^2(E,x)$. We show how similar systems may be
assigned a pair of the linear, energy-independent left- and right-acting
Hamiltonians with quasi-Hermiticity property and, hence, with the standard
probabilistic interpretation.


title: Vibrating Cavities - A numerical approach

abstract:
  We present a general formalism allowing for efficient numerical calculation
of the production of massless scalar particles from vacuum in a one-dimensional
dynamical cavity, i.e. the dynamical Casimir effect. By introducing a
particular parametrization for the time evolution of the field modes inside the
cavity we derive a coupled system of first-order linear differential equations.
The solutions to this system determine the number of created particles and can
be found by means of numerical methods for arbitrary motions of the walls of
the cavity. To demonstrate the method which accounts for the intermode coupling
we investigate the creation of massless scalar particles in a one-dimensional
vibrating cavity by means of three particular cavity motions. We compare the
numerical results with analytical predictions as well as a different numerical
approach.


title:
Effective potential analytic continuation calculations of real time
  quantum correlation functions: Asymmetric systems

abstract:
  We apply the effective potential analytic continuation (EPAC) method to
one-dimensional asymmetric potential systems to obtain the real time quantum
correlation functions at various temperatures. Comparing the EPAC results with
the exact results, we find that for an asymmetric anharmonic oscillator the
EPAC results are in very good agreement with the exact ones at low temperature,
while this agreement becomes worse as the temperature increases. We also show
that the EPAC calculation for a certain type of asymmetric potentials can be
reduced to that for the corresponding symmetric potentials.


title: Spatial non-cyclic geometric phase in neutron interferometry

abstract:
  We present a split-beam neutron interferometric experiment to test the
non-cyclic geometric phase tied to the spatial evolution of the system: the
subjacent two-dimensional Hilbert space is spanned by the two possible paths in
the interferometer and the evolution of the state is controlled by phase
shifters and absorbers. A related experiment was reported previously by some of
the authors [Hasegawa et al., PRA 53, 2486 (1996)] to verify the cyclic spatial
geometric phase. The interpretation of this experiment, namely to ascribe a
geometric phase to this particular state evolution, has met severe criticism
[Wagh, PRA 59, 1715 (1999)]. The extension to non-cyclic evolution manifests
the correctness of the interpretation of the previous experiment by means of an
explicit calculation of the non-cyclic geometric phase in terms of paths on the
Bloch-sphere. The theoretical treatment comprises the cyclic geometric phase as
a special case, which is confirmed by experiment.


title: Hawking radiation in an electro-magnetic wave-guide?

abstract:
  It is demonstrated that the propagation of electro-magnetic waves in an
appropriately designed wave-guide is (for large wave-lengths) analogous to that
within a curved space-time -- such as around a black hole. As electro-magnetic
radiation (e.g., micro-weaves) can be controlled, amplified, and detected (with
present-day technology) much easier than sound, for example, we propose a
set-up for the experimental verification of the Hawking effect. Apart from
experimentally testing this striking prediction, this would facilitate the
investigation of the trans-Planckian problem. PACS: 04.70.Dy, 04.80.-y,
42.50.-p, 84.40.Az.


title: Distant Entanglement of Macroscopic Gas Samples

abstract:
  One of the main ingredients in most quantum information protocols is a
reliable source of two entangled systems. Such systems have been generated
experimentally several years ago for light but has only in the past few years
been demonstrated for atomic systems. None of these approaches however involve
two atomic systems situated in separate environments. This is necessary for the
creation of entanglement over arbitrary distances which is required for many
quantum information protocols such as atomic teleportation. We present an
experimental realization of such distant entanglement based on an adaptation of
the entanglement of macroscopic gas samples containing about 10^11 cesium atoms
shown previously by our group. The entanglement is generated via the
off-resonant Kerr interaction between the atomic samples and a pulse of light.
The achieved entanglement distance is 0.35m but can be scaled arbitrarily. The
feasibility of an implementation of various quantum information protocols using
macroscopic samples of atoms has therefore been greatly increased. We also
present a theoretical modeling in terms of canonical position and momentum
operators X and P describing the entanglement generation and verification in
presence of decoherence mechanisms.


title:
A simple example of "Quantum Darwinism": Redundant information storage
  in many-spin environments

abstract:
  As quantum information science approaches the goal of constructing quantum
computers, understanding loss of information through decoherence becomes
increasingly important. The information about a system that can be obtained
from its environment can facilitate quantum control and error correction.
Moreover, observers gain most of their information indirectly, by monitoring
(primarily photon) environments of the "objects of interest." Exactly how this
information is inscribed in the environment is essential for the emergence of
"the classical" from the quantum substrate. In this paper, we examine how
many-qubit (or many-spin) environments can store information about a single
system. The information lost to the environment can be stored redundantly, or
it can be encoded in entangled modes of the environment. We go on to show that
randomly chosen states of the environment almost always encode the information
so that an observer must capture a majority of the environment to deduce the
system's state. Conversely, in the states produced by a typical decoherence
process, information about a particular observable of the system is stored
redundantly. This selective proliferation of "the fittest information" (known
as Quantum Darwinism) plays a key role in choosing the preferred, effectively
classical observables of macroscopic systems. The developing appreciation that
the environment functions not just as a garbage dump, but as a communication
channel, is extending our understanding of the environment's role in the
quantum-classical transition beyond the traditional paradigm of decoherence.


title: Indispensable Role of Quantum Theory in the Brain Dynamics

abstract:
  Recently, Tegmark pointed out that the superposition of ion states involved
in the superposition of firing and resting states of a neuron quickly decohere.
It undoubtedly indicates that neural networks cannot work as quantum computers,
or computers taking advantage of coherent states. Does it also mean that the
brain can be modeled as a neural network obeying classical physics? Here we
show that it does not mean that the brain can be modeled as a neural network
obeying classical physics. A brand new perspective in research of neural
networks from quantum theoretical aspect is presented.


title:
Nonexponential decay of an unstable quantum system: Small-$Q$-value
  s-wave decay

abstract:
  We study the decay process of an unstable quantum system, especially the
deviation from the exponential decay law. We show that the exponential period
no longer exists in the case of the s-wave decay with small $Q$ value, where
the $Q$ value is the difference between the energy of the initially prepared
state and the minimum energy of the continuous eigenstates in the system. We
also derive the quantitative condition that this kind of decay process takes
place and discuss what kind of system is suitable to observe the decay.


title: Quantum algorithms for a set of group theoretic problems

abstract:
  We study two group theoretic problems, GROUP INTERSECTION and DOUBLE COSET
MEMBERSHIP, in the setting of black-box groups, where DOUBLE COSET MEMBERSHIP
generalizes a set of problems, including GROUP MEMBERSHIP, GROUP FACTORIZATION,
and COSET INTERSECTION. No polynomial-time classical algorithms are known for
these problems. We show that for solvable groups, there exist efficient quantum
algorithms for GROUP INTERSECTION if one of the underlying solvable groups has
a smoothly solvable commutator subgroup, and for DOUBLE COSET MEMBERSHIP if one
of the underlying solvable groups is smoothly solvable. We also study the
decision versions of STABILIZER and ORBIT COSET, which generalizes GROUP
INTERSECTION and DOUBLE COSET MEMBERSHIP, respectively. We show that they
reduce to ORBIT COSET under certain conditions. Finally, we show that DOUBLE
COSET MEMBERSHIP and DOUBLE COSET NONMEMBERSHIP have zero knowledge proof
systems.


title: On the q-analogue of the hydrogen atom

abstract:
  The discrete spectrum of a q-analogue of the hydrogen atom is obtained from a
deformation of the Pauli equations. As an alternative, the spectrum is derived
from a deformation of the four-dimensional oscillator arising in the
application of the Kustaanheimo-Stiefel transformation to the hydrogen atom. A
model of the 2s-2p Dirac shift is proposed in the context of q-deformations.

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


title:
Quantum state transfer via the ferromagnetic chain in a spatially
  modulated field

abstract:
  We show that a perfect quantum state transmission can be realized through a
spin chain possessing a commensurate structure of energy spectrum, which is
matched with the corresponding parity. As an exposition of the mirror inversion
symmetry discovered by Albanese et. al (quant-ph/0405029), the parity matched
the commensurability of energy spectra help us to present the novel
pre-engineered spin systems for quantum information transmission. Based on the
these theoretical analysis, we propose a protocol of near-perfect quantum state
transfer by using a ferromagnetic Heisenberg chain with uniform coupling
constant, but an external parabolic magnetic field. The numerical results shows
that the initial Gaussian wave packet in this system with optimal field
distribution can be reshaped near-perfectly over a longer distance.


title: Linear optics implementation of weak values in Hardy's paradox

abstract:
  We propose an experimental setup for the implementation of weak measurements
in the context of the gedankenexperiment known as Hardy's Paradox. As Aharonov
et al. showed, these weak values form a language with which the paradox can be
resolved. Our analysis shows that this language is indeed consistent and
experimentally testable. It also reveals exactly how a combination of weak
values can give rise to an apparently paradoxical result.


title: Atomic diffraction by a thin phase grating

abstract:
  We present a semiclassical perturbation method for the description of atomic
diffraction by a weakly modulated potential. It proceeds in a way similar to
the treatment of light diffraction by a thin phase grating, and consists in
calculating the atomic wavefunction by means of action integrals along the
classical trajectories of the atoms in the absence of the modulated part of the
potential. The capabilities and the validity condition of the method are
illustrated on the well-known case of atomic diffraction by a Gaussian standing
wave. We prove that in this situation the perturbation method is equivalent to
the Raman-Nath approximation, and we point out that the usually-considered
Raman-Nath validity condition can lead to inaccuracies in the evaluation of the
phases of the diffraction amplitudes. The method is also applied to the case of
an evanescent wave reflection grating, and an analytical expression for the
diffraction pattern at any incidence angle is obtained for the first time.
Finally, the application of the method to other situations is briefly
discussed.


title: Entanglement of degenerate ground state for spin 1 and 1/2 pair

abstract:
  We study the entanglement feature of the ground state of a system composed of
spin 1 and 1/2 parts. The concurrence vector is shown to be consistent with the
measurement of von Neumann entropy for such system. In the light of the ground
state degeneracy, we suggest a average concurrence to measure the entanglement
of Hilbert subspace. The entanglement property of both a general superposition
as well as the mixture of the degenerate ground states are discussed by means
of average concurrence and the negativity respectively.


title: A modulated mirror for atomic interferometry

abstract:
  A novel atomic beam splitter, using reflection of atoms off an evanescent
light wave, is investigated theoretically. The intensity or frequency of the
light is modulated in order to create sidebands on the reflected de Broglie
wave. The weights and phases of the various sidebands are calculated using
three different approaches: the Born approximation, a semiclassical path
integral approach, and a numerical solution of the time-dependent Schr\"odinger
equation. We show how this modulated mirror could be used to build practical
atomic interferometers.


title: Separability analyses of two-qubit density matrices

abstract:
  We pursue a number of analytical directions, motivated to some extent
initially by the possibility of developing a methodology for formally proving
or disproving a certain conjecture of quantum-theoretical relevance
(quant-ph/0308037). It asserts that the 15-dimensional volume occupied by the
separable two-qubit density matrices is (\sqrt{2}-1)/3, as measured in terms of
the statistical distinguishability metric (four times the Bures or minimal
monotone metric). Somewhat disappointingly, however, the several various
analyses that we report, though we hope of independent/autonomous interest,
appear to provide small indication of how to definitively resolve the
conjecture. Among our studies here are ones of: (1) the Bures volumes of the
two-dimensional sections of Bloch vectors for a number of the
Jakobczyk-Siennicki two-qubit scenarios; (2) the structure of certain convex
polytopes of separable density matrices; and (3) the diagonalization of 15 x 15
Bures metric tensors.


title:
Selective coherence transfers in homonuclear dipolar coupled spin
  systems

abstract:
  Mapping the physical dipolar Hamiltonian of a solid-state network of nuclear
spins onto a system of nearest-neighbor couplings would be extremely useful for
a variety of quantum information processing applications, as well as NMR
structural studies. We demonstrate such a mapping for a system consisting of an
ensemble of spin pairs, where the coupling between spins in the same pair is
significantly stronger than the coupling between spins on different pairs. An
amplitude modulated RF field is applied on resonance with the Larmor frequency
of the spins, with the frequency of the modulation matched to the frequency of
the dipolar coupling of interest. The spin pairs appear isolated from each
other in the regime where the RF power (omega_1) is such that omega_weak <<
omega_1 << omega_strong. Coherence lifetimes within the two-spin system are
increased from 19 us to 11.1 ms, a factor of 572.


title: Operational distance and fidelity for quantum channels

abstract:
  We define and study a fidelity criterion for quantum channels, which we term
the minimax fidelity, through a noncommutative generalization of maximal
Hellinger distance between two positive kernels in classical probability
theory. Like other known fidelities for quantum channels, the minimax fidelity
is well-defined for channels between finite-dimensional algebras, but it also
applies to a certain class of channels between infinite-dimensional algebras
(explicitly, those channels that possess an operator-valued Radon--Nikodym
density with respect to the trace in the sense of Belavkin--Staszewski) and
induces a metric on the set of quantum channels which is topologically
equivalent to the CB-norm distance between channels, precisely in the same way
as the Bures metric on the density operators associated with statistical states
of quantum-mechanical systems, derived from the well-known fidelity
(`generalized transition probability') of Uhlmann, is topologically equivalent
to the trace-norm distance.


title: Control Theoretical Approach to Quantum Control

abstract:
  We derive the quantum stochastic master equation for bosonic systems without
measurement theory but control theory. It is shown that the quantum effect of
the measurement can be represented as the correlation between dynamical and
measurement noise. The transfer function representation allows us to analyze a
dynamical uncertainty relation which imposes strong constraints on the dynamics
of the linear quantum systems. In particular, quantum systems preserving the
minimum uncertainty are uniquely determined. For large spin systems, it is
shown that local dynamics are equivalent to bosonic systems. Considering global
behavior, we find quantum effects to which there is no classical counterparts.
A control problem of producing maximal entanglement is discussed as the
stabilization of a filtering process.


title:
Quantum dynamics of a model for two Josephson-coupled Bose--Einstein
  condensates

abstract:
  In this work we investigate the quantum dynamics of a model for two
single-mode Bose--Einstein condensates which are coupled via Josephson
tunneling. Using direct numerical diagonalisation of the Hamiltonian, we
compute the time evolution of the expectation value for the relative particle
number across a wide range of couplings. Our analysis shows that the system
exhibits rich and complex behaviours varying between harmonic and non-harmonic
oscillations, particularly around the threshold coupling between the
delocalised and self-trapping phases. We show that these behaviours are
dependent on both the initial state of the system as well as regime of the
coupling. In addition, a study of the dynamics for the variance of the relative
particle number expectation and the entanglement for different initial states
is presented in detail.


title:
Algorithm-Based Analysis of Collective Decoherence in Quantum
  Computation

abstract:
  The information in quantum computers is often stored in identical two-level
systems (spins or pseudo-spins) that are separated by a distance shorter than
the characteristic wavelength of a reservoir which is responsible for
decoherence. In such a case, the collective spin-reservoir interaction, rather
than an individual spin-reservoir interaction, may determine the decoherence
characteristics. We use computational basis states, symmetrized spin states and
spin coherent states to study collective decoherence in the implementation of
various quantum algorithms. A simple method of implementing quantum algorithms
using stable subradiant states and avoiding unstable Dicke's superradiant
states and Schrodinger's cat states is proposed.


title: Scalar Field Fluctuations between Parallel Plates

abstract:
  Quantum fluctuations of a scalar field and its derivatives are calculated
when the field is confined between two parallel plates satisfying Dirichlet or
Neumann boundary conditions. After regulation these fluctuations diverge in
general when one approaches one of the plates. The energy density and the
pressure between the plates is only consistent with the total Casimir energy
when the canonical energy-momentum tensor is augmented by the Huggins term so
to satisfy the requirement of conformal invariance for a massless, scalar
field.


title: On the notion of a macroscopic quantum system

abstract:
  It is proposed to define "quantumness" of a system (micro or macroscopic,
physical, biological, social, political) by starting with understanding that
quantum mechanics is a statistical theory. It says us only about probability
distributions. The only possible criteria of quantum behaviour are statistical
ones. Therefore I propose to consider any system which produces quantum
statistics as quantum ("quantumlike"). A possible test is based on the
interference of probabilities. I was mainly interested in using such an
approach to "quantumness" to extend the domain of applications of quantum
mathematical formalism and especially to apply it to cognitive sciences. There
were done experiments on interference of probabilities for ensembles of
students and a nontrivial interference was really found. One could say that the
quantum statistical behaviour might be expected. But the problem was not so
trivial. Yes, we might expect nonclassical statistics, but there was no reason
to get the quantum one, i.e., cos-interference. But we got it!


title:
Entanglement properties of multipartite entangled states under the
  influence of decoherence

abstract:
  We investigate entanglement properties of multipartite states under the
influence of decoherence. We show that the lifetime of (distillable)
entanglement for GHZ-type superposition states decreases with the size of the
system, while for a class of other states -namely all graph states with
constant degree- the lifetime is independent of the system size. We show that
these results are largely independent of the specific decoherence model and are
in particular valid for all models which deal with individual couplings of
particles to independent environments, described by some quantum optical master
equation of Lindblad form. For GHZ states, we derive analytic expressions for
the lifetime of distillable entanglement and determine when the state becomes
fully separable. For all graph states, we derive lower and upper bounds on the
lifetime of entanglement. To this aim, we establish a method to calculate the
spectrum of the partial transposition for all mixed states which are diagonal
in a graph state basis. We also consider entanglement between different groups
of particles and determine the corresponding lifetimes as well as the change of
the kind of entanglement with time. This enables us to investigate the behavior
of entanglement under re-scaling and in the limit of large (infinite) number of
particles. Finally we investigate the lifetime of encoded quantum superposition
states and show that one can define an effective time in the encoded system
which can be orders of magnitude smaller than the physical time. This provides
an alternative view on quantum error correction and examples of states whose
lifetime of entanglement (between groups of particles) in fact increases with
the size of the system.


title: NMR Quantum Information Processing

abstract:
  Nuclear Magnetic Resonance (NMR) has provided a valuable experimental testbed
for quantum information processing (QIP). Here, we briefly review the use of
nuclear spins as qubits, and discuss the current status of NMR-QIP. Advances in
the techniques available for control are described along with the various
implementations of quantum algorithms and quantum simulations that have been
performed using NMR. The recent application of NMR control techniques to other
quantum computing systems are reviewed before concluding with a description of
the efforts currently underway to transition to solid state NMR systems that
hold promise for scalable architectures.


title: Encoding multiple quantum coherences in non-commuting bases

abstract:
  Multiple quantum coherences are typically characterised by their coherence
number and the number of spins that make up the state, though only the
coherence number is normally measured. We present a simple set of measurements
that extend our knowledge of the multiple quantum state by recording the
coherences in both the $x$ basis and the usual $z$ basis. The coherences in the
two bases are related by a similarity transformation. We characterize the
growth of the multiple quantum coherences via measurements in the two bases,
and show that the rate varies with the coefficient of the driving term in the
Hamiltonian. Such measurements in non-commuting bases provides additional
information over the 1D method about the state of the spin system. In
particular the measurement of coherences in a basis other than the usual $z$
basis allows us to study the dynamics of the spin system under Hamiltonians,
such as the secular dipolar Hamiltonian, that conserve $z$ basis coherence
number.


title: Labels for non-individuals

abstract:
  Quasi-set theory is a first order theory without identity, which allows us to
cope with non-individuals in a sense. A weaker equivalence relation called
``indistinguishability'' is an extension of identity in the sense that if $x$
is identical to $y$ then $x$ and $y$ are indistinguishable, although the
reciprocal is not always valid. The interesting point is that quasi-set theory
provides us a useful mathematical background for dealing with collections of
indistinguishable elementary quantum particles. In the present paper, however,
we show that even in quasi-set theory it is possible to label objects that are
considered as non-individuals. We intend to prove that individuality has
nothing to do with any labelling process at all, as suggested by some authors.
We discuss the physical interpretation of our results.


title:
Resonances and adiabatic invariance in classical and quantum scattering
  theory

abstract:
  We discover that the energy-integral of time-delay is an adiabatic invariant
in quantum scattering theory and corresponds classically to the phase space
volume. The integral thus found provides a quantization condition for
resonances, explaining a series of results recently found in non-relativistic
and relativistic regimes. Further, a connection between statistical quantities
like quantal resonance-width and classical friction has been established with a
classically deterministic quantity, the stability exponent of an adiabatically
perturbed periodic orbit. This relation can be employed to estimate the rate of
energy dissipation in finite quantum systems.


title: All-fibre source of amplitude-squeezed light pulses

abstract:
  An all-fibre source of amplitude squeezed solitons utilizing the self-phase
modulation in an asymmetric Sagnac interferometer is experimentally
demonstrated. The asymmetry of the interferometer is passively controlled by an
integrated fibre coupler, allowing for the optimisation of the noise reduction.
We have carefully studied the dependence of the amplitude noise on the
asymmetry and the power launched into the Sagnac interferometer. Qualitatively,
we find good agreement between the experimental results, a semi-classical
theory and earlier numerical calculations [Schmitt etl.al., PRL Vol. 81,
p.2446, (1998)]. The stability and flexibility of this all-fibre source makes
it particularly well suited to applications in quantum information science.


title:
On a Stroboscopic Approach to Quantum Tomography of Qudits Governed by
  Gaussian Semigroups

abstract:
  In this paper, we discuss the minimal number of observables, where
expectation values at some time instant determine the trajectory of a d-level
quantum system ("qudit") governed by the Gaussian semigroup. We assume that the
macroscopic information about the system in question is given by the mean
values of n selfadjoint operators $Q_1,...,Q_n$ at some time instants
$t_1<t_2<...<t_r$, where $n<d^2-1$ and $r\leq {\rm deg} \mu(\lambda,\bBBL)$.
Here $\mu(\lambda,\bBBL)$ stands for the minimal polynomial of the generator of
the Gaussian flow.


title: Entanglement swapping without joint Measurement

abstract:
  We propose an entanglement swapping scheme in cavity QED. In the scheme, the
previously used joint measurement is not needed. The entanglement swapping in
our proposal is a non-post-selection one, i.e., after the swapping is done, the
swapped entanglement is still there.


title:
Reversible addition circuit using one ancillary bit with application to
  quantum computing

abstract:
  Most of the work on implementing arithmetic on a quantum computer has
borrowed from results in classical reversible computing (e.g. [VBE95], [BBF02],
[DKR04]). These quantum networks are inherently classical, as they can be
implemented with only the Toffoli gate. Draper [D00] has proposed an inherently
"quantum" network for addition based on the quantum Fourier transform. His
approach has the advantage that it requires no carry qubits (the previous
approaches required O(n) carry qubits). The network in [D00] uses quantum
rotation gates, which must either be implemented with exponential precision, or
else be approximated. In this paper I give a network of O(n^3) Toffoli gates
for reversibly performing in-place addition with only a single ancillary bit,
demonstrating that inherently quantum techniques are not required to achieve
this goal (provided we are willing to sacrifice quadratic circuit depth). After
posting the original version of this note it was pointed out to me by C. Zalka
that essentially the same technique for addition was used in [BCD+96]. The
scenario in that paper was different, but it is clear how the technique they
described generalizes to that in this paper.


title:
Robustness of multi-qubit entanglement in the independent decoherence
  model

abstract:
  We study the robustness of the GHZ (or ``cat'') class of multi-partite states
under decoherence. The noise model is described by a general completely
positive map for qubits independently coupled to the environment. In
particular, the robustness of N-party entanglement is studied in the large N
limit when (a) the number of spatially separated subsystems is fixed but the
size of each subsystem becomes large (b) the size of the subsystems is fixed
while their number becomes arbitrarily large. We obtain conditions for
entanglement in these two cases. Among our other results, we show that the
parity of an entangled state (i.e., whether it contains an even or odd number
of qubits) can lead to qualitatively different robustness of entanglement under
certain conditions.


title: Quantum correlations in bound-soliton pairs and trains in fiber lasers

abstract:
  Quantum correlations in pairs and arrays (trains) of bound solitons modeled
by the complex Ginzburg-Landau equation (CGLE) are calculated numerically, on
the basis of linearized equations for quantum fluctuations. We find strong
correlations between the bound solitons, even though the system is dissipative.
Some degree of the correlation between the photon-number fluctuations of stable
bound soliton pairs and trains is attained and saturates after passing a
certain distance. The saturation of the photon-number correlations is explained
by the action of non- conservative terms in the CGLE. Photon-number-correlated
bound soliton trains offer novel possibilities to produce multipartite
entangled sources for quantum communication and computation.


title:
Continuous ensembles and the $\chi$-capacity of infinite-dimensional
  channels

abstract:
  The paper is devoted to systematic study of the $\chi$-capacity (underlying
the classical capacity) of infinite dimensional quantum channels. An essential
feature of this case is the natural appearance of the input constraints and
infinite, in general, ``continuous'' state ensembles, defined as probability
measures on the set of all quantum states. By using compactness criteria from
probability theory and operator theory it is shown that the set of all
generalized ensembles with the average (barycenter) in a compact set of states
is itself a compact subset of the set of all probability measures. With this in
hand we give a sufficient condition for the existence of an optimal generalized
ensemble for a constrained quantum channel. This condition can be verified in
the case of Bosonic Gaussian channels with constrained mean energy. The
importance of the above condition is shown by considering example of a
constrained channel with no optimal generalized ensemble. In the case of convex
constraints a characterization of the optimal generalized ensemble is obtained
extending the `` maximal distance'' property.


title: Chaotic imaging in frequency downconversion

abstract:
  We analyze and realize the recovery, by means of spatial intensity
correlations, of the image obtained by a seeded frequency downconversion
process in which the seed field is chaotic and an intensity modulation is
encoded on the pump field. Although the generated field is as chaotic as the
seed field and does not carry any information about the modulation of the pump,
an image of the pump can be extracted by measuring the spatial intensity
correlations between the generated field and one Fourier component of the seed.


title: Quantum Theory: Interpretation Cannot be Avoided

abstract:
  This essay is a response to the (March 2000) Physics Today Opinion article
"Quantum Theory Needs No Interpretation" by Fuchs and Peres. It was written
several years ago and has been collecting electronic dust ever since Physics
Today said they weren't interested. We post it here with the hope that it may
still be of some interest.


title:
Exploiting the randomness of the measurement basis in quantum
  cryptography: Secure Quantum Key Growing without Privacy Amplification

abstract:
  We suggest that the randomness of the choices of measurement basis by Alice
and Bob provides an additional important resource for quantum cryptography. As
a specific application, we present a novel protocol for quantum key
distribution (QKD) which enhances the BB84 scheme by encrypting the information
sent over the classical channel during key sifting. We show that, in the limit
of long keys, this process prevents an eavesdropper from reproducing the
sifting process carried out by the legitimate users. The inability of the
eavesdropper to sift the information gathered by tapping the quantum channel
reduces the amount of information that an eavesdropper can gain on the sifted
key. We further show that the protocol proposed is self sustaining, and thus
allows the growing of a secret key.


title: Spinor representation of Lie algebra for complete linear group

abstract:
  Spinor representation of group GL(4,R) on special spinor space is developed.
Representation space has a structure of the fiber space with the space of
diagonal metricses as the base and standard spinor space as typical fiber.
  Non-isometric motions of the space-time entail spinor transformations which
are represented by translation over fibering base in addition to standard
$Spin(4,C)$ representation.


title: Wigner Rotations and Iwasawa Decompositions in Polarization Optics

abstract:
  Wigner rotations and Iwasawa decompositions are manifestations of the
internal space-time symmetries of massive and massless particles, respectively.
It is shown to be possible to produce combinations of optical filters which
exhibit transformations corresponding to Wigner rotations and Iwasawa
decompositions. This is possible because the combined effects of rotation,
phase-shift, and attenuation filters lead to transformation matrices of the
six-parameter Lorentz group applicable to Jones vectors and Stokes parameters
for polarized light waves. The symmetry transformations in special relativity
lead to a set of experiments which can be performed in optics laboratories.


title: Exact results for `bouncing' Gaussian wave packets

abstract:
  We consider time-dependent Gaussian wave packet solutions of the Schrodinger
equation (with arbitrary initial central position, x_0, and momentum, p_0, for
an otherwise free-particle, but with an infinite wall at x=0, so-called
bouncing wave packets. We show how difference or mirror solutions of the form
psi(x,t)-psi(-x,t) can, in this case, be normalized exactly, allowing for the
evaluation of a number of time-dependent expectation values and other
quantities in closed form. For example, we calculate <p^2>_t explicitly which
illustrates how the free-particle kinetic (and hence total) energy is affected
by the presence of the distant boundary. We also discuss the time dependence of
the expectation values of position, <x>_t, and momentum, <p>_t, and their
relation to the impulsive force during the `collision' with the wall. Finally,
the x_0,p_0 --> 0 limit is shown to reduce to a special case of a non-standard
free-particle Gaussian solution. The addition of this example to the literature
then expands on the relatively small number of Gaussian solutions to quantum
mechanical problems with familiar classical analogs (free particle, uniform
acceleration, harmonic oscillator, unstable oscillator, and uniform magnetic
field) available in closed form.


title: Generalized Quantum Walk in Momentum Space

abstract:
  We consider a new model of quantum walk on a one-dimensional momentum space
that includes both discrete jumps and continuous drift. Its time evolution has
two stages; a Markov diffusion followed by localized dynamics. As in the well
known quantum kicked rotor, this model can be mapped into a localized
one-dimensional Anderson model. For exceptional (rational) values of its scale
parameter, the system exhibits resonant behavior and reduce to the usual
discrete time quantum walk on the line.


title: Is repulsive Casimir force physical?

abstract:
  The Casimir force for charge-neutral, perfect conductors of non-planar
geometric configurations have been investigated. The configurations are: (1)
the plate-hemisphere, (2) the hemisphere-hemisphere and (3) the spherical
shell. The resulting Casimir forces for these physical arrangements have been
found to be attractive. The repulsive Casimir force found by Boyer for a
spherical shell is a special case requiring stringent material property of the
sphere, as well as the specific boundary conditions for the wave modes inside
and outside of the sphere. The necessary criteria in detecting Boyer's
repulsive Casimir force for a sphere are discussed at the end of this
investigation.


title: Information Measures for Inferring Quantum Mechanics

abstract:
  Starting from the Hamilton-Jacobi equation describing a classical ensemble,
one may infer a quantum dynamics using the principle of maximum uncertainty.
That procedure requires an appropriate measure of uncertainty: Such a measure
is constructed here from physically motivated constraints. It leads to a unique
single parameter extension of the classical dynamics that is equivalent to the
usual linear quantum mechanics.


title: Two questions on quantum statistics

abstract:
  The determination of a quantum observable from the first and second moments
of its measurement outcome statistics is investigated. Operational conditions
for the moments of a probability measure are given which suffice to determine
the probability measure. Differential operators are shown to lead to physically
relevant cases where the expectation values of large classes of noncommuting
observables do not distinguish superpositions of states and, in particular,
where the full moment information does not determine the probability measure.


title:
Principle of supplementarity: contextual probabilistic viewpoint to
  interference, complementarity and incompatibility

abstract:
  There is presented a contextual statistical model of the probabilistic
description of physical reality. Here contexts (complexes of physical
conditions) are considered as basic elements of reality. There is discussed the
relation with QM. We propose a realistic analogue of Bohr's principle of
complementarity. In the opposite to the Bohr's principle, our principle has no
direct relation with mutual exclusivity for observables. To distinguish our
principle from the Bohr's principle and to give better characterization, we
change the terminology and speak about supplementarity, instead of
complementarity. Supplementarity is based on the interference of probabilities.
It has quantitative expression trough a coefficient which can be easily
calculated from experimental statistical data.
  We need not appeal to the Hilbert space formalism and noncommutativity of
operators representing observables. Moreover, in our model there exists pairs
of supplementary observables which can not be represented in the complex
Hilbert space. There are discussed applications of the principle of
supplementarity outside quantum physics.


title:
Representation of the contextual statistical model by hyperbolic
  amplitudes

abstract:
  We continue the development of a so called contextual statistical model (here
context has the meaning of a complex of physical conditions). It is shown that,
besides contexts producing the conventional trigonometric $\cos$-interference,
there exist contexts producing the hyperbolic $\cos$-interference. Starting
with the corresponding interference formula of total probability we represent
such contexts by hyperbolic probabilistic amplitudes or in the abstract
formalism by normalized vectors of a hyperbolic analogue of the Hilbert space.
There is obtained a hyperbolic Born's rule. Incompatible observables are
represented by noncommutative operators.


title: Periodic square-well potential and spontaneous breakdown of PT-symmetry

abstract:
  A particle moving on a circle in a purely imaginary one-step potential is
studied in both the exact and broken $PT$-symmetric regime.