title: Transition probabilities between quasifree states

abstract:
  We obtain a general formula for the transition probabilities between any
state of the algebra of the canonical commutation relations (CCR-algebra) and a
squeezed quasifree state. Applications of this formula are made for the case of
multimode thermal squeezed states of quantum optics using a general canonical
decomposition of the correlation matrix valid for any quasifree state. In the
particular case of a one mode CCR-algebra we show that the transition
probability between two quasifree squeezed states is a decreasing function of
the geodesic distance between the points of the upper half plane representing
these states. In the special case of the purification map it is shown that the
transition probability between the state of the enlarged system and the product
state of real and fictitious subsystems can be a measure for the entanglement.


title: Contextual Deterministic Quantum Mechanics

abstract:
  We present a simple proof of quantum contextuality for a spinless particle
with a one dimensional configuration space. We then discuss how the maximally
realistic deterministic quantum mechanics recently constructed by this author
and V. Singh can be applied to different contexts.


title: Quantum Zeno effect in the decay onto an unstable level

abstract:
  Under certain assumptions it is shown that the decay of level 2 of a
three-level system onto level 1 is slowed down because of the further decay of
level 1 onto level 0. It is argued that this phenomenon may be interpreted as a
consequence of the quantum Zeno effect. The reason why this may be possible is
that the second decay (or accompanying photon radiation) may be considered as a
sign of the transition 2 -> 1 so that during the first transition the system is
under continuous observation.


title:
Decoherence-Free Subspaces for Multiple-Qubit Errors: (I)
  Characterization

abstract:
  Coherence in an open quantum system is degraded through its interaction with
a bath. This decoherence can be avoided by restricting the dynamics of the
system to special decoherence-free subspaces. These subspaces are usually
constructed under the assumption of spatially symmetric system-bath coupling.
Here we show that decoherence-free subspaces may appear without spatial
symmetry. Instead, we consider a model of system-bath interactions in which to
first order only multiple-qubit coupling to the bath is present, with
single-qubit system-bath coupling absent. We derive necessary and sufficient
conditions for the appearance of decoherence-free states in this model, and
give a number of examples. In a sequel paper we show how to perform universal
and fault tolerant quantum computation on the decoherence-free subspaces
considered in this paper.


title: Limits for entanglement measures

abstract:
  We show that {\it any} entanglement measure $E$ suitable for the regime of
high number of entangled pairs satisfies $E_D\leq E\leq E_F$ where $E_D$ and
$E_F$ are entanglement of distillation and formation respectively. We also
exhibit a general theorem on bounds for distillable entanglement. The results
are obtained by use of a very transparent reasoning based on the fundamental
principle of entanglement theory saying that entanglement cannot increase under
local operations and classical communication.


title: Theory of Quantum Error Correction for General Noise

abstract:
  Quantum error correction protects quantum information against environmental
noise. When using qubits, a measure of quality of a code is the maximum number
of errors that it is able to correct. We show that a suitable notion of
``number of errors'' e makes sense for any system in the presence of arbitrary
environmental interactions. In fact, the notion is directly related to the
lowest order in time with which uncorrectable errors are introduced, and this
in turn is derived from a grading of the algebra generated by the interaction
operators. As a result, e-error-correcting codes are effective at protecting
quantum information without requiring the usual assumptions of independence and
lack of correlation. We prove the existence of large codes for both quantum and
classical information. By viewing error-correcting codes as subsystems, we
relate codes to irreducible representations of certain operator algebras and
show that noiseless subsystems are infinite-distance error-correcting codes. An
explicit example involving collective interactions is discussed.


title:
Two dimensional nonlinear dynamics of evanescent-wave guiding atoms in
  hollow fiber

abstract: This paper has been withdrawn due to same as quant-ph/9908068


title:
Two dimensional nonlinear dynamics of evanescent-wave guided atoms in
  hollow fiber

abstract:
  We describe the classical and quantum two dimensional nonlinear dynamics of
large blue-detuned eveanescent-wave guiding cold atoms in hollow fiber. We show
that chaotic dynamics exists for classic dynamics, when the intensity of the
beam is periodically modulated. The two dimensional distributions of atoms in
(x,y) plane are simulated. We show that the atoms will accumulate on several
annular regions when the system enters a regime of global chaos. Our simulation
shows that, when the atomic flux is very small, a similar distribution will be
obtained if we detect the atomic distribution once each the modualtion period
and integrate the signals.
  For quantum dynamics, quantum collapses and revivals appear . For
periodically modulated optical potential, the variance of atomic position will
be supressed compared to the no modulation case. The atomic angular momentum
will influnce the evolution of wave function in two dimensional quantum system
of hollow fiber.


title: Relativistic quantum mechanics of a Dirac oscillator

abstract:
  The Dirac oscillator is an exactly soluble model recently introduced in the
context of many particle models in relativistic quantum mechanics. The model
has been also considered as an interaction term for modelling quark confinement
in quantum chromodynamics. These considerations should be enough for
demonstrating that the Dirac oscillator can be an excellent example in
relativistic quantum mechanics. In this paper we offer a solution to the
problem and discuss some of its properties. We also discuss a physical picture
for the Dirac oscillator's non-standard interaction, showing how it arises on
describing the behaviour of a neutral particle carrying an anomalous magnetic
moment and moving inside an uniformly charged sphere.


title:
Unextendible Product Bases, Uncompletable Product Bases and Bound
  Entanglement

abstract:
  We report new results and generalizations of our work on unextendible product
bases (UPB), uncompletable product bases and bound entanglement. We present a
new construction for bound entangled states based on product bases which are
only completable in a locally extended Hilbert space. We introduce a very
useful representation of a product basis, an orthogonality graph. Using this
representation we give a complete characterization of unextendible product
bases for two qutrits. We present several generalizations of UPBs to arbitrary
high dimensions and multipartite systems. We present a sufficient condition for
sets of orthogonal product states to be distinguishable by separable
superoperators. We prove that bound entangled states cannot help increase the
distillable entanglement of a state beyond its regularized entanglement of
formation assisted by bound entanglement.


title: On a realistic interpretation of quantum mechanics

abstract:
  The best mathematical arguments against a realistic interpretation of quantum
mechanics - that gives definite but partially unknown values to all observables
- are analysed and shown to be based on reasoning that is not compelling.
  This opens the door for an interpretation that, while respecting the
indeterministic nature of quantum mechanics, allows to speak of definite values
for all observables at any time that are, however, only partially measurable.
  The analysis also suggests new ways to test the foundations of quantum
theory.


title: Quantitative wave-particle duality and non-erasing quantum erasure

abstract:
  The notion of wave-particle duality may be quantified by the inequality
V^2+K^2 <=1, relating interference fringe visibility V and path knowledge K.
With a single-photon interferometer in which polarization is used to label the
paths, we have investigated the relation for various situations, including
pure, mixed, and partially-mixed input states. A quantum eraser scheme has been
realized that recovers interference fringes even when no which-way information
is available to erase.


title: Exact and Asymptotic Measures of Multipartite Pure State Entanglement

abstract:
  In an effort to simplify the classification of pure entangled states of multi
(m) -partite quantum systems, we study exactly and asymptotically (in n)
reversible transformations among n'th tensor powers of such states (ie n copies
of the state shared among the same m parties) under local quantum operations
and classical communication (LOCC). With regard to exact transformations, we
show that two states whose 1-party entropies agree are either locally-unitarily
(LU) equivalent or else LOCC-incomparable. In particular we show that two
tripartite Greenberger-Horne-Zeilinger (GHZ) states are LOCC-incomparable to
three bipartite Einstein-Podolsky-Rosen (EPR) states symmetrically shared among
the three parties. Asymptotic transformations result in a simpler
classification than exact transformations. We show that m-partite pure states
having an m-way Schmidt decomposition are simply parameterizable, with the
partial entropy across any nontrivial partition representing the number of
standard ``Cat'' states (|0^m>+|1^m>) asymptotically interconvertible to the
state in question. For general m-partite states, partial entropies across
different partitions need not be equal, and since partial entropies are
conserved by asymptotically reversible LOCC operations, a multicomponent
entanglement measure is needed, with each scalar component representing a
different kind of entanglement, not asymptotically interconvertible to the
other kinds. In particular the m=4 Cat state is not isentropic to, and
therefore not asymptotically interconvertible to, any combination of bipartite
and tripartite states shared among the four parties. Thus, although the m=4 cat
state can be prepared from bipartite EPR states, the preparation process is
necessarily irreversible, and remains so even asymptotically.


title: Remarks on Universal Quantum Computer

abstract:
  According to Deutsch, a universal quantum Turing machine (UQTM) is able to
perform, in repeating a fixed unitary transformation on the total system, an
arbitrary unitary transformation on an arbitrary data state, by including a
program as another part of the input state. We note that if such a UQTM really
exists, with the program state dependent on the data state, and if the
prescribed halting scheme is indeed valid, then there would be no entanglement
between the halt qubit and other qubits, as pointed out by Myers. If, however,
the program is required to be independent of the data, the concerned
entanglement appears, and is problematic no matter whether the halt qubit is
monitored or not. We also note that for a deterministic programmable quantum
gate array, as discussed by Nielson and Chuang, if the program is allowed to
depend on the data state, then its existence has not been ruled out. On the
other hand, if UQTM exists, it can be simulated by repeating the operation of a
fixed gate array. However, more importantly, we observe that it is actually
still open whether Deutsch's UQTM exists and whether a crucial concatenation
scheme, of which the halting scheme is a special case, is valid.


title: Quantum Mechanics from Symmetry and Statistical Modelling

abstract:
  A version of quantum theory is derived from a set of plausible assumptions
related to the following general setting: For a given system there is a set of
experiments that can be performed, and for each such experiment an ordinary
statistical model is defined. The parameters of the single experiments are
functions of a hyperparameter, which defines the state of the system. There is
a symmetry group acting on the hyperparameters, and for the induced action on
the parameters of the single experiment a simple consistency property is
assumed, called permissibility of the parametric function. The other
assumptions needed are rather weak. The derivation relies partly on quantum
logic, partly on a group representation of the hyperparameter group, where the
invariant spaces are shown to be in 1-1 correspondence with the equivalence
classes of permissible parametric functions. Planck's constant only plays a
role connected to generators of unitary group representations.


title: Quantum Theory from Symmetries in a General Statistical Parameter Space

abstract:
  The aim of this paper is to show a connection between an extended theory of
statistical experiments on the one hand and the foundation of quantum theory on
the other hand. The main aspects of this extension are: One assumes a
hyperparameter space $\Phi$ common to several potential experiments, and a
basic symmetry group G associated with this space. The parameter \theta_{a} of
a single experiment, looked upon as a parametric function $\theta_{a}(\cdot)$
on $\Phi$, is said to be permissible if G induces in a natural way a new group
on the image space of the function. If this is not the case, it is arranged for
by changing from G to a subgroup $G_{a}$. The Haar measure of this subgroup
(confined to the spectrum; see below) is the prefered prior when the parameter
is unknown. It is assumed that the hyperparameter itself can never be
estimated, only a set of parametric functions. Model reduction is made by
restricting the space of complex `wave' functions, also regarded as functions
on $\Phi$, to an irreducible invariant subspace $\mathcal{M}$ under G. The
spectrum of a parametric function is defined from natural group-theoretical and
statistical considerations. We establish that a unique operator can be
associated with every parametric functions $\theta_{a}(\cdot)$, and essentially
all of the ordinary quantum theory formalism can be retrieved from these and a
few related assumptions. In particular the concept of spectrum is consistent.
The scope of the theory is illustrated on the one hand by the example of a spin
1/2 particle and a related EPR discussion, on the other hand by a simple
macroscopic example.


title: Quantum Consciousness

abstract:
  In a previous paper, the author proposed a quantum mechanical interaction
that would insure that the evolution of subjective states would parallel the
evolution of biological states, as required by von Neumann's theory of
measurement. The particular model for this interaction suggested an experiment
that the author has now performed wih negative results. A modified model is
outlined in this paper that preserves the desirable features of the original
model, and is consistent with the experimental results. This model will be more
difficult to verify. However, some strategies are suggested.


title: Identity, Geometry, Permutation And The Spin-Statistics Theorem

abstract:
  We examine historic formulations of the spin-statistics theorem from a point
of view that distinguishes between the observable consequences and the
``symmetrization postulate''. In particular, we make a critical analysis of
concepts of particle identity, state distinguishability and permutation, and
particle ``labels''. We discuss how to construct unique state vectors and the
nature of the full state descriptions required for this -- in particular the
elimination of arbitrary $2\pi$ rotations on fermion spin quantization frames
and argue that the failure to do this renders the conventional symmetrization
postulate (and previous ``proofs'' of it) at best {\em incomplete}.
  We discuss particle permutation in a general way for any pairs of particles,
whether identical or not, and make an essential distinction between exchange
and pure permutation. We prove a revised symmetrization postulate that allows
us to construct state vectors that are naturally symmetric under pure
permutation, {\em for any spin}. The significance of particle labels (which, in
the exchange operation, are not permuted along with other variables) is then
that they stand in for any asymmetry (order dependence) that is present in the
full state descriptions necessary for unique state vectors but not explicit in
the regular state variables. {\em The exchange operation is then the physical
transformation that reverses any asymmetry implicit in the labels}.
  We point out a previously unremarked geometrical asymmetry between all pairs
of particles that is present whenever we choose a common frame of reference. We
compute the exchange phase for various state vectors using different spin
quantization frames, and prove the Pauli Exclusion Principle and its
generalization to arbitrary spin.


title:
Group Theoretical Quantization and the Example of a Phase Space S^1 x
  R^+

abstract:
  The group theoretical quantization scheme is reconsidered by means of
elementary systems. Already the quantization of a particle on a circle shows
that the standard procedure has to be supplemented by an additional condition
on the admissibility of group actions. A systematic strategy for finding
admissible group actions for particular subbundles of cotangent spaces is
developed, two-dimensional prototypes of which are T^*R^+ and S^1 x R^+
(interpreted as restrictions of T^*R and T^*S^1 to positive coordinate and
momentum, respectively). In this framework (and under an additional, natural
condition) an SO_+(1,2)-action on S^1 x R^+ results as the unique admissible
group action.
  For symplectic manifolds which are (specific) parts of phase spaces with
known quantum theory a simple projection method of quantization is formulated.
For T^*R^+ and S^1 x R^+ equivalent results to those of more established (but
more involved) quantization schemes are obtained. The approach may be of
interest, e.g., in attempts to quantize gravity theories where demanding
nondegenerate metrics of a fixed signature imposes similar constraints.


title: A Quantum NP Solver: NP in QP

abstract:
  A attempt at a quantum algorithm for solving NP problems is presented. Now
withdrawn because some crucial operators were not unitary.


title:
Non-maximally entangled states: production, characterization and
  utilization

abstract:
  Using a spontaneous-downconversion photon source, we produce true
non-maximally entangled states, i.e., without the need for post-selection. The
degree and phase of entanglement are readily tunable, and are characterized
both by a standard analysis using coincidence minima, and by quantum state
tomography of the two-photon state. Using the latter, we experimentally
reconstruct the reduced density matrix for the polarization. Finally, we use
these states to measure the Hardy fraction, obtaining a result that is $122
\sigma$ from any local-realistic result.


title: A single atom in free space as a quantum aperture

abstract:
  We calculate exact 3-D solutions of Maxwell equations corresponding to
strongly focused light beams, and study their interaction with a single atom in
free space. We show how the naive picture of the atom as an absorber with a
size given by its radiative cross section $\sigma =3\lambda ^{2}/2\pi $ must be
modified. The implications of these results for quantum information processing
capabilities of trapped atoms are discussed.


title: Fast quantum algorithms for numerical integrals and stochastic processes

abstract:
  We discuss quantum algorithms that calculate numerical integrals and
descriptive statistics of stochastic processes. With either of two distinct
approaches, one obtains an exponential speed increase in comparison to the
fastest known classical deterministic algorithms and a quadratic speed increase
in comparison to classical Monte Carlo (probabilistic) methods. We derive a
simpler and slightly faster version of Grover's mean algorithm, demonstrate how
to apply quantum counting to the problem, develop some variations of these
algorithms, and show how both (apparently quite different) approaches can be
understood from the same unified framework. Finally, we discuss how the
exponential speed increase appears to (but does not) violate results obtained
via the method of polynomials, from which it is known that a bounded-error
quantum algorithm for computing a total function can be only polynomially more
efficient than the fastest deterministic classical algorithm.


title: The Problem of Conscious Observation in Quantum Mechanical Description

abstract:
  Epistemological consequences of quantum nonlocality (entanglement) are
discussed under the assumption of a universally valid Schr\"odinger equation in
the absence of hidden variables. This leads inevitably to a {\it many-minds
interpretation}. The recent foundation of quasi-classical neural states in the
brain (based on environmental decoherence) permits in principle a formal
description of the whole chain of measurement interactions, including the {\it
behavior} of conscious observers, without introducing any intermediate
classical concepts (for macroscopic "pointer states") or "observables" (for
microscopic particle positions and the like) --- thus consistently formalizing
Einstein's {\it ganzer langer Weg} from the observed to the observer in quantum
mechanical terms.


title:
Cold Atoms For Testing Quantum Mechanics and Parity Violation In
  Gravitation

abstract:
  Techniques of Atom trapping and laser cooling have proved to be very
important tools in probing many aspects of fundamental physics. In this talk I
wish to present ideas on how they may used to settle certain issues in the
foundational aspects of quantum mechanics on the one hand and about some
quantum gravitational interactions of matter that violate parity and
time-reversal, on the other hand.


title: Continuity bounds for entanglement

abstract:
  This note quantifies the continuity properties of entanglement: how much does
entanglement vary if we change the entangled quantum state just a little? This
question is studied for the pure state entanglement of a bipartite system and
for the entanglement of formation of a bipartite system in a mixed state.


title:
Quantum particle constrained to a curved surface in the presence of a
  vector potential

abstract:
  The Schrodinger equation for a charged particle constrained to a curved
surface in the presence of a vector potential is derived using the method of
forms. In the limit that the particle is brought infinitesimally close to the
surface, a term arises that couples the component of the vector potential
normal to the surface to the mean curvature of the surface.


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

abstract:
  In a recent paper Coutinho, Nogami and Tomio [Phys. Rev. A 59, 2624 (1999);
quant-ph/9812073] presented an example in which, they claim, Feynman's
prescription of disregarding the Pauli principle in intermediate states of
perturbation theory fails. We show that, contrary to their claim, Feynman's
prescription is consistent with the exact solution of their example.


title: A new measure of nonclassical distance

abstract:
  We propose a new measure of the nonclassical distance in the case of Gaussian
states. Let us consider two Gaussian states one of which is fixed and the other
runs through the set of Gaussian classical states. The maximum value of the
fidelity between these two states can be used as a nonclassical distance of the
fixed state to the set of classical states, in the same extent as the Hillery
measure. This measure increases when on the fixed state acts a Gaussian noise
map i.e. the selected state becomes closer to the classical states.


title: Computability Superselection Rule and its physical explanation

abstract:
  Paper erroneously re-submitted as duplicte. Readers should look at
math-ph/9909004.


title: Quantum Algebraic Symmetries in Nuclei, Molecules and Atomic Clusters

abstract:
  Various applications of quantum algebraic techniques in nuclear structure
physics and in molecular physics are briefly reviewed and a recent application
of these techniques to the structure of atomic clusters is discussed in more
detail.


title:
The 3-Dimensional q-Deformed Harmonic Oscillator and Magic Numbers of
  Alkali Metal Clusters

abstract:
  Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator
with Uq(3) > SOq(3) symmetry are compared to experimental data for alkali metal
clusters, as well as to theoretical predictions of jellium models, Woods--Saxon
and wine bottle potentials, and to the classification scheme using the 3n+l
pseudo quantum number. The 3-dimensional q-deformed harmonic oscillator
correctly predicts all experimentally observed magic numbers up to 1500 (which
is the expected limit of validity for theories based on the filling of
electronic shells), thus indicating that Uq(3), which is a nonlinear extension
of the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic
oscillator, is a good candidate for being the symmetry of systems of alkali
metal clusters.


title: Exact solution for Morse oscillator in PT-symmetric quantum mechanics

abstract:
  The recently proposed PT-symmetric quantum mechanics works with complex
potentials which possess, roughly speaking, a symmetric real part and an
anti-symmetric imaginary part. We propose and describe a new exactly solvable
model of this type. It is defined as a specific analytic continuation of the
shape-invariant potential of Morse. In contrast to the latter well-known
example, all the new spectrum proves real, discrete and bounded below. All its
three separate subsequences are quadratic in n.


title:
Conditionally Exactly Solvable Potentials and Supersymmetric
  Transformations

abstract:
  A general procedure is presented to construct conditionally solvable (CES)
potentials using the techniques of supersymmetric quantum mechanics.The method
is illustrated with potentials related to the harmonic oscillator
problem.Besides recovering known results,new CES potentials are also obtained
within the framework of this general approach.The conditions under which this
method leads to CES potentials are also discussed.


title: Pointer states via Decoherence in a Quantum Measurement

abstract:
  We consider the interaction of a quantum system (spin-1/2) with a macroscopic
quantum apparatus (harmonic oscillator) which in turn is coupled to a bath of
harmonic oscillators. Exact solutions of the Markovian Master equation show
that the reduced density matrix of the system-apparatus combine decoheres to a
statistical mixture where up and down spins eventually correlate with pointer
states of the apparatus. For the zero temperature bath these pointer states
turn out to be coherent states of the harmonic oscillator for arbitrary initial
states of the apparatus. For a high temperature bath pointer states are
Gaussian distributions (generalized coherent states). For both cases, the
off-diagonal elements in spin-space decohere over a time scale which goes
inversely as the square of the "separation" between the "pointers". Our exact
results also demonstrate in an unambiguous way that the pointer states in this
measurement model emerge independent of the initial state of the apparatus.


title: Quantum cryptography with squeezed states

abstract:
  A quantum key distribution scheme based on the use of displaced squeezed
vacuum states is presented. The states are squeezed in one of two field
quadrature components, and the value of the squeezed component is used to
encode a character from an alphabet. The uncertainty relation between
quadrature components prevents an eavesdropper from determining both with
enough precision to determine the character being sent. Losses degrade the
performance of this scheme, but it is possible to use phase-sensitive
amplifiers to boost the signal and partially compensate for their effect.


title: Schemes for Parallel Quantum Computation Without Local Control of Qubits

abstract:
  Typical quantum computing schemes require transformations (gates) to be
targeted at specific elements (qubits). In many physical systems, direct
targeting is difficult to achieve; an alternative is to encode local gates into
globally applied transformations. Here we demonstrate the minimum physical
requirements for such an approach: a one-dimensional array composed of two
alternating 'types' of two-state system. Each system need be sensitive only to
the net state of its nearest neighbors, i.e. the number in state 1 minus the
number in state 2. Additionally, we show that all such arrays can perform quite
general parallel operations. A broad range of physical systems and interactions
are suitable: we highlight two potential implementations.


title:
Solid-state NMR quantum computer with individual access to qubits and
  some its ensemble developments

abstract:
  Here we made an analysis of the principles of a semiconductor NMR quantum
computer and its developments. The known variant of an individual-access
computer (B. Kane) and alternative solid-state bulk-ensemble approach versions
allowing to avoid some difficulties in implementing the first variant are
considered.


title: On interference: the scalar problem

abstract:
  Single-slit and two-slit interferometer measurements of electrons are
analyzed within the realistic model of particle propagation. In a step by step
procedure we show that all current models of interference are essentially
non-local and demonstrate that the treatment of the quantum theory of motion is
the simplest model for the scalar problem. In particular we give a novel
interpretation of the quantum potential Q, which should be regarded as a
non-classical and essentially statistical term describing the changes of the
quantum ensemble due to a change of the physical environment.


title:
Back-Reaction of Clocks and Limitations on Observability in Closed
  Systems

abstract:
  Measurements are ordinarily described with respect to absolute "Newtonian"
time. In reality however, the switching-on of the measuring device at the
instance of the measurement requires a timing device. Hence the classical time
$t$ must be replaced by a suitable quantum time variable $\tau$ of a physical
clock. The main issue raised in this article is that while doing so, we can no
longer neglect the {\em back-reaction} due to the measurement on the clock.
This back-reaction yields a bound on the accuracy of the measurement. When this
bound is violated the result of a measurement is generally not an eigenvalue of
the observable, and furthermore, the state of the system after the measurement
is generally not a pure state. We argue that as a consequence, a sub-class of
observables in a closed system cannot be realized by a measurement.


title: Information, Relative Entropy of Entanglement and Irreversibility

abstract:
  Previously proposed measures of entanglement, such as entanglement of
formation and assistance, are shown to be special cases of the relative entropy
of entanglement. The difference between these measures for an ensemble of mixed
states is shown to depend on the availability of classical information about
particular members of the ensemble. Based on this, relations between relative
entropy of entanglement and mutual information are derived.


title: Analysis of Quantum Functions

abstract:
  This paper initiates a systematic study of quantum functions, which are
(partial) functions defined in terms of quantum mechanical computations. Of all
quantum functions, we focus on resource-bounded quantum functions whose inputs
are classical bit strings. We prove complexity-theoretical properties and
unique characteristics of these quantum functions by recent techniques
developed for the analysis of quantum computations. We also discuss relativized
quantum functions that make adaptive and nonadaptive oracle queries.


title:
Nonclassical correlations of phase noise and photon number in quantum
  nondemolition measurements

abstract:
  The continuous transition from a low resolution quantum nondemolition
measurement of light field intensity to a precise measurement of photon number
is described using a generalized measurement postulate. In the intermediate
regime, quantization appears as a weak modulation of measurement probability.
In this regime, the measurement result is strongly correlated with the amount
of phase decoherence introduced by the measurement interaction. In particular,
the accidental observation of half integer photon numbers preserves phase
coherence in the light field, while the accidental observation of quantized
values increases decoherence. The quantum mechanical nature of this correlation
is discussed and the implications for the general interpretation of
quantization are considered.


title: Wavelets and Wavelet Packets on Quantum Computers

abstract:
  We show how periodized wavelet packet transforms and periodized wavelet
transforms can be implemented on a quantum computer. Surprisingly, we find that
the implementation of wavelet packet transforms is less costly than the
implementation of wavelet transforms on a quantum computer.


title:
q-deformed fermion oscillators, zero-point energy and
  inclusion-exclusion principle

abstract:
  The theory of Fermion oscillators has two essential ingredients: zero-point
energy and Pauli exclusion principle. We devlop the theory of the statistical
mechanics of generalized q-deformed Fermion oscillator algebra with inclusion
principle (i.e., without the exclusion principle), which corresponds to
ordinary fermions with Pauli exclusion principle in the classical limit $q \to
1$. Some of the remarkable properties of this theory play a crucial role in the
understanding of the q-deformed Fermions. We show that if we insist on the weak
exclusion principle, then the theory has the expected low temperature limit as
well as the correct classical q-limit.


title:
Non-local Correlations are Generic in Infinite-Dimensional Bipartite
  Systems

abstract:
  It was recently shown that the nonseparable density operators for a bipartite
system are trace norm dense if either factor space has infinite dimension. We
show here that non-local states -- i.e., states whose correlations cannot be
reproduced by any local hidden variable model -- are also dense. Our
constructions distinguish between the cases where both factor spaces are
infinite-dimensional, where we show that states violating the CHSH inequality
are dense, and the case where only one factor space is infinite-dimensional,
where we identify open neighborhoods of nonseparable states that do not violate
the CHSH inequality but show that states with a subtler form of non-locality
(often called "hidden" non-locality) remain dense.


title:
Efficient Algorithm for Perturbative Calculation of Multiloop Feynman
  Integrals

abstract:
  We present an efficient algorithm for calculating multiloop Feynman integrals
perturbatively.


title: Transient properties of modified reservoir-induced transparency

abstract:
  We investigate the transient response of a $\Lambda$-type system with one
transition decaying to a modified radiation reservoir with an inverse
square-root singular density of modes at threshold, under conditions of
transparency. We calculate the time evolution of the linear susceptibility for
the probe laser field and show that, depending on the strength of the coupling
to the modified vacuum and the background decay, the probe transmission can
exhibit behaviour ranging from underdamped to overdamped oscillations.
Transient gain without population inversion is also possible depending on the
system's parameters.


title:
Comparisons of spectra determined using detector atoms and spatial
  correlation functions

abstract:
  We show how two level atoms can be used to determine the local time dependent
spectrum. The method is applied to a one dimensional cavity. The spectrum
obtained is compared with the mode spectrum determined using spatially filtered
second order correlation functions. The spectra obtained using two level atoms
give identical results with the mode spectrum. One benefit of the method is
that only one time averages are needed. It is also more closely related to a
realistic measurement scheme than any other definition of a time dependent
spectrum.


title: Probability distributions consistent with a mixed state

abstract:
  A density matrix $\rho$ may be represented in many different ways as a
mixture of pure states, $\rho = \sum_i p_i |\psi_i\ra \la \psi_i|$. This paper
characterizes the class of probability distributions $(p_i)$ that may appear in
such a decomposition, for a fixed density matrix $\rho$. Several illustrative
applications of this result to quantum mechanics and quantum information theory
are given.


title: Proposal for teleportation of the wave function of a massive particle

abstract:
  We propose a scheme for teleporting an atomic center-of-mass wave function
between distant locations. The scheme uses interactions in cavity quantum
electrodynamics to facilitate a coupling between the motion of an atom trapped
inside a cavity and external propagating light fields. This enables the
distribution of quantum entanglement and the realization of the required
motional Bell-state analysis.


title:
Squeezed angular momentum coherent states: construction and time
  evolution

abstract:
  A family of angular momentum coherent states on the sphere is constructed
using previous work by Aragone et al [1]. These states depend on a complex
parameter which allows an arbitrary squeezing of the angular momentum
uncertainties. The time evolution of these states is analyzed assuming a rigid
body hamiltonian. The rich scenario of fractional revivals is exhibited with
cloning and many interference effects.


title: Spin-orbit pendulum - Relativistic extension

abstract:
  We discuss an extension of the theory of {\em spin-orbit pendulum} phenomenon
given in [1] to relativistic approach. It is done within the so called Dirac
Oscillator. Our first results, focusing on circular wave packet motion have
been published recently [2]. The scope of this paper is motion of a linear wave
packet. In relativistic approach we found {\em Zitterbewegung} in spin-orbit
motion (in Dirac representation) due to coupling to negative energy states.
This effect is washed out in the Foldy-Wouthuysen representation. Another
important change with respect to non-relativistic case is the loss of
periodicity. The phenomenon reminds the time evolution of population inversion
in Jaynes-Cummings model.


title: Thermal fluctuations in macroscopic quantum memory

abstract:
  We describe macroscopic quantum memory devices based on type-II toroidal
superconductors and estimate in one case and compute in another the rates at
which quantum information stored in these devices ``degrades'' because of
thermal fluctuations. In the case when the entire solid torus is
superconducting, the Boltzmann factor in the rate corresponds to a well-defined
critical fluctuation, and the rate is suppressed exponentially with the linear
size of the system. In the case when superconductivity is confined to the
surface of the torus, the rate is determined by diffusive motion of vortices
around the torus and does not depend exponentially on the linear size; we find,
however, that when the two dimensions of the torus are comparable the rate does
not contain the usual volume enhancement factor, i.e. it does not grow with the
total surface area of the sample. We describe a possible way to write to and
read from this quantum memory.


title: Structure behind Mechanics I: Foundation

abstract:
  This paper proposes a basic theory on physical reality and a new foundation
for quantum mechanics and classical mechanics. It presents a scenario not only
to solve the problem of the arbitrariness on the operator ordering for the
quantization procedure, but also to clarify how the classical-limit occurs.
This paper is the first of the three papers into which the previous paper
quant-ph/9906130 has been separated for readability.


title:
Structure and Properties of Hughston's Stochastic Extension of the
  Schr\"odinger Equation

abstract:
  Hughston has recently proposed a stochastic extension of the Schr\"odinger
equation, expressed as a stochastic differential equation on projective Hilbert
space. We derive new projective Hilbert space identities, which we use to give
a general proof that Hughston's equation leads to state vector collapse to
energy eigenstates, with collapse probabilities given by the quantum mechanical
probabilities computed from the initial state. We discuss the relation of
Hughston's equation to earlier work on norm-preserving stochastic equations,
and show that Hughston's equation can be written as a manifestly unitary
stochastic evolution equation for the pure state density matrix. We discuss the
behavior of systems constructed as direct products of independent subsystems,
and briefly address the question of whether an energy-based approach, such as
Hughston's, suffices to give an objective interpretation of the measurement
process in quantum mechanics.


title: Non-Resonant Effects in Implementation of Quantum Shor Algorithm

abstract:
  We simulate Shor's algorithm on an Ising spin quantum computer. The influence
of non-resonant effects is analyzed in detail. It is shown that our ``$2\pi
k$''-method successfully suppresses non-resonant effects even for relatively
large values of the Rabi frequency.


title: Propagation of local decohering action in distributed quantum systems

abstract:
  We study propagation of the decohering influence caused by a local
measurement performed on a distributed quantum system. As an example, the gas
of bosons forming a Bose-Einstein condensate is considered. We demonstrate that
the local decohering perturbation exerted on the measured region propagates
over the system in the form of a decoherence wave, whose dynamics is governed
by elementary excitations of the system. We argue that the post-measurement
evolution of the system (determined by elementary excitations) is of importance
for transfer of decoherence, while the initial collapse of the wave function
has negligible impact on the regions which are not directly affected by the
measurement.


title:
Feedback-assisted measurement of the free mass position under the
  Standard Quantum Limit

abstract:
  The Standard Quantum Limit (SQL) for the measurement of a free mass position
is illustrated, along with two necessary conditions for breaching it. A
measurement scheme that overcomes the SQL is engineered. It can be achieved in
three-steps: i) a pre-squeezing stage; ii) a standard von Neumann measurement
with momentum-position object-probe interaction and iii) a feedback. Advantages
and limitations of this scheme are discussed. It is shown that all of the three
steps are needed in order to overcome the SQL. In particular, the von Neumann
interaction is crucial in getting the right state reduction, whereas other
experimentally achievable Hamiltonians, as, for example, the radiation-pressure
interaction, lead to state reductions that on the average cannot overcome the
SQL.


title:
Quantum cryptography with a predetermined key, using continuous variable
  Einstein-Podolsky-Rosen correlations

abstract:
  Correlations of the type discussed by EPR in their original 1935 paradox for
continuous variables exist for the quadrature phase amplitudes of two spatially
separated fields. These correlations were experimentally reported in 1992. We
propose to use such EPR beams in quantum cryptography, to transmit with high
efficiency messages in such a way that the receiver and sender may later
determine whether eavesdropping has occurred. The merit of the new proposal is
in the possibility of transmitting a reasonably secure yet predetermined key.
This would allow relay of a cryptographic key over long distances in the
presence of lossy channels.


title: Quantum information distribution via entanglement

abstract:
  We present a generalization of quantum teleportation that distributes quantum
information from a sender's $d$-level particle to $N_o$ particles held by
remote receivers via an initially shared multiparticle entangled state. This
entangled state functions as a multiparty quantum information distribution
channel between the sender and the receivers. The structure of the distribution
channel determines how quantum information is processed. Our generalized
teleportation scheme allows multiple receivers at arbitrary locations, and can
be used for applications such as optimal quantum information broadcasting,
asymmetric telecloning, and quantum error correction.


title:
Simulations of Quantum Logic Operations in Quantum Computer with Large
  Number of Qubits

abstract:
  We report the first simulations of the dynamics of quantum logic operations
with a large number of qubits (up to 1000). A nuclear spin chain in which
selective excitations of spins is provided by the gradient of the external
magnetic field is considered. The spins interact with their nearest neighbors.
We simulate the quantum control-not (CN) gate implementation for remote qubits
which provides the long-distance entanglement. Our approach can be applied to
any implementation of quantum logic gates involving a large number of qubits.


title:
Solid-State Nuclear Spin Quantum Computer Based on Magnetic Resonance
  Force Microscopy

abstract:
  We propose a nuclear spin quantum computer based on magnetic resonance force
microscopy (MRFM). It is shown that an MRFM single-electron spin measurement
provides three essential requirements for quantum computation in solids: (a)
preparation of the ground state, (b) one- and two- qubit quantum logic gates,
and (c) a measurement of the final state. The proposed quantum computer can
operate at temperatures up to 1K.


title: Explanation of Quantum Mechanics

abstract:
  By assuming that the kinetic energy,potential energy,momentum,and some other
physical quantities of a particle exist in the field out of the particle,the
Schrodinger equation is an equation describing field of a particle,but not the
particle itself.


title: Quantum Logic Using Sympathetically Cooled Ions

abstract:
  One limit to the fidelity of quantum logic operations on trapped ions arises
from heating of the ions' collective modes of motion. Sympathetic cooling of
the ions during the logic operations may eliminate this source of errors. We
discuss benefits and drawbacks of this proposal, and describe possible
experimental implementations. We also present an overview of trapped-ion
dynamics in this scheme.


title:
Reliable Teleportation of Ionic Motional States Through a Mapping
  Process

abstract:
  We show how to teleport reliably an arbitrary superposition of n=0 and n=1
vibrational number state between two distant ions. This is done by first
mapping the vibrational state to be teleported into the internal degrees of
freedom of a given ion. Then we handle with the internal superposition state
following Bennett's original protocol and a recently proposed technique for
teleportation of ionic internal states [quant-ph/9903029]. Finally, the
teleportation of the vibrational state is achieved by reversing the mapping
process in the receiver ion. We remark that as in the teleportation of cavity
field and atomic states, the teleportation of vibrational states is 100%
successful for an ideal process.


title: Universal cloning of continuous quantum variables

abstract:
  The cloning of quantum variables with continuous spectra is analyzed. A
universal - or Gaussian - quantum cloning machine is exhibited that copies
equally well the states of two conjugate variables such as position and
momentum. It also duplicates all coherent states with a fidelity of 2/3. More
generally, the copies are shown to obey a no-cloning Heisenberg-like
uncertainty relation.


title:
Quantum state engineering on an optical transition and decoherence in a
  Paul trap

abstract:
  A single Ca+ ion in a Paul trap has been cooled to the ground state of
vibration with up to 99.9% probability. Starting from this Fock state |n=0> we
have demonstrated coherent quantum state manipulation on an optical transition.
Up to 30 Rabi oscillations within 1.4 ms have been observed. We find a similar
number of Rabi oscillations after preparation of the ion in the |n=1> Fock
state. The coherence of optical state manipulation is only limited by laser and
ambient magnetic field fluctuations. Motional heating has been measured to be
as low as one vibrational quantum in 190 ms.


title: Quantum Information Theory - A Quantum Bayesian Net Perspective

abstract:
  The main goal of this paper is to give a pedagogical introduction to Quantum
Information Theory-to do this in a new way, using network diagrams called
Quantum Bayesian Nets. A lesser goal of the paper is to propose a few new
ideas, such as associating with each quantum Bayesian net a very useful density
matrix that we call the meta density matrix.


title: Grover's Algorithm for Multiobject Search in Quantum Computing

abstract:
  L. K. Grover's search algorithm in quantum computing gives an optimal,
square-root speedup in the search for a single object in a large unsorted
database. In this paper, we expound Grover's algorithm in a Hilbert-space
framework that isolates its geometrical essence, and we generalize it to the
case where more than one object satisfies the search criterion.


title: Quantum Entanglement and Conditional Information Transmission

abstract:
  We propose a new measure of quantum entanglement. Our measure is defined in
terms of conditional information transmission for a Quantum Bayesian Net. We
show that our measure is identically equal to the Entanglement of Formation in
the case of a bipartite (two listener) system occupying a pure state. In the
case of mixed states, the relationship between these two measures is not known
yet. We discuss some properties of our measure. Our measure can be easily and
naturally generalized to handle n-partite (n-listener) systems. It is
non-negative for any n. It vanishes for conditionally separable states with n
listeners. It is symmetric under permutations of the n listeners. It decreases
if listeners are merged, pruned or removed. Most promising of all, it is
intimately connected with the Data Processing Inequalities. We also find a new
upper bound for classical mutual information which is of interest in its own
right.


title: Position-momentum local realism violation of the Hardy type

abstract:
  We show that it is, in principle, possible to perform local realism violating
experiments of the Hardy type in which only position and momentum measurements
are made on two particles emanating from a common source. In the optical
domain, homodyne detection of the in-phase and out-of-phase amplitude
components of an electromagnetic field is analogous to position and momentum
measurement. Hence, local realism violations of the Hardy type are possible in
optical systems employing only homodyne detection.


title:
Spontaneous emission and lifetime modification caused by an intense
  electromagnetic field

abstract:
  We study the temporal evolution of a three-level system (such as an atom or a
molecule), initially prepared in an excited state, bathed in a laser field
tuned at the transition frequency of the other level. The features of the
spontaneous emission are investigated and the lifetime of the initial state is
evaluated: a Fermi "golden rule" still applies, but the on-shell matrix
elements depend on the intensity of the laser field. In general, the lifetime
is a decreasing function of the laser intensity. The phenomenon we discuss can
be viewed as an "inverse" quantum Zeno effect and can be analyzed in terms of
dressed states.


title: Peres-Horodecki separability criterion for continuous variable systems

abstract:
  The Peres-Horodecki criterion of positivity under partial transpose is
studied in the context of separability of bipartite continuous variable states.
The partial transpose operation admits, in the continuous case, a geometric
interpretation as mirror reflection in phase space. This recognition leads to
uncertainty principles, stronger than the traditional ones, to be obeyed by all
separable states. For all bipartite Gaussian states, the Peres-Horodecki
criterion turns out to be necessary and sufficient condition for separability.


title: Information Transfer in the Course of a Quantum Interaction

abstract:
  We discuss the problem of the information transfer (exchange of states
configuration) between two interacting quantum systems along their evolution in
time. We consider the specific case of two modes of the electromagnetic field
with rotating wave coupling interaction (up-conversion in a nonlinear crystal).
We verify that for certain initial states of the fields the swapping of state
configuration occurs with conservation of the mean energy of each mode (without
energy transfer), characterising thus pure information flow.


title: Phase covariant quantum cloning

abstract:
  We consider an N -> M quantum cloning transformation acting on pure two-level
states lying on the equator of the Bloch sphere. An upper bound for its
fidelity is presented, by establishing a connection between optimal phase
covariant cloning and phase estimation. We give the explicit form of a cloning
transformation that achieves the bound for the case N=1, M=2, and find a link
between this case and optimal eavesdropping in the quantum cryptographic scheme
BB84.


title: Repulsion of Resonance States and Exceptional Points

abstract:
  Level repulsion is associated with exceptional points which are square root
singularities of the energies as functions of a (complex) interaction
parameter. This is also valid for resonance state energies. Using this concept
it is argued that level anti-crossing (crossing) must imply crossing
(anti-crossing) of the corresponding widths of the resonance states. Further,
itis shown that an encircling of an exceptional point induces a phase change of
one wave function but not of the other. An experimental setup is discussed
where this phase behaviour which differs from the one encountered at a diabolic
point can be observed.


title: On the Possibility of Unconditionally Secure Quantum Bit Commitment

abstract: This paper has been withdrawn by the author.


title: Consistent histories, quantum truth functionals, and hidden variables

abstract:
  A central principle of consistent histories quantum theory, the requirement
that quantum descriptions be based upon a single framework (or family), is
employed to show that there is no conflict between consistent histories and a
no-hidden-variables theorem of Bell, and Kochen and Specker, contrary to a
recent claim by Bassi and Ghirardi. The argument makes use of ``truth
functionals'' defined on a Boolean algebra of classical or quantum properties.


title: Path Integral Solution by Sum Over Perturbation Series

abstract:
  A method for calculating the relativistic path integral solution via sum over
perturbation series is given. As an application the exact path integral
solution of the relativistic Aharonov-Bohm-Coulomb system is obtained by the
method. Different from the earlier treatment based on the space-time
transformation and infinite multiple-valued trasformation of
Kustaanheimo-Stiefel in order to perform path integral, the method developed in
this contribution involves only the explicit form of a simple Green's function
and an explicit path integral is avoided.


title:
The Markov approximation revisited: Inconsistency of the standard
  quantum Brownian motion model

abstract:
  We revisit the Markov approximation necessary to derive ordinary Brownian
motion from a model widely adopted in literature for this specific purpose. We
show that this leads to internal inconsistencies, thereby implying that further
search for a more satisfactory model is required.


title: Maximum-likelihood estimation of the density matrix

abstract:
  We present a universal technique for quantum state estimation based on the
maximum-likelihood method. This approach provides a positive definite estimate
for the density matrix from a sequence of measurements performed on identically
prepared copies of the system. The method is versatile and can be applied to
multimode radiation fields as well as to spin systems. The incorporation of
physical constraints, which is natural in the maximum-likelihood strategy,
leads to a substantial reduction of statistical errors. Numerical
implementation of the method is based on a particular form of the Gauss
decomposition for positive definite Hermitian matrices.


title: Generalized equation of relativistic quantum mechanics

abstract:
  We develop a new concept of quantum mechanics which is based on a generalized
space-time and on an action vector space similar to it. Both spaces are
provided by algebraic properties. This allows to calculate the Dirac matrixes
and to derive quantum mechanics equations from structure equations of the
specified algebras. A new interpretation of the wave function is given as
differential of the action vector. A generalization of the Dirac equation for
8-component wave function is derived. It is interpreted as the equation for two
leptons of the same generation. A procedure of the approximate description of
free leptons is formulated. The generalized equation of quantum mechanics is
reduced to the Dirac, Pauli and Schr\"odinger equations by the sequential use
of this procedure. We explain the existence of three lepton generations.


title: States interpolating between number and coherent states

abstract: The paper has been withdraw by authors


title:
States interpolating between number and coherent states and their
  interaction with atomic systems

abstract:
  Using the eigenvalue definition of binomial states we construct new
intermediate number-coherent states which reduce to number and coherent states
in two different limits. We reveal the connection of these intermediate states
with photon-added coherent states and investigate their non-classical
properties and quasi-probability distributions in detail. It is of interest to
note that these new states, which interpolate between coherent states and
number states, neither of which exhibit squeezing, are nevertheless squeezed
states. A scheme to produce these states is proposed. We also study the
interaction of these states with atomic systems in the framework of the
two-photon Jaynes-Cummings model, and describe the response of the atomic
system as it varies between the pure Rabi oscillation and the collapse-revival
mode and investigate field observables such as photon number distribution,
entropy and the Q-function.


title: A Quantum Anti-Zeno Paradox

abstract:
  We establish an exact differential equation for the operator describing
time-dependent measurements continuous in time and obtain a series solution.
Suppose the projection operator $E(t) = U(t) E U^\dagger(t)$ is measured
continuously from t = 0 to T, where E is a projector leaving the initial state
unchanged and U(t) a unitary operator obeying U(0) = 1 and some smoothness
conditions in t. We prove that the probability of always finding E(t) = 1 from
t = 0 to T is unity. If $U(t) \neq 1$, the watched kettle is sure to `boil'.


title: Entanglement and nonextensive statistics

abstract:
  It is presented a generalization of the von Neumann mutual information in the
context of Tsallis' nonextensive statistics. As an example, entanglement
between two (two-level) quantum subsystems is discussed. Important changes
occur in the generalized mutual information, which measures the degree of
entanglement, depending on the entropic index q.


title: Universal Fault-Tolerant Computation on Decoherence-Free Subspaces

abstract:
  A general scheme to perform universal quantum computation within
decoherence-free subspaces (DFSs) of a system's Hilbert space is presented.
This scheme leads to the first fault-tolerant realization of universal quantum
computation on DFSs with the properties that (i) only one- and two-qubit
interactions are required, and (ii) the system remains within the DFS
throughout the entire implementation of a quantum gate. We show explicitly how
to perform universal computation on clusters of the four-qubit DFS encoding one
logical qubit each under "collective decoherence" (qubit-permutation-invariant
system-bath coupling). Our results have immediate relevance to a number of
solid-state quantum computer implementations, in particular those in which
quantum logic is implemented through exchange interactions, such as the
recently proposed spin-spin coupled GaAs quantum dot arrays and the Si:$^{31}$P
nuclear spin arrays.


title: Quantum interference in the fluorescence of a molecular system

abstract:
  It has been observed experimentally [H.R. Xia, C.Y. Ye, and S.Y. Zhu, Phys.
Rev. Lett. {\bf 77}, 1032 (1996)] that quantum interference between two
molecular transitions can lead to a suppression or enhancement of spontaneous
emission. This is manifested in the fluorescent intensity as a function of the
detuning of the driving field from the two-photon resonance condition. Here we
present a theory which explains the observed variation of the number of peaks
with the mutual polarization of the molecular transition dipole moments. Using
master equation techniques we calculate analytically as well as numerically the
steady-state fluorescence, and find that the number of peaks depends on the
excitation process. If the molecule is driven to the upper levels by a
two-photon process, the fluorescent intensity consists of two peaks regardless
of the mutual polarization of the transition dipole moments. If the excitation
process is composed of both a two-step one-photon process and a one-step,
two-photon process, then there are two peaks on transitions with parallel
dipole moments and three peaks on transitions with antiparallel dipole moments.
This latter case is in excellent agreement with the experiment.


title: Fidelity and Concurrence of conjugated states

abstract:
  We prove some new properties of fidelity (transition probability) and
concurrence, the latter defined by straightforward extension of Wootters
notation. Choose a conjugation and consider the dependence of fidelity or of
concurrence on conjugated pairs of density operators. These functions turn out
to be concave or convex roofs. Optimal decompositions are constructed. Some
applications to two- and tripartite systems illustrate the general theorem.


title: Coherent properties of a tripod system coupled via a continuum

abstract:
  We present results from a study of the coherence properties of a system
involving three discrete states coupled to each other by two-photon processes
via a common continuum. This tripod linkage is an extension of the standard
laser-induced continuum structure (LICS) which involves two discrete states and
two lasers. We show that in the tripod scheme, there exist two population
trapping conditions; in some cases these conditions are easier to satisfy than
the single trapping condition in two-state LICS. Depending on the pulse timing,
various effects can be observed. We derive some basic properties of the tripod
scheme, such as the solution for coincident pulses, the behaviour of the system
in the adiabatic limit for delayed pulses, the conditions for no ionization and
for maximal ionization, and the optimal conditions for population transfer
between the discrete states via the continuum. In the case when one of the
discrete states is strongly coupled to the continuum, the population dynamics
reduces to a standard two-state LICS problem (involving the other two states)
with modified parameters; this provides the opportunity to customize the
parameters of a given two-state LICS system.


title:
Essentially All Gaussian Two-Party Quantum States are a priori
  Nonclassical but Classically Correlated

abstract:
  Duan, Giedke, Cirac and Zoller (quant-ph/9908056) and, independently, Simon
(quant-ph/9909044) have recently found necessary and sufficient conditions for
the separability (classical correlation) of the Gaussian two-party (continuous
variable) states. Duan et al remark that their criterion is based on a "much
stronger bound" on the total variance of a pair of Einstein-Podolsky-Rosen-type
operators than is required simply by the uncertainty relation. Here, we seek to
formalize and test this particular assertion in both classical and
quantum-theoretic frameworks. We first attach to these states the classical a
priori probability (Jeffreys' prior), proportional to the volume element of the
Fisher information metric on the Riemannian manifold of Gaussian (quadrivariate
normal) probability distributions. Then, numerical evidence indicates that more
than ninety-nine percent of the Gaussian two-party states do, in fact, meet the
more stringent criterion for separability. We collaterally note that the prior
probability assigned to the classical states, that is those having positive
Glauber-Sudarshan P-representations, is less than one-thousandth of one
percent. We, then, seek to attach as a measure to the Gaussian two-party
states, the volume element of the associated (quantum-theoretic) Bures (minimal
monotone) metric. Our several extensive analyses, then, persistently yield
probabilities of separability and classicality that are, to very high orders of
accuracy, unity and zero, respectively, so the two apparently quite distinct
(classical and quantum-theoretic) forms of analysis are rather remarkably
consistent in their findings.


title: Smooth adiabatic evolutions with leaky power tails

abstract:
  Adiabatic evolutions with a gap condition have, under a range of
circumstances, exponentially small tails that describe the leaking out of the
spectral subspace. Adiabatic evolutions without a gap condition do not seem to
have this feature in general. This is a known fact for eigenvalue crossing. We
show that this is also the case for eigenvalues at the threshold of the
continuous spectrum by considering the Friedrichs model.

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


title:
Time dependent nonclassical properties of even and odd nonlinear
  coherent states

abstract:
  We construct even and odd nonlinear coherent states of a parametric
oscillator and examine their nonclassical properties.It has been shown that
these superpositions exhibit squeezing and photon antibunching which change
with time.


title:
Hydrodynamical formulation of quantum mechanics, Kahler structure, and
  Fisher information

abstract:
  The Schrodinger equation can be derived using the minimum Fisher information
principle. I discuss why such an approach should work, and also show that the
Kahler and Hilbert space structures of quantum mechanics result from combining
the symplectic structure of the hydrodynamical model with the Fisher
information metric.


title: Spatial Correlation Diagnostics for Atoms in Optical Lattices

abstract:
  We explore the use of first and second order same-time atomic spatial
correlation functions as a diagnostic for probing the small scale spatial
structure of atomic samples trapped in optical lattices. Assuming an ensemble
of equivalent atoms, properties of the local wave function at a given lattice
site can be measured using same-position first-order correlations. Statistics
of atomic distributions over the lattice can be measured via two-point
correlations, generally requiring the averaging of multiple realizations of
statistically similar but distinct realizations in order to obtain sufficient
signal to noise. Whereas two-point first order correlations are fragile due to
phase fluctuations from shot-to-shot in the ensemble, second order correlations
are robust. We perform numerical simulations to demonstrate these diagnostic
tools.


title:
Quantum entanglement in the NMR implementation of the Deutsch-Jozsa
  algorithm

abstract:
  A scheme to execute an n-bit Deutsch-Jozsa (D-J) algorithm using n qubits has
been implemented for up to three qubits on an NMR quantum computer. For the one
and two bit Deutsch problem, the qubits do not get entangled, hence the NMR
implementation is achieved without using spin-spin interactions. It is for the
three bit case, that the manipulation of entangled states becomes essential.
The interactions through scalar J-couplings in NMR spin systems have been
exploited to implement entangling transformations required for the three bit
D-J algorithm.


title: Short-range oscillators in power-series picture

abstract:
  A class of short-range potentials on the line is considered as an
asymptotically vanishing phenomenological alternative to the popular confining
polynomials. We propose a method which parallels the analytic Hill-Taylor
description of anharmonic oscillators and represents all our Jost solutions
non-numerically, in terms of certain infinite hypergeometric-like series. In
this way the well known solvable Rosen-Morse and scarf models are generalized.


title: q-Deformed Boson Oscillators and Zero Point Energy

abstract:
  Just as for the ordinary quantum harmonic oscillators, we expect the
zero-point energy to play a crucial role in the correct high temperature
behavior. We accordingly reformulate the theory of the statistical distribution
function for the q-deformed boson oscillators and develop an approximate theory
incorporating the zero-point energy. We are then able to demonstrate that for
small deformations, the theory reproduces the correct limits both for very high
temperatures and for very low temperatures. The deformed theory thus reduces to
the undeformed theory in these extreme cases.


title: An optically driven quantum dot quantum computer

abstract:
  We propose a quantum computer structure based on coupled asymmetric
single-electron quantum dots. Adjacent dots are strongly coupled by means of
electric dipole-dipole interactions enabling rapid computation rates. Further,
the asymmetric structures can be tailored for a long coherence time. The result
maximizes the number of computation cycles prior to loss of coherence.


title:
Counting Marbles with 'Accessible' Mass Density: A Reply to Bassi and
  Ghirardi

abstract:
  In a previous article (cf. quant-ph/9905065) we argued that, while Lewis is
correct that the enumeration principle fails in dynamical wavepacket reduction
theories, one need not following Lewis in rejecting these theories. Because the
dynamical reduction process itself prevents the failure of enumeration from
ever becoming manifest, and because one can treat the semantics for dynamical
reduction theories as not adding anything of ontological import to them, it is
reasonable to accept these theories notwithstanding Lewis's counting anomaly.
In their response to our paper (cf. quant-ph/9907050), Bassi and Ghirardi
reject our criticisms of their own response to Lewis, as well as our argument
against Lewis that dynamical reduction precludes failures of enumeration from
ever becoming manifest. Our intention here is to demonstrate that Bassi and
Ghirardi's responses to us do not succeed.


title: Nonlocal Aspects of a Quantum Wave

abstract:
  Various aspects of nonlocality of a quantum wave are discussed. In
particular, the question of the possibility of extracting information about the
relative phase in a quantum wave is analyzed. It is argued that there is a
profound difference in the nonlocal properties of the quantum wave between
fermion and boson particles. The phase of the boson quantum state can be found
from correlations between results of measurements in separate regions. These
correlations are identical to the Einstein-Podolsky-Rosen (EPR) correlations
between two entangled systems. An ensemble of results of measurements performed
on fermion quantum waves does not exhibit the EPR correlations and the relative
phase of fermion quantum waves cannot be found from these results. The
existence of a physical variable (the relative phase) which cannot be measured
locally is the nonlocality aspect of the quantum wave of a fermion.


title:
Quantum states and generalized observables: a simple proof of Gleason's
  theorem

abstract:
  A quantum state can be understood in a loose sense as a map that assigns a
value to every observable. Formalizing this characterization of states in terms
of generalized probability distributions on the set of effects, we obtain a
simple proof of the result, analogous to Gleason's theorem, that any quantum
state is given by a density operator. As a corollary we obtain a von
Neumann-type argument against non-contextual hidden variables. It follows that
on an individual interpretation of quantum mechanics, the values of effects are
appropriately understood as propensities.


title: Quantum Chaos Border for Quantum Computing

abstract:
  We study a generic model of quantum computer, composed of many qubits coupled
by short-range interaction. Above a critical interqubit coupling strength,
quantum chaos sets in, leading to quantum ergodicity of the computer
eigenstates. In this regime the noninteracting qubit structure disappears, the
eigenstates become complex and the operability of the computer is destroyed.
Despite the fact that the spacing between multi-qubit states drops
exponentially with the number of qubits $n$, we show that the quantum chaos
border decreases only linearly with $n$. This opens a broad parameter region
where the efficient operation of a quantum computer remains possible.


title: Optical qubit by conditional interferometry

abstract:
  We suggest a method to prepare any chosen superposition a0 |0> + a1 |1> of
the vacuum and one-photon states. The method is based on a conditional
double-interferometer fed by an one-photon state and a coherent state. The
scheme involves only linear optical elements and avalanche photodetectors, and
therefore it should be realizable with current technology. A realistic
description of the triggering photodetectors is employed, i.e. we assume that
they can only check, with a certain efficiency, whether or not any photon is
present. We discuss two working regimes, and show that output states with
fidelity arbitrarily close to unit may be obtained, with non vanishing
conditional probability, also for low quantum efficiency at the photodetectors.


title:
Derivation of the Lindblad Generator Structure by use of the It\^o
  Stochastic Calculus

abstract:
  We use the It\^o stochastic calculus to give a simple derivation of the
Lindblad form for the generator of a completely positive density matrix
evolution, by specialization from the corresponding global form for a
completely positive map. As a by-product, we obtain a generalized generator for
a completely positive stochastic density matrix evolution.


title: Legitimacy of wave-function expansion

abstract:
  In this letter we investigate the common procedure in which any wave function
is expanded into a series of eigenfunctions. It is shown that as far as
dynamical systems are concerned the expanding procedure involves various
mathematical and physical difficulties. With or without introducing phase
factors, such expansions do not represent dynamical wave functions.


title: The Encoding of Quantum State Information Within Subparticles

abstract:
  A method is given by which the descriptive content of quantum state
information can be encoded into subparticle coordinates. This method is
consistent with the MA-model solution to the general grand unification problem.
Subparticle mechanisms via affine or linear transformations are also discussed.


title: General equation for Zeno-like effects in spontaneous exponential decay

abstract:
  It was shown that different mechanisms of perturbation of spontaneous decay
constant: inelastic interaction of emitted particles with particle detector,
decay onto an unstable level, Rabi transition from the final state of decay
(electromagnetic field domination) and some others are really the special kinds
of one general effect - perturbation of decay constant by dissipation of the
final state of decay. Such phenomena are considered to be Zeno-like effects and
general formula for perturbed decay constant is deduced.


title: Noncommutative analysis and quantum physics I. States and ensembles

abstract:
  In this sequence of papers, noncommutative analysis is used to give a
consistent axiomatic approach to a unified conceptual foundation of classical
and quantum physics.
  The present Part I defines the concepts of observables, states and ensembles,
clarifies the logical relations and operations for them, and shows how they
give rise to dynamics and probabilities.
  States are identified with maximal consistent sets of weak equalities in the
algebra of observables (instead of, as usual, with the rays in a Hilbert
space). This leads to a concise foundation of quantum mechanics, free of
undefined terms, separating in a clear way the deterministic and the stochastic
features of quantum physics.
  The traditional postulates of quantum mechanics are derived from
well-motivated axiomatic assumptions. No special quantum logic is needed to
handle the peculiarities of quantum mechanics. Foundational problems associated
with the measurement process, such as the reduction of the state vector,
disappear.
  The new interpretation of quantum mechanics contains `elements of physical
reality' without the need to introduce a classical framework with hidden
variables. In particular, one may talk about the state of the universe without
the need of an external observer and without the need to assume the existence
of multiple universes.


title: Rigged Hilbert Space Resonances and Time Asymmetric Quantum Mechanics

abstract:
  The Rigged Hilbert Space (RHS) theory of resonance scattering and decay is
reviewed and contrasted with the standard Hilbert space (HS) theory of quantum
mechanics. The main difference is in the choice of boundary conditions. Whereas
the conventional theory allows for the in-states $\phi^+$ and the out-states
(observables) $\psi^-$ of the S-matrix elements $(\psi^-,\phi^+)=(\psi^{out},S
\phi^{in})$ any elements of the HS $\H$, $\{\psi^-\}=\{\phi^+\}(=\H)$, the RHS
theory chooses the boundary conditions~:
$\phi^+\in\Phi_-\subset\H\subset\Phi_-^\times$, $\psi^-\in\Phi_+\subset
\H\subset \Phi_+^\times$, where $\Phi_-$ ($\Phi_+$) are Hardy class spaces
associated to the lower (upper) half-plane of the second sheet of the
analytically continued S-matrix. This can be phenomenologically justified by
causality. The two RHS's for states $\phi^+$ and observables $\psi^-$ provide
new vectors which are not in $\H$, e.g. the Dirac-Lippmann-Schwinger kets
$|E^{\pm}\in\Phi_{\mp}^{\times}$ (solutions of the Lippmann-Schwinger equation
with $\pm i\epsilon$ respectively) and the Gamow vectors
$|E_R-i\Gamma/2^\pm\in\Phi_{\mp}^\times$. The Gamow vectors $|E_R-i\Gamma/2^-$
have all the properties that one heuristically needs for quasistable states. In
addition, they give rise to asymmetric time evolution expressing
irreversibility on the microphysical level.


title: What is Quantum Computation?

abstract:
  Quantum computation is a rapidly progressing field today. What are its
principles? In what sense is it distinct from conventional computation? What
are its advantages and disadvantages? What type of problems can it address? How
practical is it to make a quantum computer? I summarise some of the important
concepts of quantum computation, in an attempt to answer these questions. A
deeper understanding of them would pave the way for future development.


title:
High-efficiency quantum interrogation measurements via the quantum Zeno
  effect

abstract:
  The phenomenon of quantum interrogation allows one to optically detect the
presence of an absorbing object, without the measuring light interacting with
it. In an application of the quantum Zeno effect, the object inhibits the
otherwise coherent evolution of the light, such that the probability that an
interrogating photon is absorbed can in principle be arbitrarily small. We have
implemented this technique, demonstrating efficiencies exceeding the 50%
theoretical-maximum of the original ``interaction-free'' measurement proposal.
We have also predicted and experimentally verified a previously unsuspected
dependence on loss; efficiencies of up to 73% were observed and the feasibility
of efficiencies up to 85% was demonstrated.


title: Radiation Pressure Approach to the Repulsive Casimir Force

abstract:
  We study the Casimir force between a perfectly conducting and an infinitely
permeable plate with the radiation pressure approach. This method illustrates
how a repulsive force arises as a consequence of the redistribution of the
vacuum-field modes corresponding to specific boundary conditions. We discuss
also how the method of the zero-point radiation pressure follows from QED.


title: Completely Mixing Quantum Open Systems and Quantum Fractals

abstract:
  Departing from classical concepts of ergodic theory, formulated in terms of
probability densities, measures describing the chaotic behavior and the loss of
information in quantum open systems are proposed. As application we discuss the
chaotic outcomes of continuous measurement processes in the EEQT framework.
Simultaneous measurement of four noncommuting spin components is shown to lead
to a chaotic jump on quantum spin sphere and to generate specific fractal
images - nonlinear ifs (iterated function system). The model is purely
theoretical at this stage, and experimental confirmation of the chaotic
behavior of measuring instruments during simultaneous continuous measurement of
several noncommuting quantum observables would constitute a quantitative
verification of Event Enhanced Quantum Theory.


title: Topics in Modern Quantum Optics

abstract:
  This is the written version of lectures presented at "The 17th Symposium on
Theoretical Physics - Applied Field Theory", 29 June - 1 July, 1998, the
Sangsan Mathematical Science Building, Seoul National University, Seoul, Korea.


title: Generalized equation of relativistic quantum mechanics in a gauge field

abstract:
  We develop an unified algebraic approach to the description of gauge
interactions within the framework of a new concept of quantum mechanics. The
next step in generalizing the space-time and the action vector space is made.
The gauge field is defined through linear mappings in the generalized
space-time and the action space. Relativistic quantum mechanics equations for
particles in a gauge field are derived from the structure equations for the
action space expanded in the linear mappings of action vectors. In a special
case, these equations are reduced to the relativistic equations for the leptons
in the electroweak field. As against the standard Glashow-Weinberg-Salam model,
the set of equations includes the equation for the right neutrino interacting
only with the weak Z-field.


title:
Quantum systems coupled to a structured reservoir with multiple
  excitations

abstract:
  We present a method for dealing with quantum systems coupled to a structured
reservoir with any density of modes and with more than one excitation. We apply
the method to a two-level atom coupled to the edge of a photonic band gap and a
defect mode. Results pertaining to this system, provide the solution to the
problem of two photons in the reservoir and possible generalization is
discussed.


title:
Quantum Computers and Unstructured Search: Finding and Counting Items
  with an Arbitrarily Entangled Initial State

abstract:
  Grover's quantum algorithm for an unstructured search problem and the Count
algorithm by Brassard et al. are generalized to the case when the initial state
is arbitrarily and maximally entangled. This ansatz might be relevant with
quantum subroutines, when the computational qubits and the environment are
coupled, and in general when the control over the quantum system is partial.


title: A Co-Operative Phenomena Type Local Realistic Theory

abstract:
  We analyze a conceivable type of local realistic theory, which we call a
co-operative phenomena type local realistic theory. In an experimental
apparatus to measure second or fourth order interference effects, it images
that their exists a stable global pattern or mode in a hypothesized medium that
is at least the size of the coherence volume of all the involved beams. If you
change the position of a mirror, beam splitter, polarizer, state preparation,
or block a beam then a new and different stable global state is entered very
quickly. In an interferometer a photon passes only one arm of the apparatus but
knows if the other arm is open or closed since the global pattern through which
it travels through contains this information and guides it appropriately. In a
polarization correlation experiment, two distant polarizers are part of the
same global pattern or state which is very rapidly determined by the whole
apparatus. It is experimentally testable. The situation in relationship to the
special relativity is also discussed.


title: A scheme for total quantum teleportation

abstract:
  We address the issue of totally teleporting the quantum state of an external
particle, as opposed to studies on partial teleportation of external
single-particle states, total teleportation of coherent states and encoded
single-particle states, and intramolecular teleportation of nuclear spin
states. We find a set of commuting observables whose measurement directly
projects onto the Bell-basis and discuss a possible experiment, based on
two-photon absorption, allowing, for the first time, total teleportation of the
state of a single external photon through a direct projective measurement.


title: Comment on Identical Motion in Classical and Quantum Mechanics

abstract:
  Makowski and Konkel [Phys. Rev. A 58, 4975 (1998)] have obtained certain
classes of potentials which lead to identical classical and quantum
Hamilton-Jacobi equations. We obtain the most general form of these potential.


title: Noncyclic geometric phase and its non-Abelian generalization

abstract:
  We use the theory of dynamical invariants to yield a simple derivation of
noncyclic analogues of the Abelian and non-Abelian geometric phases. This
derivation relies only on the principle of gauge invariance and elucidates the
existing definitions of the Abelian noncyclic geometric phase. We also discuss
the adiabatic limit of the noncyclic geometric phase and compute the adiabatic
non-Abelian noncyclic geometric phase for a spin 1 magnetic (or electric)
quadrupole interacting with a precessing magnetic (electric) field.


title: Quantum Computation and Quadratically Signed Weight Enumerators

abstract:
  We prove that quantum computation is polynomially equivalent to classical
probabilistic computation with an oracle for estimating the value of simple
sums, quadratically signed weight enumerators. The problem of estimating these
sums can be cast in terms of promise problems and has two interesting variants.
An oracle for the unconstrained variant may be more powerful than quantum
computation, while an oracle for a more constrained variant is efficiently
solvable in the one-bit model of quantum computation. Thus, problems involving
estimation of quadratically signed weight enumerators yield problems in BQP
(bounded error quantum polynomial time) that are distinct from the ones studied
so far, include a canonical BQP complete problem, and can be used to define and
study complexity classes and their relationships to quantum computation.


title: Qutrit Entanglement

abstract:
  We consider the separability of various joint states for N qutrits. We derive
two results: (i) the separability condition for a two-qutrit state that is a
mixture of the maximally mixed state and a maximally entangled state (such a
state is a generalization of the Werner state for two qubits); (ii) upper and
lower bounds on the size of the neighborhood of separable states surrounding
the maximally mixed state for N qutrits.


title: Continuity of Relative Entropy of Entanglement

abstract:
  We show that an entanglement measure called relative entropy of entanglement
satisfies a strong continuity condition. If two states are close to each other
then so are their entanglements per particle pair in this measure. It follows
in particular, that the measure is appropriate for the description of
entanglement manipulations in the limit of an infinite number of pairs of
particles.


title:
Exact solutions of nonstationary Schredinger equations and geometric
  phase

abstract:
  A procedure of solving nonstationary Schredinger equations in the exact
analytic form is elaborated on the basis of exactly solvable stationary models.
The exact solutions are employed to study the nonadiabatic geometric phase.


title:
Exact Solutions of the Caldeira-Leggett Master Equation: A Factorization
  Theorem For Decoherence

abstract:
  Exact solutions of the Caldeira-Leggett Master equation for the reduced
density matrix for a free particle and for a harmonic oscillator system coupled
to a heat bath of oscillators are obtained for arbitrary initial conditions.
The solutions prove that the Fourier transform of the density matrix at time t
with respect to (x + x')/2, where x and x' are the initial and final
coordinates, factorizes exactly into a part depending linearly on the initial
density matrix and a part independent of it. The theorem yields the exact
initial state dependence of the density operator at time t and its eventual
diagonalization in the energy basis.


title:
Quantum Computation using Decoherence-Free States of the Physical
  Operator Algebra

abstract:
  The states of the physical algebra, namely the algebra generated by the
operators involved in encoding and processing qubits, are considered instead of
those of the whole system-algebra. If the physical algebra commutes with the
interaction Hamiltonian, and the system Hamiltonian is the sum of arbitrary
terms either commuting with or belonging to the physical algebra, then its
states are decoherence free. One of the considered examples shows that, for a
uniform collective coupling to the environment, the smallest number of physical
qubits encoding a decoherence free logical qubit is reduced from four to three.


title: NMR quantum computation with indirectly coupled gates

abstract:
  An NMR realization of a two-qubit quantum gate which processes quantum
information indirectly via couplings to a spectator qubit is presented in the
context of the Deutsch-Jozsa algorithm. This enables a successful comprehensive
NMR implementation of the Deutsch-Jozsa algorithm for functions with three
argument bits and demonstrates a technique essential for multi-qubit quantum
computation.


title: Quantum Dynamics of Non-Degenerate Parametric Amplification

abstract:
  A simple model of a two-mode non-resonant parametric amplifier is studied
with special regard to non-classical features such as revivals and squeezing.
The methods used apply for an arbitrary pump parameter. Detailed analytical and
explicit expressions are given when the coupling of the two modes has an
harmonic time-dependence. Despite its simplicity the model exhibits a very
broad range of intricate physical effects. We show that quantum revivals are
possible for a broad continuous range of physical parameters in the case of
initial Fock states. For coherent states we find that such revivals are
possible only for certain discrete rational number combinations of the ratio of
frequency detuning and pump parameters. Correlation effects are shown to be
very sensitive to the initial state of the system.


title: Evolution loops and spin-1/2 systems

abstract:
  The derivation of a new family of magnetic fields inducing exactly solvable
spin evolutions is presented. The conditions for which these fields generate
the evolution loops (dynamical processes for which any spin state evolves
cyclically) are studied. Their natural connection with geometric phases and the
corresponding calculation is also elaborated.


title: Backlund-type superposition and free particle n-susy partners

abstract:
  The higher order susy partners of Schroedinger Hamiltonians can be explicitly
constructed by iterating a nonlinear difference algorithm coinciding with the
Backlund superposition principle used in soliton theory. As an example, it is
applied in the construction of new higher order susy partners of the free
particle potential, which can be used as a handy tool in soliton theory.


title: Dense Coding for Continuous Variables

abstract:
  A scheme to achieve dense quantum coding for the quadrature amplitudes of the
electromagnetic field is presented. The protocol utilizes shared entanglement
provided by nondegenerate parametric down conversion in the limit of large gain
to attain high efficiency. For a constraint in the mean number of photons n
associated with modulation in the signal channel, the channel capacity for
dense coding is found to be ln(1+n+n^2), which always beats coherent-state
communication and surpasses squeezed-state communication for n>1. For n>>1, the
dense coding capacity approaches twice that of either scheme.


title:
Geometric Formulation of Nonlinear Quantum Mechanics for Density
  Matrices

abstract:
  Proposals for nonlinear extenstions of quantum mechanics are discussed. Two
different concepts of "mixed state" for any nonlinear version of quantum theory
are introduced: (i) >genuine mixture< corresponds to operational "mixing" of
different ensembles, and (ii) a mixture described by single density matrix
without having a canonical operational possibility to pick out its specific
convex decomposition is called here an >elementary mixture<. Time evolution of
a class of nonlinear extensions of quantum mechanics is introduced. Evolution
of an elementary mixture cannot be generally given by evolutions of components
of its arbitrary convex decompositions. The theory is formulated in a
"geometric form": It can be considered as a version of Hamiltonian mechanics on
infinite dimensional space of density matrices. A quantum interpretation of the
theory is sketched.


title: On Symmetries in Nonlinear Quantum Mechanics

abstract:
  It is shown how nonlinear versions of quantum mechanics can be refolmulated
in terms of a (linear) C*-algebraic theory. Then also their symmetries are
described as automorphisms of the correspondong C*-algebra. The requirement of
"conservation of transition probabilities" is discussed.


title: Transfer formalism for quantum optics problems

abstract:
  Consistent quantum formalism based on the localized basis of the Wannirer
functions in Heisenberg and Schrodinger pictures to describe propagation of
electromagnetic field in a three dimensional media including diffraction is
presented. In the Schrodinger picture the Fokker-Planck equation for the
Glauber-Sudarshan quasiprobability and corresponding Langevin equations are
given. As result the space-time description is obtained by a simple changing
variables in the temporal master equation of the field. Using this formalism it
is shown that the existence of integrals of motion in the propagation of light
in a medium under the condition of nondegenerated parametric and two-photon
interactions results in amplification of modes when nonclassical properties of
the light are conserved. Quantum propagation of light in a linear medium taking
into account the diffraction is considered and its solution is found.


title:
Intermediate coherent-phase(PB) states of radiation fields and their
  nonclassical properties

abstract:
  Intermediate states interpolating coherent states and Pegg-Barnett phase
states are investigated using the ladder operator approach. These states reduce
to coherent and Pegg-Barnett phase states in two different limits. Statistical
and squeezing properties are studied in detail.


title:
Implementation of the refined Deutsch-Jozsa algorithn on a 3-bit NMR
  quantum computer

abstract:
  We implemented the refined Deutsch-Jozsa algorithm on a 3-bit nuclear
magnetic resonance quantum computer, which is the meaningful test of quantum
parallelism because qubits are entangled. All of the balanced and constant
functions were realized exactly. The results agree well with theoretical
predictions and clearly distinguish the balanced functions from constant
functions. Efficient refocusing schemes were proposed for the soft z-pulse and
J-coupling and it is proved that the thermal equilibrium state gives the same
results as the pure state for this algorithm.


title: Stabilizing Quantum Information

abstract:
  The dynamical-algebraic structure underlying all the schemes for quantum
information stabilization is argued to be fully contained in the reducibility
of the operator algebra describing the interaction with the environment of the
coding quantum system. This property amounts to the existence of a non-trivial
group of symmetries for the global dynamics. We provide a unified framework
which allows us to build systematically new classes of error correcting codes
and noiseless subsystems. It is shown how by using symmetrization strategies
one can artificially produce noiseless subsystems supporting universal quantum
computation.


title: The supersymmetric modified Poschl-Teller and delta-well potentials

abstract:
  New supersymmetric partners of the modified Poschl-Teller and the Dirac's
delta well potentials are constructed in closed form. The resulting
one-parametric potentials are shown to be interrelated by a limiting process.
The range of values of the parameters for which these potentials are free of
singularities is exactly determined. The construction of higher order
supersymmetric partner potentials is also investigated.


title: No-Concentrating Theorem of Pure Entangled States

abstract:
  Suppose two distant observers Alice and Bob share a pure biparticle entangled
state secretly chosen from a set, it is shown that Alice (Bob) can
probabilistic concentrate the state to a maximally entangled state by applying
local operations and classical communication (LQCC) if and only if the states
in the set share the same marginal density operator for her (his) subsystem.
Applying this result, we present probabilistic superdense coding and show that
perfect purification of mixed state is impossible using only LQCC on individual
particles.