title:
The 1/N-expansion, quantum-classical correspondence and nonclassical
  states generation in dissipative higher-order anharmonic oscillators

abstract:
  We develop a method for the determination of thecdynamics of dissipative
quantum systems in the limit of large number of quanta N, based on the
1/N-expansion of Heidmann et al. [ Opt. Commun. 54, 189 (1985) ] and the
quantum-classical correspondence. Using this method, we find analytically the
dynamics of nonclassical states generation in the higher-order anharmonic
dissipative oscillators for an arbitrary temperature of a reservoir. We show
that the quantum correction to the classical motion increases with time
quadratically up to some maximal value, which is dependent on the degree of
nonlinearity and a damping constant, and then it decreases. Similarities and
differences with the corresponding behavior of the quantum corrections to the
classical motion in the Hamiltonian chaotic systems are discussed. We also
compare our results obtained for some limiting cases with the results obtained
by using other semiclassical tools and discuss the conditions for validity of
our approach.

categories: quant-ph chao-dyn nlin.CD physics.optics


title: On the Disentanglement of States

abstract:
  Disentanglement is the process which transforms a state $\rho$ of two
subsystems into an unentangled state, while not effecting the reduced density
matrices of each of the two subsystems. Recently Terno showed that an arbitrary
state cannot be disentangled into a tensor product of its reduced density
matrices. In this letter we present various novel results regarding
disentanglement of states. Our main result is that there are sets of states
which cannot be successfuly disentangled (not even into a separable state).
Thus, we prove that a universal disentangling machine cannot exist.


title: All Optical Quantum Teleportation

abstract:
  We propose an all optical, continuous variable, quantum teleportation scheme
based on optical parametric amplifiers.


title: Quantum key distribution with authentication

abstract:
  The security of the previous quantum key distribution (QKD) protocols, which
is guaranteed by the nature of physics law, is based on the legitimate users.
However, impersonation of the legitimate communicators by eavesdroppers, in
practice, will be inevitable. In fact, the previous QKD protocols is unsecure
without authentication in practical communication. In this paper, we proposed
an improved QKD protocol that can simultaneously distribute the quantum secret
key and verify the communicators' identity. This presented authentication
scheme is provably secure.


title:
Heterodyne and adaptive phase measurements on states of fixed mean
  photon number

abstract:
  The standard technique for measuring the phase of a single mode field is
heterodyne detection. Such a measurement may have an uncertainty far above the
intrinsic quantum phase uncertainty of the state. Recently it has been shown
[H. M. Wiseman and R. B. Killip, Phys. Rev. A 57, 2169 (1998)] that an adaptive
technique introduces far less excess noise. Here we quantify this difference by
an exact numerical calculation of the minimum measured phase variance for the
various schemes, optimized over states with a fixed mean photon number. We also
analytically derive the asymptotics for these variances. For the case of
heterodyne detection our results disagree with the power law claimed by
D'Ariano and Paris [Phys. Rev. A 49, 3022 (1994)].


title: TSQT `Elements of Possibility'?

abstract:
  I defend my arguments in quant-ph/9806002, which have recently been
criticized by L. Vaidman (quant-ph/9811092). I emphasize that the correct usage
of the ABL rule applies not to a genuine counterfactual statement but rather to
a conjunction of material conditionals. I argue that the only kind of valid
counterfactual statement one can make using the ABL rule is a ``might''
counterfactual, which is not adequate for the attribution of `elements of
reality' to a quantum system.


title: Laser Induced Condensation of Trapped Bosonic Gases

abstract:
  We demonstrate that an appropriate sequence of laser pulses allows to
condense a gas of trapped bosonic atoms into an arbitrary trap level.
  Such condensation is robust, can be achieved in experimentally feasible
traps, and may lead to multistability and hysteresis phenomena.


title: A family of complex potentials with real spectrum

abstract:
  We consider a two-parameter non hermitean quantum-mechanical hamiltonian that
is invariant under the combined effects of parity and time reversal
transformation. Numerical investigation shows that for some values of the
potential parameters the hamiltonian operator supports real eigenvalues and
localized eigenfunctions. In contrast with other PT symmetric models, which
require special integration paths in the complex plane, our model is integrable
along a line parallel to the real axis.


title: New perturbation method with the matching of wave functions

abstract:
  We propose a new approach to the Rayleigh-Schr\"{o}dinger perturbation
expansions of bound states in quantum mechanics. We are inspired by the
enormous flexibility of solvable interactions with several (N) discontinuities.
Their standard matching solution is modified and transferred in perturbation
regime. We employ the global renormalization freedom of the local wave
functions and derive a compact N-dimensional matrix formula for corrections. In
applications, our recipe is shown non-numerical for all polynomial
perturbations of any piece-wise constant zero order potential.


title: Adaptive Quantum Homodyne Tomography

abstract:
  An adaptive optimization technique to improve precision of quantum homodyne
tomography is presented. The method is based on the existence of so-called null
functions, which have zero average for arbitrary state of radiation. Addition
of null functions to the tomographic kernels does not affect their mean values,
but changes statistical errors, which can then be reduced by an optimization
method that "adapts" kernels to homodyne data. Applications to tomography of
the density matrix and other relevant field-observables are studied in detail.


title: Locality Is An Unnecessary Assumption of Bell's Theorem

abstract:
  Without imposing the locality condition,it is shown that quantum mechanics
cannot reproduce all the predictions of a special stochastic realistic model
used in certain spin-correlation experiments.This shows that the so-called
locality condition is an unnecessary assumption of Bell's theorem.


title: Quantum cryptography with polarizing interferometers

abstract:
  Cryptographic scheme proposed by Bennett, Brassard, and Mermin [Phys. Rev.
Lett. {\bf 68}, 557 (1992)] is reformulated in a version involving two
polarizing Mach-Zehnder interferometers. Such a form, although physically
equivalent to the original one, makes its security explicit, suggestive and
easy to explain to non-experts.


title: Modified "delta kick cooling" for studies of atomic tunneling

abstract:
  We present progress towards a planned experiment on atomic tunneling of
ultra-cold Rb atoms. As a first step in this experiment we present a
realization of an improved form of "delta-kick cooling." By application of a
pulsed magnetic field, laser cooled Rb atoms are further cooled by a factor of
10 (in 1-D) over the temperature out of molasses. Temperatures below 700 nK are
observed. The technique can be used not only to cool without fundamental limit
(but conserving phase-space density), but also to focus atoms, and as a
spin-dependent probe.


title: NQP_{C} = co-C_{=}P

abstract:
  Adleman, DeMarrais, and Huang introduced the nondeterministic quantum
polynomial-time complexity class NQP as an analogue of NP. Fortnow and Rogers
implicitly showed that, when the amplitudes are rational numbers, NQP is
contained in the complement of C_{=}P. Fenner, Green, Homer, and Pruim improved
this result by showing that, when the amplitudes are arbitrary algebraic
numbers, NQP coincides with co-C_{=}P. In this paper we prove that, even when
the amplitudes are arbitrary complex numbers, NQP still remains identical to
co-C_{=}P. As an immediate corollary, BQP differs from NQP when the amplitudes
are unrestricted.


title:
Individual addressing and state readout of trapped ions utilizing rf-
  micromotion

abstract:
  A new scheme for the individual addressing of ions in a trap is described
that does not rely on light beams tightly focused onto only one ion. The scheme
utilizes ion micromotion that may be induced in a linear trap by dc offset
potentials. Thus coupling an individual ion to the globally applied light
fields corresponds to a mere switching of voltages on a suitable set of
compensation electrodes. The proposed scheme is especially suitable for
miniaturized rf (Paul) traps with typical dimensions of about 20-40 microns.


title: On the general problem of quantum phase estimation

abstract:
  The problem of estimating a generic phase-shift experienced by a quantum
state is addressed for a generally degenerate phase shift operator. The optimal
positive operator-valued measure is derived along with the optimal input state.
Two relevant examples are analyzed: i) a multi-mode phase shift operator for
multipath interferometry; ii) the two mode heterodyne phase detection.


title: Strategies and Networks for State-Dependent Quantum Cloning

abstract:
  State-dependent cloning machines that have so far been considered either
deterministically copy a set of states approximately, or probablistically copy
them exactly. In considering the case of two equiprobable pure states, we
derive the maximum global fidelity of $N$ approximate clones given $M$ initial
exact copies, where $N>M$. We also consider strategies which interpolate
between approximate and exact cloning. A tight inequality is obtained which
expresses a trade-off between the global fidelity and success probability. This
inequality is found to tend, in the limit as $N{\to}{\infty}$, to a known
inequality which expresses the trade-off between error and inconclusive result
probabilities for state-discrimination measurements. Quantum-computational
networks are also constructed for the kinds of cloning machine we describe. For
this purpose, we introduce two gates: the distinguishability transfer and state
separation gates. Their key properties are described


title: Radiation reaction in quantum mechanics

abstract:
  The Lorentz-Dirac radiation reaction formula predicts that the position shift
of a charged particle due to the radiation reaction is of first order in
acceleration if it undergoes a small acceleration. A semi-classical calculation
shows that this is impossible at least if the acceleration is due to a
time-independent potential. Thus, the Lorentz-Dirac formula gives an incorrect
classical limit in this situation. The correct classical limit of the position
shift at the lowest order in acceleration is obtained by assuming that the
energy loss at each time is given by the Larmor formula.


title: Quantum Computation

abstract:
  In the last few years, theoretical study of quantum systems serving as
computational devices has achieved tremendous progress. We now have strong
theoretical evidence that quantum computers, if built, might be used as a
dramatically powerful computational tool. This review is about to tell the
story of theoretical quantum computation. I left out the developing topic of
experimental realizations of the model, and neglected other closely related
topics which are quantum information and quantum communication. As a result of
narrowing the scope of this paper, I hope it has gained the benefit of being an
almost self contained introduction to the exciting field of quantum
computation.
  The review begins with background on theoretical computer science, Turing
machines and Boolean circuits. In light of these models, I define quantum
computers, and discuss the issue of universal quantum gates. Quantum
algorithms, including Shor's factorization algorithm and Grover's algorithm for
searching databases, are explained. I will devote much attention to
understanding what the origins of the quantum computational power are, and what
the limits of this power are. Finally, I describe the recent theoretical
results which show that quantum computers maintain their complexity power even
in the presence of noise, inaccuracies and finite precision. I tried to put all
results in their context, asking what the implications to other issues in
computer science and physics are. In the end of this review I make these
connections explicit, discussing the possible implications of quantum
computation on fundamental physical questions, such as the transition from
quantum to classical physics.


title: Unitary relations in time-dependent harmonic oscillators

abstract:
  For a harmonic oscillator with time-dependent (positive) mass and frequency,
an unitary operator is shown to transform the quantum states of the system to
those of a harmonic oscillator system of unit mass and time-dependent
frequency, as well as operators. For a driven harmonic oscillator, it is also
shown that, there are unitary transformations which give the driven system from
the system of same mass and frequency without driving force. The transformation
for a driven oscillator depends on the solution of classical equation of motion
of the driven system. These transformations, thus, give a simple way of finding
exact wave functions of a driven harmonic oscillator system, provided the
quantum states of the corresponding system of unit mass are given.


title:
Large-order Perturbation Theory for a Non-Hermitian PT-symmetric
  Hamiltonian

abstract:
  A precise calculation of the ground-state energy of the complex PT-symmetric
Hamiltonian $H=p^2+{1/4}x^2+i \lambda x^3$, is performed using high-order
Rayleigh-Schr\"odinger perturbation theory. The energy spectrum of this
Hamiltonian has recently been shown to be real using numerical methods. The
Rayleigh-Schr\"odinger perturbation series is Borel summable, and Pad\'e
summation provides excellent agreement with the real energy spectrum. Pad\'e
analysis provides strong numerical evidence that the once-subtracted
ground-state energy considered as a function of $\lambda^2$ is a Stieltjes
function. The analyticity properties of this Stieltjes function lead to a
dispersion relation that can be used to compute the imaginary part of the
energy for the related real but unstable Hamiltonian $H=p^2+{1/4}x^2-\epsilon
x^3$.


title: Enhanced Diffusion and the Continuous Spontaneous Localization Model

abstract:
  We find an analogy between turbulence and the dynamics of the continuous
spontaneous localization model (CSL) of the wave function. The use of a
standard white noise in the localization process gives Richardson's t^3 law for
the turbulent diffusion, while the introduction of an affine noise in the CSL
allows us to obtain the intermittency corrections to this law.


title:
An algebraic construction of the coherent states of the Morse potential
  based on SUSY QM

abstract:
  By introducing the shape invariant Lie algebra spanned by the SUSY ladder
operators plus the unity operator, a new basis is presented for the quantum
treatment of the one-dimensional Morse potential. In this discrete, complete
orthonormal set, which we call the pseudo number states, the Morse Hamiltonian
is tridiagonal. By using this basis we construct coherent states algebraically
for the Morse potential, in a close analogy with the harmonic oscillator. We
also show that there exists an unitary displacement operator creating these
coherent states from the ground state. We show that our coherent states form a
continuous and overcomplete set of states. They coincide with a class of states
constructed earlier by Nieto and Simmons by using the coordinate
representation. \pacs{3.65.Fd, 02.20.Sv, 42.50.-p}


title:
Is the Statistical Interpretation of Quantum Mechanics Implied by the
  Correspondence Principle ?

abstract:
  The classical limit of the Schrodinger equation implies the orthodox
statistical interpretation for degrees of freedom in finite-dimensional
subspaces of the full Hilbert space, but the argument presented does not imply
the Born interpretation for degrees of freedom that have a classical
counterpart.


title: Endoscopic Tomography and Quantum-Non-Demolition

abstract:
  We propose to measure the quantum state of a single mode of the radiation
field in a cavity---the signal field---by coupling it via a
quantum-non-demolition Hamiltonian to a meter field in a highly squeezed state.
We show that quantum state tomography on the meter field using balanced
homodyne detection provides full information about the signal state. We discuss
the influence of measurement of the meter on the signal field.


title: Decoherence and fidelity in ion traps with fluctuating trap parameters

abstract:
  We consider two different kinds of fluctuations in an ion trap potential:
external fluctuating electrical fields, which cause statistical movement
(``wobbling'') of the ion relative to the center of the trap, and fluctuations
of the spring constant, which are due to fluctuations of the ac-component of
the potential applied in the Paul trap for ions. We write down master equations
for both cases and, averaging out the noise, obtain expressions for the heating
of the ion. We compare our results to previous results for far-off resonance
optical traps and heating in ion traps. The effect of fluctuating external
electrical fields for a quantum gate operation (controlled-NOT) is determined
and the fidelity for that operation derived.


title: Coherence properties of the stochastic oscillator

abstract:
  An oscillator with stochastic frequency is discussed as a model for
evaluating the quantum coherence properties of a physical system. It is found
that the choice of jump statistics has to be considered with care if unphysical
consequences are to be avoided. We investigate one such model, evaluate the
damping it causes, the decoherence rate and the correlations it results in and
the properties of the state for asymptotically long times. Also the choice of
initial state is discussed and its effect on the time evolution of the
correlations.


title: Impediments to mixing classical and quantum dynamics

abstract:
  The dynamics of systems composed of a classical sector plus a quantum sector
is studied. We show that, even in the simplest cases, (i) the existence of a
consistent canonical description for such mixed systems is incompatible with
very basic requirements related to the time evolution of the two sectors when
they are decoupled. (ii) The classical sector cannot inherit quantum
fluctuations from the quantum sector. And, (iii) a coupling among the two
sectors is incompatible with the requirement of physical positivity of the
theory, i.e., there would be positive observables with a non positive
expectation value.


title: Long-time-scale revivals in ion traps

abstract:
  In this contribution we investigate the interaction of a single ion in a trap
with laser beams. Our approach, based on unitary transformating the
Hamiltonian, allows its exact diagonalization without performing the Lamb-Dicke
approximation. We obtain a transformed Jaynes-Cummings type Hamiltonian, and we
demonstrate the existence of super-revivals in that system.


title: Matrix elements for a generalized spiked harmonic oscillator

abstract:
  Closed-form expressions for the singular-potential integrals <m| x^-alpha |n>
are obtained with respect to the Gol'dman and Krivchenkov eigenfunctions for
the singular potential V(x) = B x^2 + A/x^2, B > 0, A >= 0. These formulas are
generalizations of those found earlier by use of the odd solutions of the
Schroedinger equation with the harmonic oscillator potential [Aguilera-Navarro
et al, J. Math. Phys. 31, 99 (1990)].


title: Single-Step Quantum Search Using Problem Structure

abstract:
  The structure of satisfiability problems is used to improve search algorithms
for quantum computers and reduce their required coherence times by using only a
single coherent evaluation of problem properties. The structure of random k-SAT
allows determining the asymptotic average behavior of these algorithms, showing
they improve on quantum algorithms, such as amplitude amplification, that
ignore detailed problem structure but remain exponential for hard problem
instances. Compared to good classical methods, the algorithm performs better,
on average, for weakly and highly constrained problems but worse for hard
cases. The analytic techniques introduced here also apply to other quantum
algorithms, supplementing the limited evaluation possible with classical
simulations and showing how quantum computing can use ensemble properties of NP
search problems.


title: Why Quantum Mechanics is Hard to Understand

abstract:
  To understand the foundations of quantum mechanics, we have to think
carefully about how theoretical concepts are rooted in -- and limited by -- the
nature of experience, as Bohr attempted to show. Geometrical pictures of
physical phenomena are favored because of their clarity. Quantum phenomena,
however, do not permit them. Instead, the historical and dynamical aspects of
description diverge and must be expressed in different but complementary
languages. Objective historical facts are recorded in terms of objects, which
necessarily have an imprecise, empirical quality. Dynamics is based on
quantitative abstraction from recurring patterns. The "quantum of action" is
the discontinuity between these two ways of looking at the physical world.


title: Random Hamiltonian Models and Quantum Prediction Algorithms

abstract:
  This paper describes an algorithm for selecting a consistent set within the
consistent histories approach to quantum mechanics and investigates its
properties. The algorithm select from among the consistent sets formed by
projections defined by the Schmidt decomposition by making projections at the
earliest possible time. The algorithm unconditionally predicts the possible
events in closed quantum systems and ascribes probabilities to these events. A
simple random Hamiltonian model is described and the results of applying the
algorithm to this model using computer programs are discussed and compared with
approximate analytic calculations.


title: Automated 'plug & play' quantum key distribution

abstract:
  An improved "plug & play" interferometric system for quantum key distribution
is presented. Self-alignment and compensation of birefringence remain, while
limitations due to reflections are overcome. Original electronics implementing
the BB84 protocol makes adjustment simple. Key creation with 0.1 photon per
pulse at a rate of 325 Hz with a 2.9 percent QBER - corresponding to a net rate
of 210Hz - over a 23 Km installed cable was performed.


title:
Two-photon Franson-type interference experiments are not tests of local
  realism

abstract:
  We report a local hidden-variable model which reproduces quantum predictions
for the two-photon interferometric experiment proposed by Franson [Phys. Rev.
Lett. 62, 2205 (1989)]. The model works for the ideal case of full visibility
and perfect detection efficiency. This result changes the interpretation of a
series of experiments performed in the current decade.


title:
Scattering of dislocated wavefronts by vertical vorticity and the
  Aharonov-Bohm effect I: Shallow water

abstract:
  When a surface wave interacts with a vertical vortex in shallow water the
latter induces a dislocation in the incident wavefronts that is analogous to
what happens in the Aharonov-Bohm effect for the scattering of electrons by a
confined magnetic field. In addition to this global similarity between these
two physical systems there is scattering. This paper reports a detailed
calculation of this scattering, which is quantitatively different from the
electronic case in that a surface wave penetrates the inside of a vortex while
electrons do not penetrate a solenoid. This difference, together with an
additional difference in the equations that govern both physical systems lead
to a quite different scattering in the case of surface waves, whose main
characteristic is a strong asymmetry in the scattering cross section. The
assumptions and approximations under which these effects happen are carefully
considered, and their applicability to the case of scattering of acoustic waves
by vorticity is noted.


title:
Scattering of dislocated wavefronts by vertical vorticity and the
  Aharonov-Bohm effect II: Dispersive waves

abstract:
  Previous results on the scattering of surface waves by vertical vorticity on
shallow water are generalized to the case of dispersive water waves. Dispersion
effects are treated perturbatively around the shallow water limit, to first
order in the ratio of depth to wavelength. The dislocation of the incident
wavefront, analogous to the Aharonov-Bohm effect, is still observed. At short
wavelengths the scattering is qualitatively similar to the nondispersive case.
At moderate wavelengths, however, there are two markedly different scattering
regimes according to wether the capillary length is smaller or larger than
$\sqrt{3}$ times depth. The dislocation is characterized by a parameter that
depends both on phase and group velocity. The validity range of the calculation
is the same as in the shallow water case: wavelengths small compared to vortex
radius, and low Mach number. The implications of these limitations are
carefully considered.


title:
Determining Acceptance Possibility for a Quantum Computation is Hard for
  the Polynomial Hierarchy

abstract:
  It is shown that determining whether a quantum computation has a non-zero
probability of accepting is at least as hard as the polynomial time hierarchy.
This hardness result also applies to determining in general whether a given
quantum basis state appears with nonzero amplitude in a superposition, or
whether a given quantum bit has positive expectation value at the end of a
quantum computation. This result is achieved by showing that the complexity
class NQP of Adleman, Demarrais, and Huang, a quantum analog of NP, is equal to
the counting class coC$_=$P.


title:
A Limit on the Speed of Quantum Computation for Insertion into an
  Ordered List

abstract:
  We consider the problem of inserting a new item into an ordered list of N-1
items. The length of an algorithm is measured by the number of comparisons it
makes between the new item and items already on the list. Classically,
determining the insertion point requires log N comparisons. We show that, for N
large, no quantum algorithm can reduce the number of comparisons below log N/(2
loglog N).


title: Constructive inversion of energy trajectories in quantum mechanics

abstract:
  We suppose that the ground-state eigenvalue E = F(v) of the Schroedinger
Hamiltonian H = -\Delta + vf(x) in one dimension is known for all values of the
coupling v > 0. The potential shape f(x) is assumed to be symmetric, bounded
below, and monotone increasing for x > 0. A fast algorithm is devised which
allows the potential shape f(x) to be reconstructed from the energy trajectory
F(v). Three examples are discussed in detail: a shifted power-potential, the
exponential potential, and the sech-squared potential are each reconstructed
from their known exact energy trajectories.


title: Why Bohm's Quantum Theory?

abstract:
  This is a brief reply to Goldstein's article on ``Quantum Theory Without
Observers'' in Physics Today. It is pointed out that Bohm's pilot wave theory
is successful only because it keeps Schr\"odinger's (exact) wave mechanics
unchanged, while the rest of it is observationally meaningless and solely based
on classical prejudice.


title: Sampling Fourier Transforms on Different Domains

abstract:
  We isolate and generalize a technique implicit in many quantum algorithms,
including Shor's algorithms for factoring and discrete log. In particular, we
show that the distribution sampled after a Fourier transform over ${\mathbb
Z}_p$ can be efficiently approximated by transforming over ${\mathbb Z}_q$ for
any q in a large range. Our result places no restrictions on the superposition
to be transformed, generalizing the result implicit in Shor which applies only
to periodic superpositions. In addition, our proof easily generalizes to
multi-dimensional transforms for any constant number of dimensions.


title: Searching an Ordered List on a Quantum Computer

abstract:
  Withdrawn by the author due to irreparable errors.
  We present a quantum algorithm that in the black-box model performs a search
in an ordered list of N elements. Using 3/4 log N + O(1) queries, it achieves a
success probability of at least 1/2, whereas classically, log N - O(1) queries
are needed to obtain constant success probability. Moreover, our algorithm
employs the Haar transform and thus differs substantially from Grover's search
algorithm and from algorithms relying on the quantum Fourier transform.


title:
Accessible information and optimal strategies for real symmetrical
  quantum sources

abstract:
  We study the problem of optimizing the Shannon mutual information for sources
of real quantum states i.e. sources for which there is a basis in which all the
states have only real components. We consider in detail the sources ${\cal
E}_M$ of $M$ equiprobable qubit states lying symmetrically around the great
circle of real states on the Bloch sphere and give a variety of explicit
optimal strategies. We also consider general real group-covariant sources for
which the group acts irreducibly on the subset of all real states and prove the
existence of a real group-covariant optimal strategy, extending a theorem of
Davies (E. B. Davies, IEEE. Inf. Theory {\bf IT-24}, 596 (1978)). Finally we
propose an optical scheme to implement our optimal strategies, enough simple to
be realized with present technology.


title: Variational Perturbation Theory for Density Matrices

abstract:
  We develop convergent variational perturbation theory for quantum statistical
density matrices. The theory is applicable to polynomial as well as
nonpolynomial interactions. Illustrating the power of the theory, we calculate
the temperature-dependent density of a particle in a double-well and of the
electron in a hydrogen atom.


title: A simple eavesdropping strategy of BB84 protocol

abstract:
  A simplified eavesdropping-strategy for BB84 protocol in quantum cryptography
(refer to quant-ph/9812022) is proposed. This scheme implements by the
`indirect copying' technology. Under this scheme, eavesdropper can exactly
obtain the exchanged information between the legitimate users without being
detected.


title: On binary constructions of quantum codes

abstract:
  Using the notion of generalized weight we improve estimates on the parameters
of quantum codes obtained by Steane's construction from binary codes. This
yields several new families of quantum codes.


title:
On discrete symmetry for spin 1/2 and spin 1 particles in external
  monopole field and quantum-mechanical property of self-conjugacy

abstract:
  Particles of spin 1/2 and 1 in external Abelian monopole field are
considered. P-inversion like operators N-s commuting with the respective
Hamiltonians are constructed: N(bisp.) is diagonalized onto the relevant wave
functions, whereas N(vect.) does not. Such a paradox is rationalized through
noting that both these operators are not self-conjugate. It is shown that any
N-parity selection rules cannot be produced. Non-Abelian problems for doublets
of spin 1/2 and 1 particles are briefly discussed; the statement is given of
that corresponding discrete operators are self-conjugate and selection rules
are available.


title:
The doublet of Dirac fermions in the field of the non-Abelia monopole
  and parity selection rules

abstract:
  The paper concerns a problem of Dirac fermion doublet in the external
monopole potential arisen out of embedding the Abelian monopole solution in the
non-Abe- lian scheme. In this particular case, the Hamiltonian is invariant
under some symmetry operations consisting of an Abelian subgroup in the complex
rotational group SO(3.C). This symmetry results in a certain (A)-freedom in
choosing a discrete operator entering the complete set {H, j^{2}, j_{3}, N(A),
K} . The same complex number A represents a parameter of the wave functions
constructed. The generalized inversion-like operator N(A) implies its own
(A-dependent) de- finition for scalar and pseudoscalar, and further affords
some generalized N(A)-parity selection rules. It is shown that all different
sets of basis func- tions Psi(A) determine the same Hilbert space. In
particular, the functions Psi(A) decompose into linear combinations of
Psi(A=0). However, the bases con- sidered turn out to be nonorthogonal ones
when A is not real number; the latter correlates with the non-self-conjugacy
property of the operator N(A) at those A-s.
  (This is a shortened version of the paper).


title: Optimal minimal measurements of mixed states

abstract:
  The optimal and minimal measuring strategy is obtained for a two-state system
prepared in a mixed state with a probability given by any isotropic a priori
distribution. We explicitly construct the specific optimal and minimal
generalized measurements, which turn out to be independent of the a priori
probability distribution, obtaining the best guesses for the unknown state as
well as a closed expression for the maximal mean averaged fidelity. We do this
for up to three copies of the unknown state in a way which leads to the
generalization to any number of copies, which we then present and prove.


title: Phase-dependent spectra in a driven two-level atom

abstract:
  We propose a method to observe phase-dependent spectra in resonance
fluorescence, employing a two-level atom driven by a strong coherent field and
a weak, amplitude-fluctuating field. The spectra are similar to those which
occur in a squeezed vacuum, but avoid the problem of achieving squeezing over a
$4\pi $ solid angle. The system shows other interesting features, such as
pronounced gain without population inversion.


title:
Polynomial-Time Solution to the Hidden Subgroup Problem for a Class of
  non-abelian Groups

abstract:
  We present a family of non-abelian groups for which the hidden subgroup
problem can be solved efficiently on a quantum computer.


title: Large Spins in External Fields

abstract:
  Spectra and magnetic properties of large spins $J$, placed into a crystal
electric field (CEF) of an arbitrary symmetry point group, are shown to change
drastically when $J$ changes by 1/2 or 1. At a fixed field symmetry and
configuration of its $N$ extrema situated at $p$-fold symmetry axis, physical
characteristics of the spin depend periodically on $J$ with the period equal to
$p$. The problem of the spectrum and eigenstates of the large spin $J$ is
equivalent to analogous problem for a scalar charged particle confined to a
sphere $S^2$ and placed into magnetic field of the monopole with the charge
$J$. This analogy as well as strong difference between close values of $J$
stems from the Berry's phase occurring in the problem. For energies close to
the extrema of the CEF, the problem can be formulated as Harper's equation on
the sphere. The $2J+1$-dimensional space of states is splitted into smaller
multiplets of classically degenerated states. These multiplets in turn are
splitted into submultiplets of states transforming according to specific
irreducible representations of the symmetry group determined by $J$ and $p$. We
classify possible configurations and corresponding spectra. Experimental
realizations of large spins in a symmetric environment are proposed and
physical effects observable in these systems are analyzed.


title: EPR Correlations as an Angular Hanbury-Brown--Twiss Effect

abstract:
  It is shown that EPR correlations are the angular analogue to the
Hanbury-Brown--Twiss effect. As insight provided by this model, it is seen
that, analysis of the EPR experiment requires conditional probabilities which
do not admit the derivation of Bell inequalities.


title:
Validity of Feynman's prescription of disregarding the Pauli principle
  in intermediate states

abstract:
  Regarding the Pauli principle in quantum field theory and in many-body
quantum mechanics, Feynman advocated that Pauli's exclusion principle can be
completely ignored in intermediate states of perturbation theory. He observed
that all virtual processes (of the same order) that violate the Pauli principle
cancel out. Feynman accordingly introduced a prescription, which is to
disregard the Pauli principle in all intermediate processes. This ingeneous
trick is of crucial importance in the Feynman diagram technique. We show,
however, an example in which Feynman's prescription fails. This casts doubts on
the general validity of Feynman's prescription.


title:
Two definitions of the electric polarizability of a bound system in
  relativistic quantum theory

abstract:
  For the electric polarizability of a bound system in relativistic quantum
theory, there are two definitions that have appeared in the literature. They
differ depending on whether or not the vacuum background is included in the
system. A recent confusion in this connection is clarified.


title: Optimal purification of single qubits

abstract:
  We introduce a new decomposition of the multiqubit states of the form
$\rho^{\otimes N}$ and employ it to construct the optimal single qubit
purification procedure. The same decomposition allows us to study optimal
quantum cloning and state estimation of mixed states.


title:
Is an optimal quantum cloner the best choice for local copying in
  broadcasting entanglement?

abstract: The paper is temporarily withdrawn by the authors.


title:
Extension Of Bertrand's Theorem And Factorization Of The Radial
  Schr\"odinger Equation

abstract:
  The Bertrand's theorem is extended, i.e. closed orbits still may exist for
other central potentials than the power law Coulomb potential and isotropic
harmonic oscillator. It is shown that for the combined potential
$V(r)=W(r)+b/r^2$ ($W(r)=ar^{\nu}$), when (and only when) $W(r)$ is the Coulomb
potential or isotropic harmonic oscillator, closed orbits still exist for
suitable angular momentum. The correspondence between the closeness of
classical orbits and the existence of raising and lowering operators derived
from the factorization of the radial Schr\"odinger equation is investigated.


title: Decoherence and continuous measurements: Phenomenology and models

abstract:
  Decoherence of a quantum system induced by the interaction with its
environment (measuring medium) may be presented phenomenologically as a
continuous (or repeated) fuzzy quantum measurement. The dynamics of the system
subject to continuous decoherence (measurement) may be described by the
complex-Hamiltonian Schroedinger equation, stochastic Schroedinger equation of
a certain type or (nonselectively) by the Lindblad master equation. The
formulation of this dynamics with the help of restricted path integrals shows
that the dynamics of the measured system depends only on the information
recorded in the environment. With the help of the complex-Hamiltonian
Schroedinger equation, monitoring a quantum transition is shown to be possible,
at the price of decreasing the transition probability (weak Zeno effect). The
monitoring of the level transition may be realized by a long series of short
weak observations of the system which resulting in controllable slow
decoherence.


title:
Magnetic Trapping of Neutral Particles: A Study of a Physically
  Realistic Model

abstract:
  We study, both classically and quantum-mechanically, the problem of a neutral
particle with spin S, mass m and magnetic moment mue, moving in two-dimensions
in an inhomogeneous magnetic field given by B_x=B'*x; B_y=-B'*y; B_z=B;
  We identify K, the ratio between the precessional frequency of the particle
and its vibration frequency, as the relevant parameter of the problem.
  Classicaly, we find that when the magnetic moment is antiparallel to B, the
particle is trapped provided that K<sqrt{4/27}. We also find that viscous
friction, be it translational or precessional, destabilizes the system.
  Quantum-mechanically, we study the problem of spin S=h_bar/2 particle in the
same field. Treating K as a small parameter for the perturbation from the
adiabatic Hamiltonian, we find that the lifetime T_esc of the particle in its
trapped ground-state is T_esc={T_vib}/{128 pi^2} * exp{2/K} where T_vib is the
classical period of the particle when placed in the adiabatic potential V=mue
*|B(x,y)|


title: Dispersion in Femtosecond Entangled Two-Photon Interference

abstract:
  We theoretically investigate the quantum interference of entangled two-photon
states generated in a nonlinear crystal pumped by femtosecond optical pulses.
Interference patterns generated by the polarization analog of the
Hong-Ou-Mandel interferometer are studied. Attention is devoted to the effects
of the pump-pulse profile (pulse duration and chirp) and the second-order
dispersion in both the nonlinear crystal and the interferometer's optical
elements. Dispersion causes the interference pattern to have an asymmetric
shape. Dispersion cancellation occurs in some cases.


title: A Way Out of the Quantum Trap

abstract:
  We review Event Enhanced Quantum Theory (EEQT). In Section 1 we address the
question "Is Quantum Theory the Last Word". In particular we respond to some of
recent challenging staments of H.P. Stapp. We also discuss a possible future of
the quantum paradigm - see also Section 5. In Section 2 we give a short sketch
of EEQT. Examples are given in Section 3. Section 3.3 discusses a completely
new phenomenon - chaos and fractal-like phenomena caused by a simultaneous
"measurement" of several non-commuting observables (we include picture of
Barnsley's IFS on unit sphere of a Hilbert space). In Section 4 we answer
"Frequently Asked Questions" concerning EEQT.


title: Quantum entanglements and entangled mutual entropy

abstract:
  The mathematical structure of quantum entanglement is studied and classified
from the point of view of quantum compound states. We show that t he
classical-quantum correspondences such as encodings can be treated as dia gonal
(d-) entanglements. The mutual entropy of the d-compound and entangled states
lead to two different types of entropies for a given quantum state: t he von
Neumann entropy, which is achieved as the supremum of the information over all
d-entanglements, and the dimensional entropy, which is achieved at the standard
entanglement, the true quantum entanglement, coinciding with a d-entanglement
only in the case of pure marginal states. The q-capacity of a quantum noiseless
channel, defined as the supremum over all entanglements, i s given by the
logarithm of the dimensionality of the input algebra. It doub les the classical
capacity, achieved as the supremum over all d-entanglement s (encodings), which
is bounded by the logarithm of the dimensionality of a maximal Abelian
subalgebra.


title: Narrow resonances with excitation of finite bandwidth field

abstract:
  The effect of the laser linewidth on the resonance fluorescence spectrum of a
two-level atom is revisited. The novel spectral features, such as hole-burning
and dispersive profiles at line centre of the fluorescence spectrum are
predicted when the laser linewidth is much greater than its intensity. The
unique features result from quantum interference between different
dressed-state transition channels.


title:
Optimal squeezing, pure states, and amplification of squeezing in
  resonance fluorescence

abstract:
  It is shown that 100% squeezed output can be produced in the resonance
fluorescence from a coherently driven two-level atom interacting with a
squeezed vacuum. This is only possible for $N=1/8$ squeezed input, and is
associated with a pure atomic state, i.e., a completely polarized state. The
quadrature for which optimal squeezing occurs depends on the squeezing phase
$\Phi ,$ the Rabi frequency $\Omega ,$ and the atomic detuning $\Delta $. Pure
states are described for arbitrary $\Phi ,$ not just $\Phi =0$ or $\pi $ as in
previous work. For small values of $N,$ there may be a greater degree of
squeezing in the output field than the input - i.e., we have squeezing
amplification.


title:
Measuring the entangled Bell and GHZ aspects using a single-qubit
  shuttle

abstract:
  A complete, non-demolition procedure is established for measuring multi-qubit
entangled states, such as the Bell-states and the GHZ-states, which is
essential in certain processes of quantum communication, computation, and
teleportation. No interaction between the individual parts of the entangled
system, nor with any environment is required. A small probe (e.g. a single
qubit) takes care of all interaction with the system, and is used repeatedly.
The probe-qubit interaction is of the simplest form, and only this one type of
interaction is required to perform a complete measurement. The process may be
divided into elementary local operations and interactions, taking place
sequentially as the probe visits each of the qubits. A shuttle mode is
described, which may be repeated indefinitely. By the quantum Zeno effect, the
entangled states can be maintained until released in a predictable state. This
shuttle process is stable, and self-correcting, by virtue of the standard
measurements performed repeatedly on the probe.


title:
Principles and Demonstrations of Quantum Information Processing by NMR
  Spectroscopy

abstract:
  This paper surveys our recent research on quantum information processing by
nuclear magnetic resonance (NMR) spectroscopy. We begin with a geometric
introduction to the NMR of an ensemble of indistinguishable spins, and then
show how this geometric interpretation is contained within an algebra of
multispin product operators. This algebra is used throughout the rest of the
paper to demonstrate that it provides a facile framework within which to study
quantum information processing more generally. The implementation of quantum
algorithms by NMR depends upon the availability of special kinds of mixed
states, called pseudo-pure states, and we consider a number of different
methods for preparing these states, along with analyses of how they scale with
the number of spins. The quantum-mechanical nature of processes involving such
macroscopic pseudo-pure states also is a matter of debate, and in order to
discuss this issue in concrete terms we present the results of NMR experiments
which constitute a macroscopic analogue Hardy's paradox. Finally, a detailed
product operator description is given of recent NMR experiments which
demonstrate a three-bit quantum error correcting code, using field gradients to
implement a precisely-known decoherence model.


title: Complete Quantum Communication with Security

abstract:
  The long-standing problem of quantum information processing is to remove the
classical channel from quantum communication. Introducing a new information
processing technique, it is discussed that both insecure and secure quantum
communications are possible without the requirement of classical channel.


title: Quantum correlations are not local elements of reality

abstract:
  I show a situation of multiparticle entanglement which cannot be explained in
the framework of an interpretation of quantum mechanics recently proposed by
Mermin. This interpretation is based on the assumption that correlations
between subsystems of an individual isolated composed quantum system are real
objective local properties of that system.


title: Quantum slow motion

abstract:
  We simulate the center of mass motion of cold atoms in a standing, amplitude
modulated, laser field as an example of a system that has a classical mixed
phase-space. We show a simple model to explain the momentum distribution of the
atoms taken after any distinct number of modulation cycles. The peaks
corresponding to a classical resonance move towards smaller velocities in
comparison to the velocities of the classical resonances. We explain this by
showing that, for a wave packet on the classical resonances, we can replace the
complicated dynamics in the quantum Liouville equation in phase-space by the
classical dynamics in a modified potential. Therefore we can describe the
quantum mechanical motion of a wave packet on a classical resonance by a purely
classical motion.


title: Non-Fuchsian Singularities in Quantum Mechanics

abstract:
  A modification of the spiked harmonic oscillator is studied in the case for
which the perturbation potential contains both an inverse power and a linear
term. It is then possible to evaluate trial functions by solving an integral
equation due to the occurrence of the linear term. The general form of such
integral equation is obtained by using a Green-function method, and adding a
modified Bessel function of second kind which solves an homogeneous problem
with Dirichlet boundary condition at the origin.


title:
The magnetic field generated by an electron bound in angular-momentum
  eigenstates

abstract:
  The magnetic field generated by an electron bound in a spherically symmetric
potential is calculated for eigenstates of the orbital and total angular
momentum. General expressions are presented for the current density in such
states and the magnetic field is calculated through the vector potential, which
is obtained from the current density by direct integration. The method is
applied to the hydrogen atom, for which we reproduce and extend known results.


title: Quantum trajectories of interacting pseudo-spin-networks

abstract:
  We consider quantum trajectories of composite systems as generated by the
stochastic unraveling of the respective Lindblad-master-equation. Their
classical limit is taken to correspond to local jumps between orthogonal
states. Based on statistical distributions of jump- and inter-jump-distances we
are able to quantify the non-classicality of quantum trajectories. To account
for the operational effect of entanglement we introduce the novel concept of
"co-jumps".


title: Absence of Chaos in Bohmian Dynamics

abstract:
  The Bohm motion for a particle moving on the line in a quantum state that is
a superposition of n+1 energy eigenstates is quasiperiodic with n frequencies.


title: Statistics of light in Raman and Brillouin nonlinear couplers

abstract:
  Statistical properties of optical fields in nonlinear couplers composed of
two waveguides in which Raman or Brillouin processes (with classical pumping)
are in operation and which are mutually connected through the Stokes and/or
anti-Stokes linear interactions are investigated within the framework of
generalized superposition of coherent fields and quantum noise. Heisenberg
equations describing the couplers are solved both analytically under special
conditions and numerically in general cases. Regimes for nonclassical
properties of optical fields, such as sub-Poissonian photon-number statistics,
negative reduced moments of integrated intensity and squeezing of quadrature
fluctuations are discussed for the cases of single and compound fields. General
results are compared with those from short-length approximation.


title:
Interplay of creation, propagation, and relaxation of an excitation in a
  dimer

abstract:
  Interplay of simultaneous creation, annihilation, propagation, and relaxation
of an excitation in molecular condensates interacting with an ultrashort
quantum optical pulse is studied in general and specialized to a dimer. A
microscopic model appropriate for such systems (with strong exciton-phonon
coupling) is presented. It also incorporates effects of (quantum) noise in the
optical field. A variety of new features in the initial stage of excitation
dynamics (when it is being created) is revealed; a strong influence of the
coherent excitation propagation on the processes of excitation creation and
annihilation in a molecule strongly interacting with phonons is the most
remarkable one.


abstract:
  This is a review of ``Potentiality, Entanglement and Passion-at-a-Distance:
Quantum Mechanical Studies for Abner Shimony, Volume Two''. The Festschrift
contains contributions from some of the most eminent workers in foundations of
quantum mechanics such as Aharonov, Anandan, Busch, d'Espagnat, Ghirardi,
Hardy, Howard, Mermin, Mittelstaedt, Peres, Popescu, Primas, Redhead, Rimini,
Rohrlich, Stachel, Stein, Vaidman, and Weber (along with a few others). In this
review of the Festschrift I have tried to give an overview (from my own
perspective) of the current state of the foundations of quantum mechanics --
especially with regard to the interpretational problems infesting the theory,
along with comments on several other significant lines of investigation.


title:
Exact Solution of the Energy Shift in each Quantum Mechanical Energy
  Levels in a One Dimensional Symmetrical Linear Harmonic Oscillator

abstract:
  An exact solution of the energy shift in each quantum mechanical energy
levels in a one dimensional symmetrical linear harmonic oscillator has been
investigated. The solution we have used here is firstly derived by manipulating
Schrodinger differential equation to be confluent hypergeometric differential
equation. The final exact numerical results of the energy shifts are then found
by calculating the final analytical solution of the confluent hypergeometric
equation with the use of a software (Mathcad Plus 6.0) or a program programmed
by using Turbo Pascal 7.0. We find that the results of the energy shift in our
exact solution method are almost the same as that in Barton et. al.
approximation method. Thus, the approximation constants (obliquity factors)
appeared in Barton et. al. method can also be calculated using the results of
the exact method.

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


title:
Preparation and measurement: two independent sources of uncertainty in
  quantum mechanics

abstract:
  In the Copenhagen interpretation the Heisenberg uncertainty relation is
interpreted as the mathematical expression of the concept of complementarity,
quantifying the mutual disturbance necessarily taking place in a simultaneous
or joint measurement of incompatible observables. This interpretation has
already been criticized by Ballentine a long time ago, and has recently been
challenged in an experimental way. These criticisms can be substantiated by
using the generalized formalism of positive operator-valued measures, from
which a new inequality can be derived, precisely illustrating the Copenhagen
concept of complementarity. The different roles of preparation and measurement
in creating uncertainty in quantum mechanics are discussed.


title:
The doublet of Dirac fermions in the field of the non-Abelian monopole,
  isotopic chiral symmetry, and parity selection rules

abstract:
  The paper concerns a problem of the Dirac fermion doublet in the external
monopole potential obtained by embedding the Abelian monopole solution in the
non-Abelian scheme. In this case, the doublet-monopole Hamiltonian is invariant
under operations consisting of a complex and one parametric Abelian subgroup in
S0(3.C). This symmetry results in a certain freedom in choosing a discrete
operator N(A) (A is a complex number) entering the complete set of quantum
variables. The same complex number A represents an additional parameter at the
basis functions. The generalized inversion like operator N(A) affords certain
generalized N(A)-parity selection rules. All the different sets of basis
functions Psi(A) determine the same Hilbert space. The functions Psi(A)
decompose into linear combinations of Psi(A=0): Psi(A) = F(A) Psi(A=0).
However, the bases considered turn out to be nonorthogonal ones when A is a
complex number; the latter correlates with the non-self-conjugacy of the N(A)
at complex A-s. The meaning of possibility to violate the quantum-mechanical
regulation on self-conjugacy as regards the operator N(A) is discussed. Also,
the problem of possible physical status for the matrix F(A) at real A-s is
considered in full detail: since the matrix belongs formally to the gauge group
SU(2), but being a symmetry for the Hamiltonian this F(A) generates linear
transformations on basis wave functions.


title: How many functions can be distinguished with k quantum queries?

abstract:
  Suppose an oracle is known to hold one of a given set of D two-valued
functions. To successfully identify which function the oracle holds with k
classical queries, it must be the case that D is at most 2^k. In this paper we
derive a bound for how many functions can be distinguished with k quantum
queries.


title: Questions on the concept of time

abstract:
  Some notes and questions about the concept of time are exposed. Particular
reference is given to the problem in quantum mechanics, in connection with the
indeterminacy principle.


title: Tomographic measurement of nonclassical radiation states

abstract:
  We propose to experimentally test the nonclassicality of quantum states
through homodyne tomography. For single-mode states we check violations of
inequalities involving the photon-number probability. For two-mode states we
test the nonclassicality by reconstructing some suitable number-operator
functions. The test can be performed with available quantum efficiency of
homodyne detection, by measuring the pertaining quantities on the corresponding
noisy states.


title: Operator for Describing Polarization States of a Photon

abstract:
  Based on the quantized electromagnetic field described by the
Riemann-Silberstein complex vector $F$, we construct the eigenvector set of $%
F$, which makes up an orthonormal and complete representation. In terms of $% F
$ we then introduce a new operator which can describe the relative ratio of the
left-handed and right-handed polarization states of a polarized photon .In
$F^{\prime}s$ eigenvector basis the operator manifestly exhibits a behaviour
which is similar to a phase difference between two orientations of polarization
of a light beam in classical optics.


title: Lamb shift calculated by simple noncovariant method

abstract:
  The Lamb Shift (LS) of Hydrogenlike atom is evaluated by a simple method of
quantum electrodynamics in noncovariant form, based on the relativistic
stationary Schr\"odinger equation. An induced term proportional to
$\overrightarrow{p}^4$ in the effective Hamiltonian is emphasized. Perturbative
calculation of second order leads to the LS of $ 1S_{1/2}$ state and that of
$2S_{1/2}-2P_{1/2}$ states in H atom with the high accuracy within 0.1%


title: Thoughts on Commutation Relations and Measurement Accuracy

abstract:
  We show that measuring the trajectories of charged particles to finite
accuracy leads to the commutation relations needed for the derivation of the
free space Maxwell equations using the {\it discrete ordered calculus} (DOC).
We note that the finite step length derivation of the discrete difference
version of the single particle Dirac equation implies the discrete version of
the p,q commutation relations for a free particle. We speculate that a careful
operational analysis of the change in momenta occurring in a step-wise
continuous solution of the discrete Dirac equation could supply the missing
source-sink terms in the DOC derivation of the Maxwell equations, and lead to a
finite and discrete (``renormalized'') quantum electrodynamics (QED).


title:
Comparison among Klein-Gordon equation, Dirac equation and Relativistic
  Stationary Schrodinger equation

abstract:
  A particle is always not pure. It always contains hiding antiparticle
ingredient which is the essence of special relativity. Accordingly, the
Klein-Gordon (KG) equation and Dirac equation are restudied and compared with
the Relativistic Stationary Schr\"odinger Equation (RSSE). When an electron is
bound in a Hydrogenlike atom with pointlike nucleus having charge number $Z$,
the critical value of $Z, Z_c$, equals to 137 in Dirac equation whereas
$Z_c=\sqrt{M/\mu} (137)$ in RSSE with $M$ and $\mu$ being the total mass of
atom and the reduced mass of the electron.


title: Uncertainty principle for proper time and mass

abstract:
  We review Bohr's reasoning in the Bohr-Einstein debate on the photon box
experiment. The essential point of his reasoning leads us to an uncertainty
relation between the proper time and the rest mass of the clock. It is shown
that this uncertainty relation can be derived if only we take the fundamental
point of view that the proper time should be included as a dynamic variable in
the Lagrangian describing the system of the clock. Some problems and some
positive aspects of our approach are then discussed.


title:
Quantum photon emission from a moving mirror in the nonperturbative
  regime

abstract:
  We consider the coupling of the electromagnetic vacuum field with an
oscillating perfectly-reflecting mirror in the nonrelativistic approximation.
As a consequence of the frequency modulation associated to the motion of the
mirror, low frequency photons are generated. We calculate the photon emission
rate by following a nonperturbative approach, in which the coupling between the
field sidebands is taken into account. We show that the usual perturbation
theory fails to account correctly for the contribution of TM-polarized vacuum
fluctuations that propagate along directions nearly parallel to the plane
surface of the mirror.
  As a result of the modification of the field eigenfunctions, the resonance
frequency for photon emission is shifted from its unperturbed value.


title: Searching in Grover's Algorithm

abstract:
  Grover's algorithm is usually described in terms of the iteration of a
compound operator of the form $Q = - H I_{0} H I_{x_0}$. Although it is quite
straightforward to verify the algebra of the iteration, this gives little
insight into why the algorithm works. What is the significance of the compound
structure of $Q$? Why is there a minus sign? Later it was discovered that $H$
could be replaced by essentially any unitary $U$. What is the freedom involved
here? We give a description of Grover's algorithm which provides some
clarification of these questions.


title:
The Quantization of Free EM Fields: An Alternative Approach to solve the
  Vacuum Catastrophe

abstract:
  It is shown that the canonical quantum field theory of radiation based on the
field theoretical generalization of a recently proposed [1] commutation
relation between position and momentum operators of massless particles leads to
zero vacuum energy. This may be considered as a step toward the solution of the
cosmological constant problem at least for the electromagnetic (EM) field's
contribution.


title: Phases of Wave Functions and Level Repulsion

abstract:
  Avoided level crossings are associated with exceptional points which are the
singularities of the spectrum and eigenfunctions, when they are considered as
functions of a coupling parameter. It is shown that the wave function of {\it
one} state changes sign but not the other, if the exceptional point is
encircled in the complex plane. An experimental setup is suggested where this
peculiar phase change could be observed.


title:
Quantum-Classical Complexity-Security Tradeoff In Secure Multi-Party
  Computation

abstract:
  I construct a secure multi-party scheme to compute a classical function by a
succinct use of a specially designed fault-tolerant random polynomial quantum
error correction code. This scheme is secure provided that (asymptotically)
strictly greater than five-sixths of the players are honest. Moreover, the
security of this scheme follows directly from the theory of quantum error
correcting code, and hence is valid without any computational assumption. I
also discuss the quantum-classical complexity-security tradeoff in secure
multi-party computation schemes and argue why a full-blown quantum code is
necessary in my scheme.


title: How to share a quantum secret

abstract:
  We investigate the concept of quantum secret sharing. In a ((k,n)) threshold
scheme, a secret quantum state is divided into n shares such that any k of
those shares can be used to reconstruct the secret, but any set of k-1 or fewer
shares contains absolutely no information about the secret. We show that the
only constraint on the existence of threshold schemes comes from the quantum
"no-cloning theorem", which requires that n < 2k, and, in all such cases, we
give an efficient construction of a ((k,n)) threshold scheme. We also explore
similarities and differences between quantum secret sharing schemes and quantum
error-correcting codes. One remarkable difference is that, while most existing
quantum codes encode pure states as pure states, quantum secret sharing schemes
must use mixed states in some cases. For example, if k <= n < 2k-1 then any
((k,n)) threshold scheme must distribute information that is globally in a
mixed state.


title: Noncomplemetary Wave-Particle Phenomena Revisited

abstract:
  The simultaneous verification of wave and particle property in some recently
suggested experiments has been reviewed in the light of Hilbert space
formalism. In this respect, the recent analysis of biprism experiment [J. L.
Cereceda, Am. J. Phys. 64 (1996) 459] is criticized.


title: Quantum channels of the Einstein-Podolski-Rosen kind

abstract:
  Assume the quantum state of a bipartite system is known. The result of local
von Neumann measurements can be described by maps from one subsystem to the
other one. Main properties of these antilinear ''EPR-channel'' maps are shortly
discussed. Talk in honour of Jan Lopuszanski.


title: Measurement-induced quantum diffusion

abstract:
  The dynamics of a kicked quantum system undergoing repeated measurements of
momentum is investigated. A diffusive behavior is obtained even when the
dynamics of the classical counterpart is not chaotic. The diffusion coefficient
is explicitly computed for a large class of Hamiltonians and compared to the
classical case.


title: A Quantum Observable for the Graph Isomorphism Problem

abstract:
  Suppose we are given two graphs on $n$ vertices. We define an observable in
the Hilbert space $\Co[(S_n \wr S_2)^m]$ which returns the answer ``yes'' with
certainty if the graphs are isomorphic and ``no'' with probability at least
$1-n!/2^m$ if the graphs are not isomorphic. We do not know if this observable
is efficiently implementable.


title: Some general bounds for 1-D scattering

abstract:
  One-dimensional scattering problems are of wide physical interest and are
encountered in many diverse applications. In this article I establish some very
general bounds for reflection and transmission coefficients for one-dimensional
potential scattering. Equivalently, these results may be phrased as general
bounds on the Bogolubov coefficients, or statements about the transfer matrix.
A similar analysis can be provided for the parametric change of frequency of a
harmonic oscillator. A number of specific examples are discussed---in
particular I provide a general proof that sharp step function potentials always
scatter more effectively than the corresponding smoothed potentials. The
analysis also serves to collect together and unify what would otherwise appear
to be quite unrelated results.


title: Uncertainty principle for proper time and mass II

abstract:
  When we quantize a system consisting of a single particle, the proper time
$\tau $ and the rest mass $m$ are usually dealt with as parameters. In the
present article, however, we introduce a new quantization rule by which these
quantities are regarded as operators in addition to the position and the
momentum. Applying this new rule to a scalar particle and to a particle with
spin $ 1/2 $, we analyze the time evolution of the operator $\tau $. In the
former case, the evolution of the proper time perfectly matches several
well-established classical formulae. In the case of the particle with spin 1/2,
our new rule implies that an oscillation appears in the time evolution of the
operator $\tau $. This oscillation is similar to Zitterbewegung which is
well-known in the ordinary Dirac theory. We formulate one physical effect of
this oscillation by considering the interaction with a gravitational field, and
estimate how small it is.


title: Ultracold atoms interacting with a sinusoidal mode of a high-Q cavity

abstract:
  We consider the interaction of two level ultracold atoms resonant with a
sinusoidal mode of the electromagnetic field in a high Q cavity. We found that
well resolved resonances appear in the transmission coefficients even for
actual interaction and cavity parameters. The probability of emission of one
photon and the probability of transmission of an atom, when a number of
coherent states is initially present in the cavity, are discussed. The
interplay between the increasing width of the resonances and multi-peak
steady-state photon-statistics is also studied. Furthermore, we compare our
results with those of a constant field mode.


title: Uncertainty relation of Anandan-Aharonov and Intelligent states

abstract:
  The quantum states which satisfy the equality in the generalised uncertainty
relation are called intelligent states. We prove the existence of intelligent
states for the Anandan-Aharonov uncertainty relation based on the geometry of
the quantum state space for arbitrary parametric evolutions of quantum states
when the initial and final states are non-orthogonal.


title: Hidden Subgroup States are Almost Orthogonal

abstract:
  It is well known that quantum computers can efficiently find a hidden
subgroup $H$ of a finite Abelian group $G$. This implies that after only a
polynomial (in $\log |G|$) number of calls to the oracle function, the states
corresponding to different candidate subgroups have exponentially small inner
product. We show that this is true for noncommutative groups also. We present a
quantum algorithm which identifies a hidden subgroup of an arbitrary finite
group $G$ in only a linear (in $\log |G|$) number of calls to the oracle
function. This is exponentially better than the best classical algorithm.
However our quantum algorithm requires an exponential amount of time, as in the
classical case.


title:
The cost of exactly simulating quantum entanglement with classical
  communication

abstract:
  We investigate the amount of communication that must augment classical local
hidden variable models in order to simulate the behaviour of entangled quantum
systems. We consider the scenario where a bipartite measurement is given from a
set of possibilities and the goal is to obtain exactly the same correlations
that arise when the actual quantum system is measured. We show that, in the
case of a single pair of qubits in a Bell state, a constant number of bits of
communication is always sufficient--regardless of the number of measurements
under consideration. We also show that, in the case of a system of n Bell
states, a constant times 2^n bits of communication are necessary.


title:
Exact Solutions to the Schr\"{o}dinger Equation for the Inverse-Power
  Potential in Two Dimensions

abstract:
  Utilizing an ${\it ansatz}$ for the eigenfunctions, we arrive at an exact
closed form solution to the Schr\"{o}dinger equation with the inverse-power
potential, $V(r)=ar^{-4}+br^{-3}+cr^{-2}+dr^{-1}$ in two dimensions, where the
parameters of the potential $a, b, c, d$ satisfy a constraint.


title:
The Exact Solution to the Schr\"{o}dinger Equation with the Octic
  Potential

abstract:
  The Schr\"{o}dinger equation with the central potential is first studied in
the arbitrary dimensional spaces and obtained an analogy of the two-dimensional
Schr\"{o}dinger equation for the radial wave function through a simple
transformation. As an example, applying an ${\it ansatz}$ to the
eigenfunctions, we then arrive at an exact closed form solution to the modified
two-dimensional Schr\"{o}dinger equation with the octic potential,
$V(r)=ar^2-br^4+cr^6-dr^4+er^{10}$.


title: Multiphoton Coincidence Spectroscopy

abstract:
  We extend the analysis of photon coincidence spectroscopy beyond bichromatic
excitation and two-photon coincidence detection to include multichromatic
excitation and multiphoton coincidence detection. Trichromatic excitation and
three-photon coincidence spectroscopy are studied in detail, and we identify an
observable signature of a triple resonance in an atom-cavity system.


title:
Fibre bundle formulation of nonrelativistic quantum mechanics. IV. Mixed
  states and evolution transport's curvature

abstract:
  We propose a new systematic fibre bundle formulation of nonrelativistic
quantum mechanics. The new form of the theory is equivalent to the usual one
but it is in harmony with the modern trends in theoretical physics and
potentially admits new generalizations in different directions. In it a pure
state of some quantum system is described by a state section (along paths) of a
(Hilbert) fibre bundle. It's evolution is determined through the bundle
(analogue of the) Schr\"odinger equation. Now the dynamical variables and the
density operator are described via bundle morphisms (along paths). The
mentioned quantities are connected by a number of relations derived in this
work.
  The present fourth part of this series is devoted mainly to the fibre bundle
description of mixed quantum states. We show that to the conventional density
operator there corresponds a unique density morphism (along paths) for which
the corresponding equations of motion are derived. It is also investigated the
bundle description of mixed quantum states in the different pictures of motion.
We calculate the curvature of the evolution transport and prove that it is
curvature free iff the values of the Hamiltonian operator at different moments
commute.


title: Barrier traversal times using a phenomenological track formation model

abstract:
  A phenomenological model for a measurement of barrier traversal times for
particles is proposed. Two idealized detectors for passage and arrival provide
entrance and exit times for the barrier traversal. The averaged traversal time
is computed over the ensemble of particles detected twice, before and after the
barrier. The Hartman effect can still be found when passage detectors that
conserve the momentum distribution of the incident packet are used.


title: Average local values and local variances in quantum mechanics

abstract:
  Several definitions for the average local value and local variance of a
quantum observable are examined and compared with their classical counterparts.
An explicit way to construct an infinite number of these quantities is
provided. It is found that different classical conditions may be satisfied by
different definitions, but none of the quantum definitions examined is entirely
consistent with all classical requirements.


title: Phase space formalisms of quantum mechanics with singular kernel

abstract:
  The equivalence of the Rivier-Margenau-Hill and Born-Jordan-Shankara phase
space formalisms to the conventional operator approach of quantum mechanics is
demonstrated. It is shown that in spite of the presence of singular kernels the
mappings relating phase space functions and operators back and forth are
possible.


title:
Quantum cryptography and long distance Bell experiments: How to control
  decoherence

abstract:
  Several mechanisms that affect one and two photon coherence in optical fibers
and their remedies are discussed. The results are illustrated on quantum
cryptography experiments and on long distance Bell inequality tests.


title: Broadband detection of squeezed vacuum: A spectrum of quantum states

abstract:
  We demonstrate the simultaneous quantum state reconstruction of the spectral
modes of the light field emitted by a continuous wave degenerate optical
parametric amplifier. The scheme is based on broadband measurement of the
quantum fluctuations of the electric field quadratures and subsequent Fourier
decomposition into spectral intervals. Applying the standard reconstruction
algorithms to each bandwidth-limited quantum trajectory, a "spectrum" of
density matrices and Wigner functions is obtained. The recorded states show a
smooth transition from the squeezed vacuum to a vacuum state. In the time
domain we evaluated the first order correlation function of the squeezed output
field, showing good agreement with the theory.


title:
Inference of Planck action constant by a classical fluctuative postulate
  holding for stable microscopic and macroscopic dynamical systems

abstract:
  The possibility is discussed of inferring or simulating some aspects of
quantum dynamics by adding classical statistical fluctuations to classical
mechanics. We introduce a general principle of mechanical stability and derive
a necessary condition for classical chaotic fluctuations to affect confined
dynamical systems, on any scale, ranging from microscopic to macroscopic
domains. As a consequence we obtain, both for microscopic and macroscopic
aggregates, dimensional relations defining the minimum unit of action of
individual constituents, yielding in all cases Planck action constant.


title: Einstein-Podolsky-Rosen Paradox and Antiparticle

abstract:
  The original version of Einstein-Podolsky-Rosen (EPR) paradox is discussed to
show the completeness of Quantum Mechanics (QM). The unique solution leads to
the wave function of antiparticle unambiguously, which implies the essential
conformity between QM and Special Relativity (SR).


title: Computation on a Noiseless Quantum Code and Symmetrization

abstract:
  Let ${\cal H}$ be the state-space of a quantum computer coupled with the
environment by a set of error operators spanning a Lie algebra ${\cal L}.$
Suppose ${\cal L}$ admits a noiseless quantum code i.e., a subspace ${\cal
C}\subset{\cal H}$ annihilated by ${\cal L}.$ We show that a universal set of
gates over $\cal C$ is obtained by any generic pair of ${\cal L}$-invariant
gates. Such gates - if not available from the outset - can be obtained by
resorting to a symmetrization with respect to the group generated by ${\cal
L}.$ Any computation can then be performed completely within the coding
decoherence-free subspace.


title: Path Integral on Relativistic Spinless Potential Problems

abstract:
  The formulation of the relativistic spinless path integral on the general
affine space is presented. For the one dimensional space, the Duru-Kleinert
(DK) method and the $\delta $-function perturbation technique are applied to
solve the relativistic path integrals of the smooth potential and the Dirichlet
boundary condition problems, respectively.


title: Quantum Conditions of the Relativistic Potential Problems

abstract:
  The quantum conditions of the relativistic integrable systems whose classical
motion is multiply periodic are given by considering the single-valuedness of
the linear superposition of the approximate solutions $R_{i}\exp
{\{iS_{i}/\hbar \}}$ with $R_{i}$ and $S_{i}$ being the solutions of the
different branches of the current conservation equation and the relativistic
Hamilton-Jacobian equation, respectively.


title: Quantization via Classical Orbits

abstract:
  A systematic method for calculating higher-order corrections of the
relativistic semiclassical fixed-energy amplitude is given. The central scheme
in computing corrections of all orders is related to a time ordering operation
of an operator involving the Van Vleck determinant. This study provides us a
new viewpoint for quantization.


title:
Green's Function of the Relativistic Coulomb System via Duru-Kleinert
  Method

abstract:
  In this paper the fixed-energy amplitude (Green's function) of the
relativistic Coulomb system is solved by Duru-Kleinert (DK) method. In the
course of the calculations we observe an equivalence between the relativistic
Coulomb system and a radial oscillator.


title:
Green's function for the Relativistic Coulomb System via Sum Over
  Perturbation Series

abstract:
  We evaluate the Green's function of the D-dimensional relativistic Coulomb
system via sum over perturbation series which is obtained by expanding the
exponential containing the potential term $V({\bf x)}$ in the path integral
into a power series. The energy spectra and wave functions are extracted from
the resulting amplitude.


title: Optimal Manipulations with Qubits: Universal NOT Gate

abstract:
  It is not a problem to complement a classical bit, i.e. to change the value
of a bit, a 0 to a 1 and vice versa. This is accomplished by a NOT gate.
Complementing a qubit in an unknown state, however, is another matter. We show
that this operation cannot be done perfectly. We define the Universal-NOT
(U-NOT) gate which out of N identically prepared pure input qubits generates M
output qubits in a state which is as close as possible to the perfect
complement. This gate can be realized by classical estimation and subsequent
re-preparation of complements of the estimated state. Its fidelity is therefore
equal to the fidelity F= (N+1)/(N+2) of optimal estimation, and does not depend
on the required number of outputs. We also show that when some additional a
priori information about the state of input qubit is available, than the
fidelity of the quantum NOT gate can be much better than the fidelity of
estimation.


title: Controlled quantum evolutions

abstract:
  We perform a detailed analysis of the non stationary solutions of the
evolution (Fokker-Planck) equations associated to either stationary or non
stationary quantum states by the stochastic mechanics. For the excited
stationary states of quantum systems with singular velocity fields we
explicitely discuss the exact solutions for the HO case. Moreover the
possibility of modifying the original potentials in order to implement
arbitrary evolutions ruled by these equations is discussed with respect to both
possible models for quantum measurements and applications to the control of
particle beams in accelerators.


title: Consistent-Histories Description of A World of Increasing Entropy

abstract:
  A distinction is made between two kinds of consistent histories: (1) robust
histories consistent by virtue of decoherence, and (2) verifiable histories
consistent through the existence of accessible records. It is events in
verifiable histories which describe amplified quantum fluctuations. If the
consistent-histories formalism is to improve on the Copenhagen interpretation
by providing a self-contained quantum representation of the quasi-classical
world, the appropriate quantum state must track closely all macroscopic
phenomena, and the von Neumann entropy of that quantum state ought to change in
the same direction as the statistical entropy of the macro-world. Since the von
Neumann entropy tends to decrease under successive branchings, the evolution of
an entropy-increasing quasi-classical world is not described by the process of
branchings only: mergings of previously separate histories must also occur. As
a consequence, the number of possible quasi-classical worlds does not have to
grow indefinitely as in the many-world picture.


title: High-sensitivity optical measurement of mechanical Brownian motion

abstract:
  We describe an experiment in which a laser beam is sent into a high-finesse
optical cavity with a mirror coated on a mechanical resonator. We show that the
reflected light is very sensitive to small mirror displacements. We have
observed the Brownian motion of the resonator with a very high sensitivity.


title: Effective mass in quantum effects of radiation pressure

abstract:
  We study the quantum effects of radiation pressure in a high-finesse cavity
with a mirror coated on a mechanical resonator. We show that the optomechanical
coupling can be described by an effective susceptibility which takes into
account every acoustic modes of the resonator and their coupling to the light.
At low frequency this effective response is similar to a harmonic response with
an effective mass smaller than the total mass of the mirror. For a plano-convex
resonator the effective mass is related to the light spot size and becomes very
small for small optical waists, thus enhancing the quantum effects of
optomechanical coupling.


title: On the Path Integral of the Relativistic Electron

abstract:
  We revisit the path integral description of the motion of a relativistic
electron. Applying a minor but well motivated conceptional change to Feynman's
chessboard model, we obtain exact solutions of the Dirac equation. The
calculation is performed by means of a particular simple method different from
both the combinatorial approach envisaged by Feynman and its Ising model
correspondence.


title: Invariant Quantum Algorithms for Insertion into an Ordered List

abstract:
  We consider the problem of inserting one item into a list of N-1 ordered
items. We previously showed that no quantum algorithm could solve this problem
in fewer than log N/(2 log log N) queries, for N large. We transform the
problem into a "translationally invariant" problem and restrict attention to
invariant algorithms. We construct the "greedy" invariant algorithm and show
numerically that it outperforms the best classical algorithm for various N. We
also find invariant algorithms that succeed exactly in fewer queries than is
classically possible, and iterating one of them shows that the insertion
problem can be solved in fewer than 0.53 log N quantum queries for large N
(where log N is the classical lower bound). We don't know whether a o(log N)
algorithm exists.


title: Quantum Anti-Zeno Effect

abstract:
  We demonstrate that near threshold decay processes may be accelerated by
repeated measurements. Examples include near threshold photodetachment of an
electron from a negative ion, and spontaneous emission in a cavity close to the
cutoff frequency, or in a photon band gap material.


title: Quantum Key Distribution: from Principles to Practicalities

abstract:
  We review the main protocols for key distribution based on principles of
quantum mechanics, describing the general underlying ideas, discussing
implementation requirements and pointing out directions of current experiments.
The issue of security is addressed both from a principal and real-life point of
view.


title:
Tunneling of Bound Systems at Finite Energies: Complex Paths Through
  Potential Barriers

abstract:
  We adapt the semiclassical technique, as used in the context of instanton
transitions in quantum field theory, to the description of tunneling
transmissions at finite energies through potential barriers by complex quantum
mechanical systems. Even for systems initially in their ground state, not
generally describable in semiclassical terms, the transmission probability has
a semiclassical (exponential) form. The calculation of the tunneling exponent
uses analytic continuation of degrees of freedom into a complex phase space as
well as analytic continuation of the classical equations of motion into the
complex time plane. We test this semiclassical technique by comparing its
results with those of a computational investigation of the full quantum
mechanical system, finding excellent agreement.


title: Time as a statistical variable and intrinsic decoherence

abstract:
  We propose a novel approach to intrinsic decoherence without adding new
assumptions to standard quantum mechanics. We generalize the Liouville equation
just by requiring the dynamical semigroup property of time evolution and
dropping the unitarity requirement. With no approximations and statistical
assumptions we find a generalized Liouville equation which depends on two
characteristic time t1 and t2 and reduces to the usual equation in the limit t1
= t2 -> 0. However, for t1 and t2 arbitrarily small but finite, our equation
can be written as a finite difference equation which predicts state reduction
to the diagonal form in the energy representation. The rate of decoherence
becomes faster at the macroscopic limit as the energy scale of the system
increases. In our approach the evolution time appears, a posteriori, as a
statistical variable with a Poisson-gamma function probability distribution as
if time evolution would take place randomly at average intervals t2 each
evolution having a time width t1. This view point is supported by the
derivation of a generalized Tam Mandelstam inequality. The relation with
previous work by Milburn, with laser and micromaser theory and many
experimental testable examples are described.


title: Quantum homodyne tomography with a priori constraints

abstract:
  I present a novel algorithm for reconstructing the Wigner function from
homodyne statistics. The proposed method, based on maximum-likelihood
estimation, is capable of compensating for detection losses in a numerically
stable way.


title:
On the importance of the Bohmian approach for interpreting CP-violation
  experiments

abstract:
  We argue that the inference of CP violation in experiments involving the
$K^0-\bar{K^0}$ system in weak interactions of particle physics is facilitated
by the assumption of particle trajectories for the decaying particles and the
decay products. A consistent explanation in terms of such trajectories is
naturally incorporated within the Bohmian interpretation of quantum mechanics.


title:
Aharonov-Bohm scattering of charged particles and neutral atoms: the
  role of absorption

abstract:
  The Aharonov-Bohm scattering of charged particles by the magnetic field of an
infinitely long and infinitely thin solenoid (magnetic string) in an absorbing
medium is studied. We discuss the partial-wave approach to this problem and
show that standard partial-wave method can be adjusted to this case. The effect
of absorption leads to oscillations of the AB cross section.
  Based on this we investigate the scattering of neutral atoms with induced
electric dipole moments by a charge wire of finite radius which is placed in an
uniform magnetic field. The physical realistic and practically important case
that all atoms which collide with the wire are totally absorbed at its surface,
is studied in detail. The dominating terms of the scattering amplitude are
evaluated analytically for different physical constellations. The rest terms
are written in a form suitable for a numerical computation. We show that if the
magnetic field is absent, the absorbing charged wire causes oscillations of the
cross section. In the presence of the magnetic field the cross section
increases and the dominating Aharonov--Bohm peak appears in the forward
direction, suppressing the oscillations.


title: Optimal receiver for quantum cryptography with two coherent states

abstract:
  A setup for discriminating between arbitrary two coherent states of a single
light mode with the highest success rate allowed by quantum mechanics is
presented. Its application to time-multiplexed quantum key distribution is
discussed.


title: Could Grover's quantum algorithm help in searching an actual database?

abstract:
  I investigate whether it would technologically and economically make sense to
build database search engines based on Grover's quantum search algorithm. The
answer is not fully conclusive but in my judgement rather negative.


title: Entangling Atoms in Photonic Crystals

abstract:
  We propose a method for entangling a system of two-level atoms in photonic
crystals. The atoms are assumed to move in void regions of a photonic crystal.
The interaction between the atoms is mediated either via a defect mode or via
resonant dipole-dipole interaction. We show that these interactions can produce
pure entangled atomic states. We analyze the problem with parameters typical
for currently existing photonic crystals and Rydberg atoms. We show that the
atoms can emerge from photonic crystals in entangled states. Depending on the
linear dimensions of the crystal and on their velocity of the entangled atoms
can be separated by tens of centimeters.


title: Universe of Fluctuations II

abstract:
  We throw further light on a recently discussed Kerr-Newman type formulation
of Fermions and the related cosmological scheme which predicted an ever
expanding universe, as indeed has subsequently been confirmed. In the spirit of
the correspondence principle, it is shown how the quark picture emerges at the
Compton wavelength and the Big Bang scenario at the Planck length. At the same
time we obtain a theoretical justification for the peculiar characteristics of
the quarks namely their fractional charge, handedness and confinement, as also
the order of magnitude of their masses, all of which were hitherto adhoc
features.


title: Entanglement and State Preparation

abstract:
  When a subset of particles in an entangled state is measured, the state of
the subset of unmeasured particles is determined by the outcome of the
measurement. This first measurement may be thought of as a state preparation
for the remaining particles. In this paper, we examine how the duration of the
first measurement effects the state of the unmeasured subsystem. The state of
the unmeasured subsytem will be a pure or mixed state depending on the nature
of the measurement.
  In the case of quantum teleportation we show that there is an eigenvalue
equation which must be satisfied for accurate teleportation. This equation
provides a limitation to the states that can be accurately teleported.


title: Spin flips and quantum information for anti-parallel spins

abstract:
  We consider two different ways to encode quantum information, by parallel or
anti-parallel pairs of spins. We find that there is more information in the
anti-parallel ones. This purely quantum mechanical effect is due to
entanglement, not of the states but occuring in the course of the measuring
process. We also introduce a range of quantum information processing machines,
such as spin-flip and anti-cloning.


title: The linewidth of a non-Markovian atom laser

abstract:
  We present a fully quantum mechanical treatment of a single mode atom laser
including pumping and output coupling. By ignoring atom-atom interactions, we
have solved this model without making the Born-Markov approximation. We find
substantially less gain narrowing than is predicted under that approximation.


title: Modeling the Singlet State with Local Variables

abstract:
  A local-variable model yielding the statistics from the singlet state is
presented for the case of inefficient detectors and/or lowered visibility. It
has independent errors and the highest efficiency at perfect visibility is
77.80%, while the highest visibility at perfect detector-efficiency is 63.66%.
Thus, the model cannot be refuted by measurements made to date.


title:
Excess noise for coherent radiation propagating through amplifying
  random media

abstract:
  A general theory is presented for the photodetection statistics of coherent
radiation that has been amplified by a disordered medium. The beating of the
coherent radiation with the spontaneous emission increases the noise above the
shot-noise level. The excess noise is expressed in terms of the transmission
and reflection matrices of the medium, and evaluated using the methods of
random-matrix theory. Inter-mode scattering between $N$ propagating modes
increases the noise figure by up to a factor of $N$, as one approaches the
laser threshold. Results are contrasted with those for an absorbing medium.


title:
Numerical evaluation of coherent-state path integrals with applications
  to time-dependent problems

abstract:
  We study the application of the coherent-state path integral as a numerical
tool for wave-packet propagation. The numerical evaluation of path integrals is
reduced to a matrix-vector multiplication scheme. Together with a
split-operator technique we apply our method to a time-dependent double-well
potential.


title: Collapse Models

abstract:
  This is a review of formalisms and models (nonrelativistic and relativistic)
which modify Schrodinger's equation so that it describes wavefunction collapse
as a dynamical physical process.


title:
Two - Level Atom - Field Interaction: Exact Master Equations for
  Non-Markovian Dynamics, Decoherence and Relaxation

abstract:
  We perform a first- principles derivation of the general master equation to
study the non-Markovian dynamics of a two-level atom (2LA) interacting with an
electromagnetic field (EMF). We use the influence functional method which can
incorporate the full backreaction of the field on the atom, while adopting
Grassmannian variables for the 2LA and the coherent state representation for
the EMF. We find exact master equations for the cases of a free quantum field
and a cavity field in the vacuum. In response to the search for mechanisms to
preserve maximal coherence in quantum computations in ion trap prototypes, we
apply these equations to analyse the decoherence of a 2LA in an EMF, and fine
that decoherence time is close to relaxation time. This is at variance to the
claims by authors who studied the same system but used a different coupling
model. We explain the source of difference and argue that, contrary to common
belief, the EMF when resonantly coupled to an atom does not decohere it as
efficiently as a bath does on a quantum Brownian particle. The master-equations
for non-Markovian dynamics derived here is expected to be useful for exploring
new regimes of 2LA-EMF interaction, which is becoming physically important
experimentally.


title: Transport properties of fermionic systems

abstract:
  We extend the method discovered by A Y Alekseev et al to the case of fermions
in external fields. A general formula for conductance G is proved. In the
(1+1)-D case with symmetry at time reflection, it is shown that: G=e^2/h+o(a^),
where a is the strength of the external field. In (3+1)-D free case, it is
checked that G=n*e^2/h, where n is the number of the filled energetic bands of
the transversal quantization.


title: Squeezing spectra of the output field by high density exciton laser

abstract:
  The effect of the non-linear interaction between the high density Wannier
excitons is analysed. We use the Fokker-Planck equation in the positive P
presentation and the corresponding stochastic differential equation to study
the composite system of a single mode cavity field and exciton under classical
field pumping. The small fluctuation approximation is made to get the
quadrature squeezing spectra of the output light field. The conditions for the
squeezing of the either quadrature component of the output light are given.


title: Path Integral Quantization for a Toroidal Phase Space

abstract:
  A Wiener-regularized path integral is presented as an alternative way to
formulate Berezin-Toeplitz quantization on a toroidal phase space. Essential to
the result is that this quantization prescription for the torus can be
constructed as an induced representation from anti-Wick quantization on its
covering space, the plane. When this construction is expressed in the form of a
Wiener-regularized path integral, symmetrization prescriptions for the
propagator emerge similar to earlier path-integral formulas on
multiply-connected configuration spaces.