title:
Deterministic Bell states and measurement of the motional state of two
  trapped ions

abstract:
  We present a method for the deterministic generation of all the electronic
Bell states of two trapped ions. It involves the combination of a purely
dispersive with a resonant laser excitation of vibronic transitions of the
ions. In contrast to other methods presented up to now, our proposal does not
require differential laser addressing of the individual ions and may be easily
implemented with present available techniques. It is further shown that this
excitation scheme is highly adequate for the complete determination of the
motional state of the ions.


title:
Photon-photon interactions in cavity electromagnetically induced
  transparency

abstract:
  Dissipation-free photon-photon interaction at the single photon level is
studied in the context of cavity electromagnetically induced transparency
(EIT). For a single multilevel atom exhibiting EIT in the strong
cavity-coupling regime, the anharmonicity of the atom-cavity system has an
upper bound determined by single atom-photon coupling strength. Photon blockade
is inferred to occur for both single and multi-atom cases from the behaviour of
transition rates between dressed states of the system. Numerical calculations
of the second order coherence function indicate that photon antibunching in
both single and two-atom cases are strong and comparable.


title:
A study of quantum decoherence in a system with Kolmogorov-Arnol'd-Moser
  tori

abstract:
  We present an experimental and numerical study of the effects of decoherence
on a quantum system whose classical analogue has Kolmogorov-Arnol'd-Moser (KAM)
tori in its phase space. Atoms are prepared in a caesium magneto-optical trap
at temperatures and densities which necessitate a quantum description. This
real quantum system is coupled to the environment via spontaneous emission. The
degree of coupling is varied and the effects of this coupling on the quantum
coherence of the system are studied. When the classical diffusion through a
partially broken torus is < hbar, diffusion of quantum particles is inhibited.
We find that increasing decoherence via spontaneous emission increases the
transport of quantum particles through the boundary.


title:
Semiclassical Calculation of Transition Matrix Elements for Atoms in
  External Fields

abstract:
  Closed orbit theory is generalized to the semiclassical calculation of
cross-correlated recurrence functions for atoms in external fields. The
cross-correlation functions are inverted by a high resolution spectral analyzer
to obtain the semiclassical eigenenergies and transition matrix elements. The
method is demonstrated for dipole transitions of the hydrogen atom in a
magnetic field. This is the first semiclassical calculation of individual
quantum transition strengths from closed orbit theory.

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


title:
Somewhere in the Universe: Where is the Information Stored When
  Histories Decohere?

abstract:
  We investigate the idea that decoherence is connected with the storage of
information about the decohering system somewhere in the universe. The known
connection between decoherence of histories and the existence of records is
extended from the case of pure initial states to mixed states. Records may
still exist but are necessarily imperfect. We formulate an
information-theoretic conjecture about decoherence due to an environment: the
number of bits required to describe a set of decoherent histories is
approximately equal to the number of bits of information thrown away to the
environment in the coarse-graining process. This idea is verified in a simple
model consisting of a particle coupled to an environment that can store only
one bit of information. We explore the decoherence and information storage in
the quantum Brownian motion model. It is shown that the variables that the
environment naturally measures and stores information about are the Fourier
components of the function $x(t)$ (describing the particle trajectory). The
records storing the information about the Fourier modes are the positions and
momenta of the environmental oscillators at the final time. Decoherence is
possible even if there is only one oscillator in the environment. The
information count of the histories and records in the environment add up
according to our conjecture. These results give quantitative content to the
idea that decoherence is related to ``information lost''.


title: Heating of trapped atoms near thermal surfaces

abstract:
  We study the electromagnetic coupling and concomitant heating of a particle
in a miniaturized trap close to a solid surface. Two dominant heating
mechanisms are identified: proximity fields generated by thermally excited
currents in the absorbing solid and time-dependent image potentials due to
elastic surface distortions (Rayleigh phonons). Estimates for the lifetime of
the trap ground state are given. Ions are particularly sensitive to electric
proximity fields: for a silver substrate, we find a lifetime below one second
at distances closer than some ten micrometer to the surface. Neutral atoms may
approach the surface more closely: if they have a magnetic moment, a minimum
distance of one micrometer is estimated in tight traps, the heat being
transferred via magnetic proximity fields. For spinless atoms, heat is
transferred by inelastic scattering of virtual photons off surface phonons. The
corresponding lifetime, however, is estimated to be extremely long compared to
the timescale of typical experiments.


title: Quantum Triangulation and Violation of Conservation of Trouble

abstract:
  A scheme is described that allows Alice to communicate to Bob where on earth
she is, even though she doesn't know herself. The situation described shows how
the generalization of a recent result of Gisin and Popescu [quant-ph/9901072]
could be useful.


title: Comment on "Quantum Theory of Dispersive Electromagnetic Fields"

abstract:
  Recently Drummond and Hillery [Phys. Rev.A 59, 691(1999)] presented a quantum
theory of dispersion based on the analysis of a coupled system of the
electromagnetic field and atoms in the multipolar QED formulation. The theory
has led to the explicit mode-expansions for various field-operators in a
homogeneous medium characterized by an arbitrary number of resonant transitions
with different frequencies. In this Comment, we drawn attention to a similar
multipolar study by Juzeliunas [Phys. Rev.A 53, 3543 (1996); 55, 929 (1997)] on
the field quantization in a discrete molecular (or atomic) medium. A
comparative analysis of the two approaches is carried out, highlighting both
common and distinctive features.


title: A role of antiquantum bits for superdense coding and quantum computing

abstract:
  We define an anti-quantum bit state via analogous way as the anti-state in
Particle Physics.We show the quantum information Feymann diagrams for the
teleportations and superdense coding, which preserve the information flow. The
role of information vacuum and anihilation between error information and
anti-information is mentioned for the stability of quantum computing.


title: On the parametric approximation in quantum optics

abstract:
  We perform the exact numerical diagonalization of the Hamiltonians that
describe both degenerate and nondegenerate parametric amplifiers, by exploiting
the conservation laws pertaining each device. We clarify the conditions under
which the parametric approximation holds, showing that the most relevant
requirement is the coherence of the pump after the interaction, rather than its
undepletion.


title:
Towards Quantifying Non-Local Information Transfer: Finite-Bit
  Non-Locality

abstract:
  The advent of Bell's inequalities provoked the possibility that entangled
quantum phenomena is non-local in nature. Since teleportation only requires a
finite amount of classical information, i.e. two bits, the author asks whether
or not it is possible to further characterize the nature of internal
correlation in terms of information. Towards this end, the issue of the amount
of information that is transferred internally and non-locally is addressed.
There are two possibilities: the amount is infinite or the amount is finite. A
partial answer to this problem is given: it is shown that models exist whereby
the amount is finite. The EPR-Bell cosine correlation can be reproduced exactly
using on average 1.48 bits. The issue of simultaneity and the problems it poses
are also examined in this context. Several extensions are suggested.


title:
Double Solution with Chaos: Dynamic Redundance and Causal Wave-Particle
  Duality

abstract:
  A system of two interacting, physically real, initially homogeneous fields is
considered as the simplest basis for the world construction in which one of
them, a 'protofield' of electromagnetic nature, is attracted to another
protofield, or medium, responsible for the eventually emerging gravitational
effects. The interaction process is analysed within the generalised 'effective
(optical) potential method' in which we avoid any usual perturbative reduction.
It then appears that for generic system parameters the protofields, instead of
simply 'falling' one onto another and forming a fixed 'bound state', are
engaged in a self-sustained process of nonlinear pulsation, or 'quantum beat',
consisting in unceasing cycles of self-amplified auto-squeeze, or 'collapse'
('reduction'), of a portion of the extended protofields to a small volume
followed by the inverse phase of extension. Centres of consecutive reductions
form the physical 'points' of thus emerging, intrinsically discrete space, and
each of them is 'selected' by the system in a causally random fashion among
many equally possible versions (or 'realisations'). This is a manifestation of
the dynamic redundance forming the unified basis of dynamically complex
(chaotic) behaviour of any real system with interaction (physics/9806002). The
sequence of reduction events constitutes the elementary physical 'clock' of the
world providing it with the unceasing, intrinsically irreversible time flow.
The complex-dynamical quantum beat process in the system of two interacting
protofields is observed as the massive elementary particle (like the electron)
which naturally possesses the property of physically real wave-particle duality
completing the double solution concept of Louis de Broglie (see also
quant-ph/9902016, gr-qc/9906077).


title:
Double Solution with Chaos: Completion of de Broglie's Nonlinear Wave
  Mechanics and Its Intrinsic Unification with the Causally Extended Relativity

abstract:
  A system of two interacting protofields with generic parameters is unstable
with respect to unceasing cycles of nonlinear squeeze (reduction) to randomly
chosen centres and reverse extension which form the causally probabilistic
process of quantum beat observed as elementary particle (quant-ph/9902015).
Here we show that the emerging wave-particle duality, space, and time lead to
the equations of special relativity and quantum mechanics thus providing their
causal extension and unification. Relativistic inertial mass (energy) is
universally defined as the temporal rate (frequency) of the chaotic quantum
beat process(es). The same complex dynamical processes and mass account for
universal gravitation, since any reduction event in the electromagnetic
protofield involves also the (directly unobservable) gravitational protofield
thus increasing its tension and influencing quantum beat frequencies of other
particles. This complex dynamical mechanism of universal gravitation provides
causal extension of general relativity intrinsically unified with causal
quantum mechanics and special relativity, as well as physical origin and
unification of all the four 'fundamental forces' (also gr-qc/9906077). The
dynamic origin of the Dirac quantization rules is also revealed and used for
the first-principles derivation of the Dirac and Schroedinger equations
describing the same irreducibly complex, internally nonlinear interaction
processes within field-particles and their simplest systems (quant-ph/9511034 -
quant-ph/9511038). The classical, dynamically localised behaviour naturally
emerges as a higher level of complexity appearing as formation of elementary
bound systems (like atoms).


title:
Path Integral Solutions for Deformed P"oschl-Teller-like and
  Conditionally Solvable Potentials

abstract:
  I discuss in this paper the behaviour of the solutions of the so-called
q-hyperbolic potentials, i.e. P"oschl-Teller-like and conditionally solvable
potentials, in terms of the path integral formalism. The differences in
comparison to the usual P"oschl-Teller-like potentials are investigated,
including the discrete energy spectra and the bound state wave-functions.


title:
Quantum spacetime without observers: ontological clarity and the
  conceptual foundations of quantum gravity

abstract:
  We explore the possibility of a Bohmian approach to the problem of finding a
quantum theory incorporating gravitational phenomena. The major conceptual
problems of canonical quantum gravity are the problem of time and the problem
of diffeomorphism invariant observables. We find that these problems are
artifacts of the subjectivity and vagueness inherent in the framework of
orthodox quantum theory. When we insist upon ontological clarity---the
distinguishing characteristic of a Bohmian approach---these conceptual problems
vanish. We shall also discuss the implications of a Bohmian perspective for the
significance of the wave function, concluding with unbridled speculation as to
why the universe should be governed by laws so apparently bizarre as those of
quantum mechanics.


title: On the role of Spin in Quantum Mechanics

abstract:
  From the invariance properties of the Schrodinger equation and the isotropy
of space we show that a generic (non-relativistic) quantum system is endowed
with an ``external'' motion, which can be interpreted as the motion of the
centre of mass, and an ``internal'' one, whose presence disappears in the
classical limit. The latter is caused by the spin of the particle, whatever is
its actual value (different from zero). The quantum potential in the
Schrodinger equation, which is responsible of the quantum effects of the
system, is then completely determined from the properties of the internal
motion, and its ``unusual'' properties have a simple and physical explanation
in the present context. From the impossibility to fix the initial conditions
relevant for the internal motion follows, finally, the need of a probabilistic
interpretation of quantum mechanics.


title: Pattern formation in quantum Turing machines

abstract:
  We investigate the iteration of a sequence of local and pair unitary
transformations, which can be interpreted to result from a Turing-head
(pseudo-spin $S$) rotating along a closed Turing-tape ($M$ additional
pseudo-spins). The dynamical evolution of the Bloch-vector of $S$, which can be
decomposed into $2^{M}$ primitive pure state Turing-head trajectories, gives
rise to fascinating geometrical patterns reflecting the entanglement between
head and tape. These machines thus provide intuitive examples for quantum
parallelism and, at the same time, means for local testing of quantum network
dynamics.


title: Probing the Vacuum Induced Coherence in a $\Lambda$-system

abstract:
  We propose a simple test to demonstrate and detect the presence of vacuum
inducde coherence in a $\Lambda$-system. We show that the probe field
absorption is modulated due to the presence of such a coherence which is
unobservable in fluorescence. We present analytical and numerical results for
the modulated absorption, the cosine and sine components of which display
different types of behavior.


title: Optimal Entanglement Enhancement for Mixed States

abstract:
  We consider the actions of protocols involving local quantum operations and
classical communication (LQCC) on a single system consisting of two separated
qubits. We give a complete description of the orbits of the space of states
under LQCC and characterise the representatives with maximal entanglement of
formation. We thus obtain a LQCC entanglement concentration protocol for a
single given state (pure or mixed) of two qubits which is optimal in the sense
that the protocol produces, with non-zero probability, a state of maximal
possible entanglement of formation. This defines a new entanglement measure,
the maximum extractable entanglement.


title: Entanglement splitting of pure bipartite quantum states

abstract:
  The concept of entanglement splitting is introduced by asking whether it is
possible for a party possessing half of a pure bipartite quantum state to
transfer some of his entanglement with the other party to a third party. We
describe the unitary local transformation for symmetric and isotropic splitting
of a singlet into two branches that leads to the highest entanglement of the
output. The capacity of the resulting quantum channels is discussed. Using the
same transformation for less than maximally entangled pure states, the
entanglement of the resulting states is found. We discuss whether they can be
used to do teleportation and to test the Bell inequality. Finally we generalize
to entanglement splitting into more than two branches.


title: Moving quantum agents in a finite environment

abstract:
  We investigate an all-quantum-mechanical spin network, in which a subset of
spins, the $K$ ``moving agents'', are subject to local and pair unitary
transformations controlled by their position with respect to a fixed ring of
$M$ ``environmental''-spins. We demonstrate that a ``flow of coherence''
results between the various subsystems. Despite entanglement between the agents
and between agent and environment, local (non-linear) invariants may persist,
which then show up as fascinating patterns in each agent's Bloch-sphere. Such
patterns disappear, though, if the agents are controlled by different rules.
Geometric aspects thus help to understand the interplay between entanglement
and decoherence.


title:
Experimental evidence for the role of cantori as barriers in a quantum
  system

abstract:
  We investigate the effect of cantori on momentum diffusion in a quantum
system. Ultracold caesium atoms are subjected to a specifically designed
periodically pulsed standing wave. A cantorus separates two chaotic regions of
the classical phase space. Diffusion through the cantorus is classically
predicted. Quantum diffusion is only significant when the classical phase-space
area escaping through the cantorus per period greatly exceeds Planck's
constant. Experimental data and a quantum analysis confirm that the cantori act
as barriers.


title: Complete positivity and neutron interferometry

abstract:
  We analyze the dynamics of neutron beams in interferometry experiments using
quantum dynamical semigroups. We show that these experiments could provide
stringent limits on the non-standard, dissipative terms appearing in the
extended evolution equations.


title: Non-Mechanism in Quantum Oracle Computing

abstract:
  A typical oracle problem is finding which software program is installed on a
computer, by running the computer and testing its input-output behaviour. The
program is randomly chosen from a set of programs known to the problem solver.
As well known, some oracle problems are solved more efficiently by using
quantum algorithms; this naturally implies changing the computer to quantum,
while the choice of the software program remains sharp. In order to highlight
the non-mechanistic origin of this higher efficiency, also the uncertainty
about which program is installed must be represented in a quantum way.


title: The Universe of Chaos and Quanta

abstract:
  In recent papers it was shown that stochastic processes in the universe as a
whole lead to discrete space time at Compton scales as also non-relativistic
Quantum Mechanics. In this paper, we deduce the Dirac equation and thence a
unified formulation of quarks and leptons. In the process several puzzling
empirical results and coincidences are shown to be a consequence of the theory.
These include the discreteness of the charge, handedness of quarks, their
fractional charge, confinement and masses and the handedness of neutrinos, the
so called accidental relation that the classical Kerr- Newman metric describes,
the field of an electron including the purely quantum mechanical gyromagnetic
ratio g=2, as also the many large number coincidences made famous by Dirac and
Weinberg's mysterious empirical formula that relates the pion mass to the
Hubble Constant. A cosmology based on fluctuations related to the above
stochastic space-time discretization, consistent with latest observations is
also seen to follow.


title: Time as a statistical variable and intrinsic decoherence

abstract:
  We propose a novel approach to intrinsic decoherence without adding new
assumptions to standard Quantum Mechanics. We generalize the Liouville equation
just by requiring the dynamical semigroup property of time evolution and
dropping the unitarity requirement. With no approximations and specific
statistical assumptions we find a generalized Liouville equation which depends
on two characteristic time t1 and t2 and reduces to the usual equation in the
limit t1 = t2 --> 0. However, for t1 and t2 arbitrarily small but finite, our
equation can be written as a finite difference equation which predicts state
reduction to the diagonal form in the energy representation. The rate of
decoherence becomes faster at the macroscopic limit as the energy scale of the
system increases. In our approach the evolution time appears, a posteriori, as
a statistical variable as if time evolution would take place randomly at
average intervals t2, each evolution having a time width t1. A generalized Tam
Mandelstam inequality is derived. The relation with previous work by Milburn is
discussed. The agreement with recent experiments on damped Rabi oscillations is
described.


title: Broadband teleportation

abstract:
  Quantum teleportation of an unknown broadband electromagnetic field is
investigated. The continuous-variable teleportation protocol by Braunstein and
Kimble [Phys. Rev. Lett. {\bf 80}, 869 (1998)] for teleporting the quantum
state of a single mode of the electromagnetic field is generalized for the case
of a multimode field with finite bandwith. We discuss criteria for
continuous-variable teleportation with various sets of input states and apply
them to the teleportation of broadband fields. We first consider as a set of
input fields (from which an independent state preparer draws the inputs to be
teleported) arbitrary pure Gaussian states with unknown coherent amplitude
(squeezed or coherent states). This set of input states, further restricted to
an alphabet of coherent states, was used in the experiment by Furusawa {\it et
al.} [Science {\bf 282}, 706 (1998)]. It requires unit-gain teleportation for
optimizing the teleportation fidelity. In our broadband scheme, the excess
noise added through unit-gain teleportation due to the finite degree of the
squeezed-state entanglement is just twice the (entanglement) source's squeezing
spectrum for its ``quiet quadrature.'' The teleportation of one half of an
entangled state (two-mode squeezed vacuum state), i.e., ``entanglement
swapping,'' and its verification are optimized under a certain nonunit gain
condition. We will also give a broadband description of this
continuous-variable entanglement swapping based on the single-mode scheme by
van Loock and Braunstein [Phys. Rev. A {\bf 61}, 10302 (2000)]


title:
Quantum gates by coupled asymmetric quantum dots and controlled-NOT-gate
  operation

abstract:
  A quantum computer based on an asymmetric coupled dot system has been
proposed and shown to operate as the controlled-NOT-gate. The basic idea is (1)
the electron is localized in one of the asymmetric coupled dots. (2)The
electron transfer takes place from one dot to the other when the energy-levels
of the coupled dots are set close. (3)The Coulomb interaction between the
coupled dots mutually affects the energy levels of the other coupled dots. The
decoherence time of the quantum computation and the measurement time are
estimated. The proposed system can be realized by developing the technology of
the single-electron memory using Si nanocrystals and the direct combination of
the quantum circuit and the conventional circuit is possible.


title:
A non-Markovian quantum trajectory approach to radiation into structured
  continuum

abstract:
  We present a non-Markovian quantum trajectory method for treating atoms
radiating into a reservoir with a non-flat density of states. The results of an
example numerical simulation of the case where the free space modes of the
reservoir are altered by the presence of a cavity are presented and compared
with those of an extended system approach.


title: Entanglement of pure states for a single copy

abstract:
  An optimal local conversion strategy between any two pure states of a
bipartite system is presented. It is optimal in that the probability of success
is the largest achievable if the parties which share the system, and which can
communicate classically, are only allowed to act locally on it. The study of
optimal local conversions sheds some light on the entanglement of a single copy
of a pure state. We propose a quantification of such an entanglement by means
of a finite minimal set of new measures from which the optimal probability of
conversion follows.


title:
On intrinsic structure of wave function of fermion triplet in external
  monopole field

abstract:
  Using the Weyl-Tetrode-Fock spinor formalism, the fermion triplet in the 't
Hooft-Polyakov monopole field is examined all over again. Spherical solutions
corresponding to the total conserved momentum J =l + S + T are constructed. The
angular dependence is expressed in terms of the Wigner's functions. The radial
system of 12 equations decomposes into two sub-systems by diagonalizing some
complicated inversion operator. The case of minimal j = 1/2 is considered
separately. A more detailed analysis is accomplished for the case of simplest
monopole field: namely, the one produced by putting the Dirac potential into
the non-Abelian scheme. Now a discrete operation diagonalized contains an
additional complex parameter A. The same parameter enters wave functions. This
quantity can manifest itself at matrix elements. In particular, there have been
analyzed the N(A)-parity selection rules: those depending on the A. As shown,
the A-freedom is a consequence of the existence of additional symmetry of the
relevant Hamiltonian. The wave functions exhibit else one kind of freedom:
B-freedom associated in turn with its own symmetry of the Hamiltonian. There
has been examined both A and B-transformations relating functions associated
with different A and B.


title: Time Dependence in Quantum Mechanics

abstract:
  It is shown that the time-dependent equations (Schr\"odinger and Dirac) for a
quantum system can be always derived from the time-independent equation for the
larger object of the system interacting with its environment, in the limit that
the dynamical variables of the environment can be treated semiclassically. The
time which describes the quantum evolution is then provided parametrically by
the classical evolution of the environment variables. The method used is a
generalization of that known for a long time in the field of ion-atom
collisions, where it appears as a transition from the full quantum mechanical
{\it perturbed stationary states} to the {impact parameter} method in which the
projectile ion beam is treated classically.


title: Multi-particle entanglement and its applications to cryptography

abstract:
  Entanglement between three or more parties exhibits a realm of properties
unknown to two-party states. Bipartite states are easily classified using the
Schmidt decomposition. The Schmidt coefficients of a bipartite pure state
encompass all the non-local properties of the state and can be "seen" by
looking at one party's density matrix only.
  Pure states of three and more parties however lack such a simple form. They
have more invariants under local unitary transformations than any one party can
"see" on their sub-system. These "hidden non-localities" will allow us to
exhibit a class of multipartite states that cannot be distinguished from each
other by any party. Generalizing a result of BPRST and using a recent result by
Nielsen we will show that these states cannot be transformed into each other by
local actions and classical communication. Furthermore we will use an
orthogonal subset of such states to hint at applications to cryptography and
illustrate an extension to quantum secret sharing (using recently suggested
((n,k))-threshold schemes).


title: A New Interpretation of Quantum Theory -- Time as Hidden Variable

abstract:
  Using 2 more time variables as the quantum hidden variables, we derive the
equation of Dirac field under the principle of classical physics, then we
extend our method into the quantum fields with arbitrary spin number. The spin
of particle is shown naturally as the topological property of 3-dimensional
time + 3-dimensional space . One will find that the quantum physics of single
particle can be interpreted as the behavior of the single particle in 3+3
time-space .


title: Quantum Key Distribution Using Three Basis States

abstract:
  This note presents a method of public key distribution using quantum
communication of n photons that simultaneously provides a high probability that
the bits have not been tampered. It is a three-state variant of the quantum
method of Bennett and Brassard (BB84) where the transmission states have been
decreased from 4 to 3 and the detector states have been increased from 2 to 3.
Under certain assumptions regarding method of attack, it provides superior
performance (in terms of the number of usable key bits) for n < 18 m, where m
is the number of key bits used to verify the integrity of the process in the
BB84-protocol.


title: Quantum revivals and carpets in some exactly solvable systems

abstract:
  We consider the revival properties of quantum systems with an eigenspectrum
E_{n} proportional to n^{2}, and compare them with the simplest member of this
class - the infinite square well. In addition to having perfect revivals at
integer multiples of the revival time t_{R}, these systems all enjoy perfect
fractional revivals at quarterly intervals of t_{R}. A closer examination of
the quantum evolution is performed for the Poeschel-Teller and Rosen-Morse
potentials, and comparison is made with the infinite square well using quantum
carpets.


title:
Quantum noise in the position measurement of a cavity mirror undergoing
  Brownian motion

abstract:
  We perform a quantum theoretical calculation of the noise power spectrum for
a phase measurement of the light output from a coherently driven optical cavity
with a freely moving rear mirror. We examine how the noise resulting from the
quantum back action appears among the various contributions from other noise
sources. We do not assume an ideal (homodyne) phase measurement, but rather
consider phase modulation detection, which we show has a different shot noise
level. We also take into account the effects of thermal damping of the mirror,
losses within the cavity, and classical laser noise. We relate our theoretical
results to experimental parameters, so as to make direct comparisons with
current experiments simple. We also show that in this situation, the standard
Brownian motion master equation is inadequate for describing the thermal
damping of the mirror, as it produces a spurious term in the steady-state phase
fluctuation spectrum. The corrected Brownian motion master equation [L. Diosi,
Europhys. Lett. {\bf 22}, 1 (1993)] rectifies this inadequacy.


title: Robustness of Decoherence-Free Subspaces for Quantum Computation

abstract:
  It was shown recently [D.A. Lidar et al., Phys. Rev. Lett. 81, 2594 (1998)]
that within the framework of the semigroup Markovian master equation,
decoherence-free (DF) subspaces exist which are stable to first order in time
to a perturbation. Here this result is extended to the non-Markovian regime and
generalized. In particular, it is shown that within both the semigroup and the
non-Markovian operator sum representation, DF subspaces are stable to all
orders in time to a symmetry-breaking perturbation. DF subspaces are thus ideal
for quantum memory applications. For quantum computation, however, the
stability result does not extend beyond the first order. Thus, to perform
robust quantum computation in DF subspaces, they must be supplemented with
quantum error correcting codes.


title: Quantum logic. A brief outline

abstract:
  Quantum logic has been introduced by Birkhoff and von Neumann as an attempt
to base the logical primitives, the propositions and the relations and
operations among them, on quantum theoretical entities, and thus on the related
empirical evidence of the quantum world. We give a brief outline of quantum
logic, and some of its algebraic properties, such as nondistributivity, whereby
emphasis is given to concrete experimental setups related to quantum logical
entities. A probability theory based on quantum logic is fundamentally and
sometimes even spectacularly different from probabilities based on classical
Boolean logic. We give a brief outline of its nonclassical aspects; in
particular violations of Boole-Bell type consistency constraints on joint
probabilities, as well as the Kochen-Specker theorem, demonstrating in a
constructive, finite way the scarcity and even nonexistence of two-valued
states interpretable as classical truth assignments. A more complete
introduction of the author can be found in the book "Quantum Logic" (Springer,
1998)


title: Non-Markovian quantum state diffusion: Perturbation approach

abstract:
  We present a perturbation theory for non-Markovian quantum state diffusion
(QSD), the theory of diffusive quantum trajectories for open systems in a
bosonic environment [Physical Review {\bf A 58}, 1699, (1998)]. We establish a
systematic expansion in the ratio between the environmental correlation time
and the typical system time scale. The leading order recovers the Markov
theory, so here we concentrate on the next-order correction corresponding to
first-order non-Markovian master equations. These perturbative equations
greatly simplify the general non-Markovian QSD approach, and allow for
efficient numerical simulations beyond the Markov approximation. Furthermore,
we show that each perturbative scheme for QSD naturally gives rise to a
perturbative scheme for the master equation which we study in some detail.
Analytical and numerical examples are presented, including the quantum Brownian
motion model.


title: Operational Time of Arrival in Quantum Phase Space

abstract:
  An operational time of arrival is introduced using a realistic position and
momentum measurement scheme. The phase space measurement involves the dynamics
of a quantum particle probed by a measuring device. For such a measurement an
operational positive operator valued measure in phase space is introduced and
investigated. In such an operational formalism a quantum mechanical time
operator is constructed and analyzed. A phase space time and energy uncertainty
relation is derived.


title:
The classical communication cost of entanglement manipulation: Is
  entanglement an inter-convertible resource?

abstract:
  Entanglement bits or ``ebits'' have been proposed as a quantitative measure
of a fundamental resource in quantum information processing. For such an
interpretation to be valid, it is important to show that the same number of
ebits in different forms or concentrations are inter-convertible in the
asymptotic limit. Here we draw attention to a very important but hitherto
unnoticed aspect of entanglement manipulation --- the classical communication
cost. We construct an explicit procedure which demonstrates that for bi-partite
pure states, in the asymptotic limit, entanglement can be concentrated or
diluted with vanishing classical communication cost. Entanglement of bi-partite
pure states is thus established as a truly inter-convertible resource.


title: Relativistic Collapse Model With Tachyonic Features

abstract:
  A finite relativistic model for free particles, which describes the collapse
of the statevector, is presented.


title:
One-Parameter Gaussian State of Anharmonic Oscillator: Nonlinear
  Realization of Bogoliubov Transformation

abstract:
  We find a one-parameter Gaussian state for an anharmonic oscillator with
quadratic and quartic terms, which depends on the energy expectation value. For
the weak coupling constant, the Gaussian state is a squeezed state of the
vacuum state. However, for the strong coupling constant, the Gaussian state
represents a different kind of condensation of bosonic particles through a
nonlinear Bogoliubov transformation of the vacuum state.


title:
Quantum cryptography on noisy channels: quantum versus classical
  key-agreement protocols

abstract:
  When the 4-state or the 6-state protocol of quantum cryptography is carried
out on a noisy (i.e. realistic) quantum channel, then the raw key has to be
processed to reduce the information of an adversary Eve down to an arbitrarily
low value, providing Alice and Bob with a secret key. In principle, quantum
algorithms as well as classical algorithms can be used for this processing. A
natural question is: up to which error rate on the raw key is a secret-key
agreement at all possible? Under the assumption of incoherent eavesdropping, we
find that the quantum and classical limits are precisely the same: as long as
Alice and Bob share some entanglement both quantum and classical protocols
provide secret keys.


title:
A Grover-based quantum search of optimal order for an unknown number of
  marked elements

abstract:
  We want to find a marked element out of a black box containing N elements.
When the number of marked elements is known this can be done elegantly with
Grover's algorithm, a variant of which even gives a correct result with
certainty. On the other hand, when the number of marked elements is not known
the problem becomes more difficult. For every prescribed success probability I
give an algorithm consisting of several runs of Grover's algorithm that matches
a recent bound by Buhrman and de Wolf on the order of the number of queries to
the black box. The improvement in the order over a previously known algorithm
is small and the number of queries can clearly still be reduced by a constant
factor.


title: On the volume of the set of mixed entangled states II

abstract:
  The problem of of how many entangled or, respectively, separable states there
are in the set of all quantum states is investigated. We study to what extent
the choice of a measure in the space of density matrices describing
N--dimensional quantum systems affects the results obtained. We demonstrate
that the link between the purity of the mixed states and the probability of
entanglement is not sensitive to the measure chosen. Since the criterion of
partial transposition is not sufficient to distinguish all separable states for
N > 6, we develop an efficient algorithm to calculate numerically the
entanglement of formation of a given mixed quantum state, which allows us to
compute the volume of separable states for N=8 and to estimate the volume of
the bound entangled states in this case.


title:
Generating Functionals for Harmonic Expectation Values of Paths with
  Fixed End Points. Feynman Diagrams for Nonpolynomial Interactions

abstract:
  We introduce a general class of generating functionals for the calculation of
quantum-mechanical expectation values of arbitrary functionals of fluctuating
paths with fixed end points in configuration or momentum space. The generating
functionals are calculated explicitly for harmonic oscillators with
time-dependent frequency, and used to derive a smearing formulas for
correlation functions of polynomial and nonpolynomials functions of
time-dependent positions and momenta. These formulas summarize the effect of
thermal and quantum fluctuations, and serve to derive generalized Wick rules
and Feynman diagrams for perturbation expansions of nonpolynomial interactions.


title: Einstein-Podolsky-Rosen paradox and measurement of quantum system

abstract:
  Einstein-Podolsky-Rosen (EPR) paradox is considered in a relation to a
measurement of an arbitrary quantum system . It is shown that the EPR paradox
always appears in a gedanken experiment with two successively joined measuring
devices.


title: A better lower bound for quantum algorithms searching an ordered list

abstract:
  We show that any quantum algorithm searching an ordered list of n elements
needs to examine at least 1/12 log n-O(1) of them. Classically, log n queries
are both necessary and sufficient. This shows that quantum algorithms can
achieve only a constant speedup for this problem. Our result improves lower
bounds of Buhrman and de Wolf(quant-ph/9811046) and Farhi, Goldstone, Gutmann
and Sipser (quant-ph/9812057).


title: Generation of even and odd nonlinear coherent states

abstract:
  We show that a class of even and odd nonlinear coherent states, defined as
the eigenstates of product of a nonlinear function of the number operator and
the square of the boson annihilation operator, can be generated in the
center-of-mass motion of a trapped and bichromatically laser-driven ion. The
nonclasscial properties of the states are studied.


title: Models of Quantum Computers and Decoherence Problem

abstract:
  Mathematical models of quantum computers such as a multidimensional quantum
Turing machine and quantum circuits are described and its relations with
lattice spin models are discussed. One of the main open problems one has to
solve if one wants to build a quantum computer is the decoherence due to the
coupling with the environment. We propose a possible solution of this problem
by using a control of parameters of the system. This proposal is based on the
analysis of the spin-boson Hamiltonian performed in the stochastic limit
approximation.


title:
Nonlocality without inequalities using unambiguous discrimination
  between non-orthogonal states

abstract: This paper has been withdrawn.


title:
Systems with Higher-Order Shape Invariance: Spectral and Algebraic
  Properties

abstract:
  We study a complex intertwining relation of second order for Schroedinger
operators and construct third order symmetry operators for them. A modification
of this approach leads to a higher order shape invariance. We analyze with
particular attention irreducible second order Darboux transformations which
together with the first order act as building blocks. For the third order
shape-invariance irreducible Darboux transformations entail only one sequence
of equidistant levels while for the reducible case the structure consists of up
to three infinite sequences of equidistant levels and, in some cases, singlets
or doublets of isolated levels.

categories: quant-ph math-ph math.MP nlin.SI solv-int


title: Spin systems, spin coherent states and quasi-exactly solvable models

abstract:
  Spin coherent states play a crucial role in defining QESM (quasi-exactly
solvable models) establishing a strict correspondence between energy spectra of
spin systems and low-lying quantum states for a particle moving in a potential
field of a certain form. Spin coherent states are also used for finding the
Wigner-Kirkwood expansion and quantum corrections to energy quantization rules.
The closed equation which governs dynamics of a quantum system is obtained in
the spin coherent representation directly for observable quantities.

categories: quant-ph cond-mat hep-th math-ph math.MP math.RT math.SP


abstract:
  The interpretations of a particular quantum gedanken experiment provided by
Bohmian mechanics and consistent histories are shown to contradict each other,
both in the absence and in the presence of a measuring device. The consistent
history result seems closer to standard quantum mechanics, and shows no
evidence of the mysterious nonlocal influences present in the Bohmian
description.


title: Quantum phenomenology and the Continuum Problem

abstract:
  A new approach to quantum mechanics based on independence of the Continuum
Hypothesis is proposed. In one-dimensional case, it is shown that the
properties of the set of intermediate cardinality coincide with quantum
phenomenology.


title: Geometric Phases for Three State Systems

abstract:
  The adiabatic geometric phases for general three state systems are discussed.
An explicit parameterization for space of states of these systems is given. The
abelian and non-abelian connection one-forms or vector potentials that would
appear in a three dimensional quantum system with adiabatic characteristics are
given explicitly. This is done in terms of the Euler angle parameterization of
SU(3) which enables a straight-forward calculation of these quantities and its
immediate generalization.


title: A Rudimentary Quantum Compiler(2cnd Ed.)

abstract:
  We present a new algorithm for reducing an arbitrary unitary matrix U into a
sequence of elementary operations (operations such as controlled-nots and qubit
rotations). Such a sequence of operations can be used to manipulate an array of
quantum bits (i.e., a quantum computer). Our algorithm applies recursively a
mathematical technique called the CS Decomposition to build a binary tree of
matrices whose product, in some order, equals the original matrix U. We show
that the Fast Fourier Transform (FFT) algorithm is a special case of our
algorithm. We report on a C++ program called "Qubiter" that implements the
ideas of this paper. Qubiter(PATENT PENDING) source code is publicly available.


title: State estimation for large ensembles

abstract:
  We consider the problem of estimating the state of a large but finite number
$N$ of identical quantum systems. In the limit of large $N$ the problem
simplifies. In particular the only relevant measure of the quality of the
estimation is the mean quadratic error matrix. Here we present a bound on the
mean quadratic error which is a new quantum version of the Cram\'er-Rao
inequality. This new bound expresses in a succinct way how in the quantum case
one can trade information about one parameter for information about another
parameter. The bound holds for arbitrary measurements on pure states, but only
for separable measurements on mixed states--a striking example of non-locality
without entanglement for mixed but not for pure states. Cram\'er-Rao bounds are
generally derived under the assumption that the estimator is unbiased. We also
prove that under additional regularity conditions our bound also holds for
biased estimators. Finally we prove that when the unknown states belong to a 2
dimensional Hilbert space our quantum Cram\'er-Rao bound can always be attained
and we provide an explicit measurement strategy that attains our bound. This
therefore provides a complete solution to the problem of estimating as
efficiently as possible the unknown state of a large ensemble of qubits in the
same pure state. For qubits in the same mixed state, this also provides an
optimal estimation strategy if one only considers separable measurements.


title: Formulation of the Classical Mechanics in the Ring of Operators

abstract:
  By making use of the Weyl-Wigner-Groenewold-Moyal association rules, a
commutative product and a new quantum bracket are constructed in the ring of
operators \cal{F}(H). In this way, an isomorphism between Lie algebra of
classical observables (with Poisson bracket) and the Lie algebra of quantum
observables with this new bracket is established. By these observations, a
formulation of the classical mechanics in \cal{F}(H} is obtained and is shown
to be \hbar\to 0 limit of the Heisenberg picture formulation of the quantum
mechanics.


title: Differential structure of Greechie logics

abstract:
  A liaison between quantum logics and non-commutative differential geometry is
outlined: a class of quantum logics are proved to possess the structure of
discrete differential manifolds. We show that the set of proper elements of an
arbitrary atomic Greechie logic is naturally endowed by Koszul's differential
calculus.


title:
Formation of Giant Quasibound Cold Diatoms by Strong Atom-Cavity
  Coupling

abstract:
  We show that giant quasi-bound diatomic complexes, whose size is typically
hundreds of nm, can be formed by intra-cavity cold diatom photoassociation or
photodissociation in the strong atom-cavity coupling regime.


title:
Comments on: "Quantum mechanics as a gauge theory of metaplectic spinor
  fields" by M. Reuter [Int.J.Mod.Phys. A13 (1998), 3835-3884; hep-th/9804036]

abstract:
  We point out how some mathematically incorrect passages in the paper of M.
Reuter can be formulated in a rigorous way. The fibre bundle approach to
quantum mechanics developed in quant-ph/9803083, quant-ph/9803084,
quant-ph/9804062, quant-ph/9806046, quant-ph/9901039, and quant-ph/9902068 is
compared with the one contained in loc. cit.


title:
Fibre bundle formulation of nonrelativistic quantum mechanics. V.
  Theory's interpretation, summary and discussion

abstract:
  We propose a new systematic fibre bundle formulation of nonrelativistic
quantum mechanics. The new form of the theory is equivalent to the usual one
but it is in harmony with the modern trends in theoretical physics and
potentially admits new generalizations in different directions. In it a pure
state of some quantum system is described by a state section (along paths) of a
(Hilbert) fibre bundle. It's evolution is determined through the bundle
(analogue of the) Schr\"odinger equation. Now the dynamical variables and the
density operator are described via bundle morphisms (along paths). The
mentioned quantities are connected by a number of relations derived in this
work.
  This is the fifth closing part of our investigation. We briefly discuss the
observer's role in the theory and different realizations of the space-time
model used as a base space in the bundle approach to quantum mechanics. We
point the exact conditions for the equivalence of Hilbert bundle and Hilbert
space formulations of the theory. A comparison table between the both
description of nonrelativistic quantum mechanics is presented. We discuss some
principal moments of the Hilbert bundle description and show that it is more
general than the Hilbert space one. Different directions for further research
are pointed too.


title: Royal Road to Coupling Classical and Quantum Dynamics

abstract:
  We present a consistent framework of coupled classical and quantum dynamics.
Our result allows us to overcome severe limitations of previous
phenomenological approaches, like evolutions that do not preserve the
positivity of quantum states or that allow to activate quantum nonlocality for
superluminal signaling. A `hybrid' quantum-classical density is introduced and
its evolution equation derived. The implications and applications of our result
are numerous: it incorporates the back-reaction of quantum on classical
variables, it resolves fundamental problems encountered in standard mean field
theories, and remarkably, also the quantum measurement process, i.e. the most
controversial example of quantum-classical interaction is consistently
described within our approach, leading to a theory of dynamical collapse.


title:
Statistics of the single mode light in the transparent medium with cubic
  nonlinearity

abstract:
  The quantum statistics of the light in the transparent medium with cubic
nonlinearity is considered. Two types of transparent media are treated, namely,
the cold transparent medium with a ground working level and the inversion-free
medium with the lasing levels of the same population. The spectra of light
fluctuation are found on the basis of both Scully-Lamb and Haken theories. The
conditions for the use of effective Hamiltonian are determined. Basing on the
exact solution of the Fokker-Plank equation for the Glauber-Sudarshan
P-function the inversion-free medium with cubic nonlinearity is shown to be the
source of spontaneous radiation with non-Gaussian statistics.


title:
Autofeedback scheme for preservation of macroscopic coherence in
  microwave cavities

abstract:
  We present a scheme for controlling the decoherence of a linear superposition
of two coherent states with opposite phases in a high-Q microwave cavity, based
on the injection of appropriately prepared ``probe'' and ``feedback'' Rydberg
atoms, improving the one presented in [D. Vitali et al., Phys. Rev. Lett. 79,
2442 (1997)]. In the present scheme, the information transmission from the
probe to the feedback atom is directly mediated by a second auxiliary cavity.
The detection efficiency for the probe atom is no longer a critical parameter,
and the decoherence time of the superposition state can be significantly
increased using presently available technology.


title:
Comment on "Self-Isospectral Periodic Potentials and Supersymmetric
  Quantum Mechanics"

abstract:
  We show that the formalism of supersymmetric quantum mechanics applied to the
solvable elliptic function potentials $V(x) = mj(j+1){sn}^2(x,m)$ produces new
exactly solvable one-dimensional periodic potentials.


title: Broadcasting of entanglement and universal quantum cloners

abstract:
  We study broadcasting of entanglement where we use universal quantum cloners
(in general less optimal) to perform local cloning operations. We show that
there is a lower bound on the fidelity of the universal quantum cloners that
can be used for broadcasting. We prove that an entanglement is optimally
broadcast only when optimal quantum cloners are used for local copying. We also
show that broadcasting of entanglement into more than two entangled pairs is
forbidden using only local operations.


title: Thermodynamics of the Casimir effect

abstract:
  A complete thermodynamic treatment of the Casimir effect is presented.
Explicit expressions for the free and the internal energy, the entropy and the
pressure are discussed. As an example we consider the Casimir effect with
different temperatures between the plates ($T$) resp. outside of them ($T'$).
For $T'<T$ the pressure of heat radiation can eventually compensate the Casimir
force and the total pressure can vanish. We consider both an isothermal and an
adiabatic treatment of the interior region. The equilibrium point (vanishing
pressure) turns out instable in the isothermal case. In the adiabatic situation
we have both an instable and a stable equilibrium point, if $T'/T$ is
sufficiently small. Quantitative aspects are briefly discussed.


title:
Diffraction in time in terms of Wigner distributions and tomographic
  probabilities

abstract:
  Long ago appeared a discussion in quantum mechanics of the problem of opening
a completely absorbing shutter on which were impinging a stream of particles of
definite velocity. The solution of the problem was obtained in a form entirely
analogous to the optical one of diffraction by a straight edge. The argument of
the Fresnel integrals was though time dependent and thus the first part in the
title of this article. In section 1 we briefly review the original formulation
of the problem of diffraction in time. In section 2 and 3 we reformulate
respectively this problem in Wigner distributions and tomographical
probabilities. In the former case the probability in phase space is very simple
but, as it takes positive and negative values, the interpretation is ambiguous,
but it gives a classical limit that agrees entirely with our intuition. In the
latter case we can start with our initial conditions in a given reference frame
but obtain our final solution in an arbitrary frame of reference.


title:
Spontaneous emission and level shifts in absorbing disordered
  dielectrics and dense atomic gases: A Green's function approach

abstract:
  Spontaneous emission and Lamb shift of atoms in absorbing dielectrics are
discussed. A Green's-function approach is used based on the multipolar
interaction Hamiltonian of a collection of atomic dipoles with the quantised
radiation field. The rate of decay and level shifts are determined by the
retarded Green's-function of the interacting electric displacement field, which
is calculated from a Dyson equation describing multiple scattering. The
positions of the atomic dipoles forming the dielectrics are assumed to be
uncorrelated and a continuum approximation is used. The associated unphysical
interactions between different atoms at the same location is eliminated by
removing the point-interaction term from the free-space Green's-function (local
field correction). For the case of an atom in a purely dispersive medium the
spontaneous emission rate is altered by the well-known Lorentz local-field
factor. In the presence of absorption a result different from previously
suggested expressions is found and nearest-neighbour interactions are shown to
be important.


title:
Non-Markovian quantum feedback from homodyne measurements: the effect of
  a non-zero feedback delay time

abstract:
  We solve exactly the non-Markovian dynamics of a cavity mode in the presence
of a feedback loop based on homodyne measurements, in the case of a non-zero
feedback delay time. With an appropriate choice of the feedback parameters,
this scheme is able to significantly increase the decoherence time of the
cavity mode, even for delay times not much smaller than the decoherence time
itself.


title: Quantum simulations of optical systems

abstract:
  We show how two level atoms can be used to build microscopic models for
mirrors and beamsplitters. The mirrors can have arbitrary shape allowing closed
cavities to be built. It is possible to build networks or mirrors and
beamsplitters and follow the time-evolution of the intensity of the radiation
through the system.


title: Conventional Quantum Mechanics Without Wave Function and Density Matrix

abstract:
  The tomographic invertable map of the Wigner function onto the positive
probability distribution function is studied. Alternatives to the Schr\"odinger
evolution equation and to the energy level equation written for the positive
probability distribution are discussed. Instead of the transition probability
amplitude (Feynman path integral) a transition probability is introduced.
  A new formulation of the conventional quantum mechanics (without wave
function and density matrix) based on the ``probability representation'' of
quantum states is given. An equation for the propagator in the new formulation
of quantum mechanics is derived. Some paradoxes of quantum mechanics are
reconsidered.


title: Photon Polarization Measurements without the Quantum Zeno Effect

abstract:
  We consider a photon beam incident on a stack of polarizers as an example of
a von Neumann projective measurement, theoretically leading to the quantum Zeno
effect. The Maxwell theory (which is equivalent to the single photon
Schr\"odinger equation) describes measured polarization phenomena, but without
recourse to the notion of a projective measurement.


title:
Exact Solutions of the Schrodinger Equation with Inverse-Power Potential
  in Two Dimensions

abstract:
  The Schrodinger equation for stationary states is studied in a central
potential V(r) proportional to the inverse power of r of degree beta in an
arbitrary number of spatial dimensions. The presence of a single term in the
potential makes it impossible to use previous algorithms, which only work for
quasi-exactly-solvable problems. Nevertheless, the analysis of the stationary
Schrodinger equation in the neighbourhood of the origin and of the point at
infinity is found to provide relevant information about the desired solutions
for all values of the radial coordinate. The original eigenvalue equation is
mapped into a differential equation with milder singularities, and the role
played by the particular case beta=4 is elucidated. In general, whenever the
parameter beta is even and larger than 4, a recursive algorithm for the
evaluation of eigenfunctions is obtained. Eventually, in the particular case of
two spatial dimensions, the exact form of the ground-state wave function is
obtained for a potential containing a finite number of inverse powers of r,
with the associated energy eigenvalue.


title:
Generating entangled superpositions of macroscopically distinguishable
  states within a parametric oscillator

abstract:
  We suggest a variant of the recently proposed experiment for the generation
of a new kind of Schroedinger-cat states, using two coupled parametric
down-converter nonlinear crystals [F. De Martini, Phys. Rev. Lett. 81, 2842
(1998)]. We study the parametric oscillator case and find that an entangled
Schroedinger-cat type state of two cavities, whose mirrors are placed along the
output beams of the nonlinear crystals, can be realized under suitable
conditions.


title: Classification of Maximally Entangled States of Spin-1/2 Particles

abstract: This paper has been withdrawn temporarily.


title: Decoherence and Programmable Quantum Computation

abstract:
  An examination of the concept of using classical degrees of freedom to drive
the evolution of quantum computers is given. Specifically, when externally
generated, coherent states of the electromagnetic field are used to drive
transitions within the qubit system, a decoherence results due to the back
reaction from the qubits onto the quantum field. We derive an expression for
the decoherence rate for two cases, that of the single-qubit Walsh-Hadamard
transform, and for an implementation of the controlled-NOT gate. We examine the
impact of this decoherence mechanism on Grover's search algorithm, and on the
proposals for use of error-correcting codes in quantum computation.


title: Time Asymmetric Quantum Physics

abstract:
  Mathematical and phenomenological arguments in favor of asymmetric time
evolution of micro-physical states are presented.


title: Semiclassical treatment of logarithmic perturbation theory

abstract:
  The explicit semiclassical treatment of logarithmic perturbation theory for
the nonrelativistic bound states problem is developed. Based upon
$\hbar$-expansions and suitable quantization conditions a new procedure for
deriving perturbation expansions for the one-dimensional anharmonic oscillator
is offered. Avoiding disadvantages of the standard approach, new handy
recursion formulae with the same simple form both for ground and exited states
have been obtained. As an example, the perturbation expansions for the energy
eigenvalues of the harmonic oscillator perturbed by $\lambda x^{6}$ are
considered.


title:
Emergence of Classicality: From Collapse Phenomenologies to Hybrid
  Dynamics

abstract:
  In the past ten-fifteen years, stochastic models of continuous wave function
collapse were being proposed to describe the continuous emergence of
classicality from quantum. We advocate that the hybrid dynamics of canonically
coupled quantum and classical systems is a more basic concept. Continuous
collapse formalisms are obtained as special cases. To illustrate our claim we
show how von Neumann collapse follows from hybrid dynamical equations.


title:
A Method of Areas for Manipulating the Entanglement Properties of One
  Copy of a Two-Particle Pure State

abstract:
  We consider the problem of how to manipulate the entanglement properties of a
general two-particle pure state, shared between Alice and Bob, by using only
local operations at each end and classical communication between Alice and Bob.
A method is developed in which this type of problem is found to be equivalent
to a problem involving the cutting and pasting of certain shapes along with a
certain colouring problem. We consider two problems. Firstly we find the most
general way of manipulating the state to obtain maximally entangled states.
After such a manipulation the entangled state |11>+|22>+....|mm> is obtained
with probability p_m. We obtain an expression for the optimal average
entanglement. Also, some results of Lo and Popescu pertaining to this problem
are given simple geometric proofs. Secondly, we consider how to manipulate one
two particle entangled pure state to another with certainty. We derive
Nielsen's theorem (which states the necessary and sufficient condition for this
to be possible) using the method of areas.


title:
``Classical'' Propagator and Path Integral in the Probability
  Representation of Quantum Mechanics

abstract:
  In the probability representation of the standard quantum mechanics, the
explicit expression (and its quasiclassical van-Fleck approximation) for the
``classical'' propagator (transition probability distribution), which
completely describes the quantum system's evolution, is found in terms of the
quantum propagator. An expression for the ``classical'' propagator in terms of
path integral is derived. Examples of free motion and harmonic oscillator are
considered. The evolution equation in the Bargmann representation of the
optical tomography approach is obtained.


title: Characterizing teleportation in optics

abstract:
  We discuss the characterization of continuous variable, optical quantum
teleportation in terms of the two quadrature signal transfer and conditional
variances between the input and output states. We derive criteria which clearly
define the classical limits and highlight interesting operating points which
are not obvious from a calculation of the fidelity of the teleportation alone.


title: Entanglement degree for Jaynes-Cummings model

abstract:
  Recently, it has been known that a quantum entangled state plays an important
role in the field ofquantum information theory such as quantum teleportation
and quantum computation. The research on quantifying entangled states has been
done by several measures. In this letter, we will adopt the method using
quantum mutual entropy to measure the degree of entanglement of Jaynes-Cummings
model.


title:
Path Integral Evaluation of the Free Propagator on the (D-1)-dimensional
  Pseudosphere

abstract:
  We present an explicit path integral evaluation of the free Hamiltonian
propagator on the (D-1)-dimensional pseudosphere, in the horicyclic
coordinates, using the integral equation method. This method consists in
deriving an integral equation for the propagator that turns out to be of Abel's
type.


title: Quantum counter erasure

abstract:
  Interference comes from coherent mixing. It can be suppressed by
entanglement, and the latter can be erased so as to revive interference. If the
entanglement is a mimal-term one (with minimal-term mixing), as is the case in
most thought and real experiments reported, there appears the possibility of
counter erasure and counter interference. This peculiar phenomenon of
minimal-term mixing and minimal-term entanglement is investigated in detail. In
particular, all two-term mixings of an (arbitrary) given minimal-term mixed
state are explicitly exhibited. And so are their possible laboratory
realizations in terms of distant ensemble decomposition.


title:
How to protect the interpretation of the wave function against
  protective measurements

abstract:
  A new type of procedures, called protective measurements, has been proposed
by Aharonov, Anandan and Vaidman. These authors argue that a protective
measurement allows the determination of arbitrary observables of a single
quantum system and claim that this favors a realistic interpretation of the
quantum state. This paper proves that only observables that commute with the
system's Hamiltonian can be measured protectively. It is argued that this
restriction saves the coherence of alternative interpretations.


title: Classical computing, quantum computing, and Shor's factoring algorithm

abstract:
  This is an expository talk written for the Bourbaki Seminar. After a brief
introduction, Section 1 discusses in the categorical language the structure of
the classical deterministic computations. Basic notions of complexity icluding
the P/NP problem are reviewed. Section 2 introduces the notion of quantum
parallelism and explains the main issues of quantum computing. Section 3 is
devoted to four quantum subroutines: initialization, quantum computing of
classical Boolean functions, quantum Fourier transform, and Grover's search
algorithm. The central Section 4 explains Shor's factoring algorithm. Section 5
relates Kolmogorov's complexity to the spectral properties of computable
function. Appendix contributes to the prehistory of quantum computing.


title:
Reflection and Transmission in a Neutron-Spin Test of the Quantum Zeno
  Effect

abstract:
  The dynamics of a quantum system undergoing frequent "measurements", leading
to the so-called quantum Zeno effect, is examined on the basis of a
neutron-spin experiment recently proposed for its demonstration. When the
spatial degrees of freedom are duely taken into account, neutron-reflection
effects become very important and may lead to an evolution which is totally
different from the ideal case.


title:
On Solutions to the Nonlinear Phase Modification of the Schroedinger
  Equation

abstract:
  We present some physically interesting, in general non-stationary,
one-dimensional solutions to the nonlinear phase modification of the
Schr\"{o}dinger equation proposed recently. The solutions include a coherent
state, a phase-modified Gaussian wave packet in the potential of harmonic
oscillator whose strength varies in time, a free Gaussian soliton, and a
similar soliton in the potential of harmonic oscillator comoving with the
soliton. The last of these solutions implies that there exist an energy level
in the spectrum of harmonic oscillator which is not predicted by the linear
theory. The free solitonic solution can be considered a model for a particle
aspect of the wave-particle duality embodied in the quantum theory. The
physical size of this particle is naturally rendered equal to its Compton
wavelength in the subrelativistic framework in which the self-energy of the
soliton is assumed to be equal to its rest-mass energy. The solitonic solutions
exist only for the negative coupling constant for which the Gaussian wave
packets must be larger than some critical finite size if their energy is to be
bounded, i.e., they cannot be point-like objects.


title: Topology measurement within the histories approach

abstract:
  An idealised experiment estimating the spacetime topology is considered in
both classical and quantum frameworks. The latter is described in terms of
histories approach to quantum theory. A procedure creating combinatorial models
of topology is suggested. The correspondence between these models and
discretised spacetime models is established.


title: Separability and entanglement in 2xN composite quantum systems

abstract:
  We show that all density operators of 2$\times N$--dimensional quantum
systems that remain invariant after partial transposition with respect to the
first system are separable. Based on this criterion, we derive a sufficient
separability condition for general density operators in such quantum systems.
We also give a simple proof of the separability criterion in $2\times
2$--dimensional systems [A. Peres, Phys. Rev. Lett {\bf 77}, 1413 (1996)]


title:
Negative Binomial States of the Radiation Field and their Excitations
  are Nonlinear Coherent States

abstract:
  We show that the well-known negative binomial states of the radiation field
and their excitations are nonlinear coherent states. Excited nonlinear coherent
state are still nonlinear coherent states with different nonlinear functions.
We finally give exponential form of the nonlinear coherent states and remark
that the binomial states are not nonlinear coherent states.


title: Characterizations of 1-Way Quantum Finite Automata

abstract:
  The 2-way quantum finite automaton introduced by Kondacs and Watrous can
accept non-regular languages with bounded error in polynomial time. If we
restrict the head of the automaton to moving classically and to moving only in
one direction, the acceptance power of this 1-way quantum finite automaton is
reduced to a proper subset of the regular languages.
  In this paper we study two different models of 1-way quantum finite automata.
The first model, termed measure-once quantum finite automata, was introduced by
Moore and Crutchfield, and the second model, termed measure-many quantum finite
automata, was introduced by Kondacs and Watrous.
  We characterize the measure-once model when it is restricted to accepting
with bounded error and show that, without that restriction, it can solve the
word problem over the free group. We also show that it can be simulated by a
probabilistic finite automaton and describe an algorithm that determines if two
measure-once automata are equivalent.
  We prove several closure properties of the classes of languages accepted by
measure-many automata, including inverse homomorphisms, and provide a new
necessary condition for a language to be accepted by the measure-many model
with bounded error. Finally, we show that piecewise testable languages can be
accepted with bounded error by a measure-many quantum finite automaton, in the
process introducing new construction techniques for quantum automata.


title: Disentanglement of pure bipartite quantum states by local cloning

abstract:
  We discuss disentanglement of pure bipartite quantum states within the
framework of the schemes developed for entanglement splitting and broadcasting
of entanglement.


title: Levinson's theorem for the Schr\"{o}dinger equation in one dimension

abstract:
  Levinson's theorem for the one-dimensional Schr\"{o}dinger equation with a
symmetric potential, which decays at infinity faster than $x^{-2}$, is
established by the Sturm-Liouville theorem. The critical case, where the
Schr\"{o}dinger equation has a finite zero-energy solution, is also analyzed.
It is demonstrated that the number of bound states with even (odd) parity
$n_{+}$ ($n_{-}$) is related to the phase shift $\eta_{+}(0)[\eta_{-}(0)]$ of
the scattering states with the same parity at zero momentum as
$\eta_{+}(0)+\pi/2=n_{+}\pi, \eta_{-}(0)=n_{-}\pi$, for the non-critical case,
$\eta_{+}(0)=n_{+}\pi, \eta_{-}(0)-\pi/2=n_{-}\pi$, for the critical case.


title: Thermal photon statistics in laser light above threshold

abstract:
  We show that the reduction in photon number fluctuations at laser threshold
often cited as a fundamental laser property does not occur in typical
semiconductor lasers such as the ones commonly used in modern technological
applications today. Indeed, such lasers may still exhibit thermal intensity
fluctuations far above threshold. We therefore conclude that sub-thermal
intensity fluctuations cannot be regarded as a necessary property of laser
light. Rather, one should distinguish betwen a thermal laser regime and a
sub-thermal laser regime.

categories: quant-ph adap-org cond-mat nlin.AO physics.optics


title: Separability and distillability of multiparticle quantum systems

abstract:
  We present a family of 3--qubit states to which any arbitrary state can be
depolarized. We fully classify those states with respect to their separability
and distillability properties. This provides a sufficient condition for
nonseparability and distillability for arbitrary states. We generalize our
results to $N$--particle states.


title: The accelerated observer with back-reaction effects

abstract:
  The quantum mechanical evolution of an accelerated extended detector coupled
to a massless scalar field is exhibited and the back-reaction due to emission
or absorption processes computed at first order in the change of the detector's
mass and acceleration. An analogy with black hole evaporation is found and
illustrated.


title:
Quon Statistics for Composite Systems and a Limit on the Violation of
  the Pauli Principle for Nucleons and Quarks

abstract:
  The quon algebra gives a description of particles, ``quons,'' that are
neither fermions nor bosons. The parameter $q$ attached to a quon labels a
smooth interpolation between bosons, for which $q = +1$, and fermions, for
which $q = -1$. Wigner and Ehrenfest and Oppenheimer showed that a composite
system of identical bosons and fermions is a fermion if it contains an odd
number of fermions and is a boson otherwise. Here we generalize this result to
composite systems of identical quons. We find
$q_{composite}=q_{constituent}^{n^2}$ for a system of $n$ identical quons. This
result reduces to the earlier result for bosons and fermions. Using this
generalization we find bounds on possible violations of the Pauli exclusion
principle for nucleons and quarks based on such bounds for nuclei.


title:
Probability Distributions and Hilbert Spaces: Quantum and Classical
  Systems

abstract:
  We use the fact that some linear Hamiltonian systems can be considered as
``finite level'' quantum systems, and the description of quantum mechanics in
terms of probabilities, to associate probability distributions with this
particular class of linear Hamiltonian systems.


title:
Exact Diagonalization of Two Quantum Models for the Damped Harmonic
  Oscillator

abstract:
  The damped harmonic oscillator is a workhorse for the study of dissipation in
quantum mechanics. However, despite its simplicity, this system has given rise
to some approximations whose validity and relation to more refined descriptions
deserve a thorough investigation. In this work, we apply a method that allows
us to diagonalize exactly the dissipative Hamiltonians that are frequently
adopted in the literature. Using this method we derive the conditions of
validity of the rotating-wave approximation (RWA) and show how this approximate
description relates to more general ones. We also show that the existence of
dissipative coherent states is intimately related to the RWA. Finally, through
the evaluation of the dynamics of the damped oscillator, we notice an important
property of the dissipative model that has not been properly accounted for in
previous works; namely, the necessity of new constraints to the application of
the factorizable initial conditions.


title: Quantum jumps in a two-level atom

abstract:
  A strongly-driven ($\Omega >> \gamma$) two level atom relaxes towards an
equilibrium state rho which is almost completely mixed. One interpretation of
this state is that it represents an ensemble average, and that an individual
atom is at any time in one of the eigenstates of $\rho$. The theory of Teich
and Mahler [Phys. Rev. A 45, 3300 (1992)] makes this interpretation concrete,
with an individual atom jumping stochastically between the two eigenstates when
a photon is emitted. The dressed atom theory is also supposed to describe the
quantum jumps of an individual atom due to photo-emissions. But the two
pictures are contradictory because the dressed states of the atom are almost
orthogonal to the eigenstates of $\rho$. In this paper we investigate three
ways of measuring the field radiated by the atom, which attempt to reproduce
the simple quantum jump dynamics of the dressed state or Teich and Mahler
models. These are: spectral detection (using optical filters), two-state jumps
(using adaptive homodyne detection) and orthogonal jumps (another adaptive
homodyne scheme). We find that the three schemes closely mimic the jumps of the
dressed state model, with errors of order $(3/4) (\gamma/\Omega)^{2/3}$, $(1/4)
(\gamma/\Omega)^{2}$, and $(3/4) (\gamma/\Omega)^{2}$ respectively. The
significance of this result to the program of environmentally-induced
superselection is discussed.


title: Creation of coherence in Bose-Einstein condensates by atom detection

abstract:
  We investigate the creation of a relative phase between two Bose-Einstein
condensates, initially in number states, by detection of atoms and show how the
system approaches a coherent state. Two very distinct time scales are found:
one for the creation of the interference is of the order of the detection time
for a few single atoms and another, for the preparation of coherent states, of
the order of the detection time for a significant fraction of the total number
of atoms. Approximate analytic solutions are derived and compared with exact
numerical results.


title: Quantum Mechanics of Extended Objects

abstract:
  We propose a quantum mechanics of extended objects that accounts for the
finite extent of a particle defined via its Compton wavelength. The Hilbert
space representation theory of such a quantum mechanics is presented and this
representation is used to demonstrate the quantization of spacetime. The
quantum mechanics of extended objects is then applied to two paradigm examples,
namely, the fuzzy (extended object) harmonic oscillator and the Yukawa
potential. In the second example, we theoretically predict the phenomenological
coupling constant of the $\omega$ meson, which mediates the short range and
repulsive nucleon force, as well as the repulsive core radius.

categories: quant-ph gr-qc hep-th math-ph math.MP nucl-th


title: Elementary Particles in a New Quantum Scheme

abstract:
  Proceeding from the main principles of the non-unitary quantum theory of
relativistic bi-Hamiltonian systems, a system of Lagrangian fields
characterized by a certain dispersion law (mass spectrum of particles),
interactions between them and their coupling constants are constructed. In this
article the mass spectrum formula for ``bare'' fundamental hadrons is
introduced, and an a priori normalization of particle fields is found as well.
Numerical values of some parameters of the present theory are determined.


title: Direct measurement of the Wigner function by photon counting

abstract:
  We report a direct measurement of the Wigner function characterizing the
quantum state of a light mode. The experimental scheme is based on the
representation of the Wigner function as an expectation value of a displaced
photon number parity operator. This allowed us to scan the phase space
point-by-point, and obtain the complete Wigner function without using any
numerical reconstruction algorithms.


title: Semiclassical Series from Path Integrals

abstract:
  We derive the semiclassical series for the partition function in Quantum
Statistical Mechanics (QSM) from its path integral representation. Each term of
the series is obtained explicitly from the (real) minima of the classical
action. The method yields a simple derivation of the exact result for the
harmonic oscillator, and an accurate estimate of ground-state energy and
specific heat for a single-well quartic anharmonic oscillator. As QSM can be
regarded as finite temperature field theory at a point, we make use of Feynman
diagrams to illustrate the non-perturbative character of the series: it
contains all powers of $\hbar$ and graphs with any number of loops; the usual
perturbative series corresponds to a subset of the diagrams of the
semiclassical series. We comment on the application of our results to other
potentials, to correlation functions and to field theories in higher
dimensions.


title: Reliable teleportation in trapped ions

abstract:
  We study a method for the implementation of a reliable teleportation protocol
(theoretically, 100% of success) of internal states in trapped ions. The
generation of the quantum channel (any of four Bell states) may be done
respecting technical limitations on individual addressing and without claiming
the Lamb-Dicke regime. An adequate Bell analyzer, that transforms unitarily the
Bell basis into a completely disentangled one, is considered. Probable sources
of error and fidelity estimations of the teleportation process are studied.
Finally, we discuss experimental issues, proposing a scenario in which the
present scheme could be implemented.


title: State determination in continuous measurement

abstract:
  The possibility of determining the state of a quantum system after a
continuous measurement of position is discussed in the framework of quantum
trajectory theory. Initial lack of knowledge of the system and external noises
are accounted for by considering the evolution of conditioned density matrices
under a stochastic master equation. It is shown that after a finite time the
state of the system is a pure state and can be inferred from the measurement
record alone. The relation to emerging possibilities for the continuous
experimental observation of single quanta, as for example in cavity quantum
electrodynamics, is discussed.


title:
Comment on ``Consistency, amplitudes and probabilities in quantum
  theory'' by A. Caticha

abstract:
  A carefully written paper by A. Caticha [Phys. Rev. A57, 1572 (1998)] applies
consistency arguments to derive the quantum mechanical rules for compounding
probability amplitudes in much the same way as earlier work by the present
author [J. Math. Phys. 29, 398 (1988) and Int. J. Theor. Phys. 27, 543 (1998)].
These works are examined together to find the minimal assumptions needed to
obtain the most general results.


title: Analytic solutions to the problem of Coulomb and confining potentials

abstract:
  The oscillator representation method is presented and used to calculate the
energy spectra for a superposition of Coulomb and power-law potentials and for
Coulomb and Yukawa potentials. The method provides an efficient way to obtain
analytic results for arbitrary values of the parameters specifying the
above-type potentials. The calculated energies of the ground and excited states
of the quantum systems in question are found to comply well with exact results.


title:
Quantum entanglement and classical communication through a depolarising
  channel

abstract:
  We analyse the role of entanglement for transmission of classical information
through a memoryless depolarising channel. Using the isotropic character of
this channel we prove analytically that the mutual information cannot be
increased by encoding classical bits into entangled states of two qubits.


title:
Cooperative effects in the light and dark periods of two
  dipole-interacting atoms

abstract:
  If an atom is able to exhibit macroscopic dark periods, or electron shelving,
then a driven system of two atoms has three types of fluorescence periods
(dark, single and double intensity). We propose to use the average durations of
these fluorescence types as a simple and easily accessible indicator of
cooperative effects. As an example we study two dipole-interacting V systems by
simulation techniques. We show that the durations of the two types of light
periods exhibit marked separation-dependent oscillations and that they vary in
phase with the real part of the dipole-dipole coupling constant.


title: Quantum Bounded Query Complexity

abstract:
  We combine the classical notions and techniques for bounded query classes
with those developed in quantum computing. We give strong evidence that quantum
queries to an oracle in the class NP does indeed reduce the query complexity of
decision problems. Under traditional complexity assumptions, we obtain an
exponential speedup between the quantum and the classical query complexity of
function classes.
  For decision problems and function classes we obtain the following results: o
P_||^NP[2k] is included in EQP_||^NP[k] o P_||^NP[2^(k+1)-2] is included in
EQP^NP[k] o FP_||^NP[2^(k+1)-2] is included in FEQP^NP[2k] o FP_||^NP is
included in FEQP^NP[O(log n)] For sets A that are many-one complete for PSPACE
or EXP we show that FP^A is included in FEQP^A[1]. Sets A that are many-one
complete for PP have the property that FP_||^A is included in FEQP^A[1]. In
general we prove that for any set A there is a set X such that FP^A is included
in FEQP^X[1], establishing that no set is superterse in the quantum setting.


title:
Determination of When an Outcome is Actualised in a Quantum Measurement
  using DNA - Photolyase System

abstract:
  The biochemical attachment of photolyase to ultraviolet (uv) absorbed DNA
molecules provides a method for registering whether a source has emitted
photons. Here using laws of chemical kinetics and related experimental methods
we argue that the instant after which this information becomes discernible can
be empirically determined by retrodicting from relevant data when the
photolyase binding to uv-absorbed DNA molecules has started occuring. Thus an
empirically investigable twist is provided to the quantum measurement problem.


title: What is "system" : the arguments from the decoherence theory

abstract:
  Within the decoherence theory we investigate the physical background of the
condition of the separability (diagonalizability in noncorrelated basis) of the
interaction Hamiltonian of the composite system, "system plus environment". It
proves that the condition of the separability may serve as a criterion for
defining "system", but so that "system" cannot be defined unless it is
simultaneously defined with its "environment". When extended to a set of the
mutually interacting composite systems, this result implies that the
separability conditions of the local interactions are mutually tied. The task
of defining "system" (and "environment") via investigating the separability of
the Hamiltonian is a sort of the inverse task of the decoherence theory. A
simple example of doing the task is given.


title: Quantum superposition of multiple clones and the novel cloning machine

abstract:
  we envisage a novel quantum cloning machine, which takes an input state and
produces an output state whose success branch can exist in a linear
superposition of multiple copies of the input state and the failure branch
exist in a superposition of composite state independent of the input state. We
prove that unknown non-orthogonal states chosen from a set $\cal S$ can evolve
into a linear superposition of multiple clones by a unitary process if and only
if the states are linearly independent. We derive a bound on the success
probability of the novel cloning machine. We argue that the deterministic and
probabilistic clonings are special cases of our novel cloning machine.


title:
Experimental Proposal for Achieving Superadditive Communication
  Capacities with a Binary Quantum Alphabet

abstract:
  We demonstrate superadditivity in the communication capacity of a binary
alphabet consisting of two nonorthogonal quantum states. For this scheme,
collective decoding is performed two transmissions at a time. This improves
upon the previous schemes of Sasaki et al. [Phys. Rev. A 58, 146 (1998)] where
superadditivity was not achieved until a decoding of three or more
transmissions at a time. This places superadditivity within the regime of a
near-term laboratory demonstration. We propose an experimental test based upon
an alphabet of low photon-number coherent states where the signal decoding is
done with atomic state measurements on a single atom in a high-finesse optical
cavity.


title:
Long-lived Quantum Coherence between Macroscopically Distinct States in
  Superradiance

abstract:
  The dephasing influence of a dissipative environment reduces linear
superpositions of macroscopically distinct quantum states (sometimes also
called Schr\"odinger cat states) usually almost immediately to a statistical
mixture. This process is called decoherence. Couplings to the environment with
a certain symmetry can lead to slow decoherence. In this Letter we show that
the collective coupling of a large number of two-level atoms to an
electromagnetic field mode in a cavity that leads to the phenomena of
superradiance has such a symmetry, at least approximately. We construct
superpositions of macroscopically distinct quantum states decohering only on a
classical time scale and propose an experiment in which the extraordinarily
slow decoherence should be observable.


title: Slow Decoherence of Superpositions of Macroscopically Distinct States

abstract:
  Linear superpositions of macroscopically distinct quantum states (sometimes
also called Schr\"odinger cat states) are usually almost immediately reduced to
a statistical mixture if exposed to the dephasing influence of a dissipative
environment. Couplings to the environment with a certain symmetry can lead to
slow decoherence, however. We give specific examples of slowly decohering
Schr\"odinger cat states in a realistic quantum optical system and discuss how
they might be constructed experimentally.


title: An Almost-Quadratic Lower Bound for Quantum Formula Size

abstract:
  We show that Nechiporuk's method for proving lower bound for Boolean formulas
can be extended to the quantum case. This leads to an n^2 / log^2 n lower bound
for quantum formulas computing an explicit function. The only known previous
explicit lower bound for quantum formulas (by Yao) states that the majority
function does not have a linear-size quantum formula.


title:
A Possible Anisotropy in Blackbody Radiation Viewed through Non-uniform
  Gaseous Matter

abstract:
  A non-local gauge symmetry of a complex scalar field, which can be trivially
extended to spinor fields, was demonstrated in a recent paper (Mod.Phys.Lett.
A13, 1265 (1998) ; hep-th/9902020). The corresponding covariant Lagrangian
density yielded a new, non-local Quantum Electrodynamics. In this letter we
show that as a consequence of this new QED, a blackbody radiation viewed
through gaseous matter appears to show a slight deviation from the Planck
formula, and propose an experimental test to check this effect. We also show
that a non-uniformity in this gaseous matter distribution leads to an
(apparent) spatial anisotropy in the blackbody radiation.


title: Spin-spin interaction and spin-squeezing in an optical lattice

abstract:
  We show that by displacing two optical lattices with respect to each other,
we may produce interactions similar to the ones describing ferro-magnetism in
condensed matter physics. We also show that particularly simple choices of the
interaction lead to spin-squeezing, which may be used to improve the
sensitivity of atomic clocks. Spin-squeezing is generated even with partially,
and randomly, filled lattices, and our proposal may be implemented with current
technology.


title:
Inverse problem and Darboux transformations for two-dimensional
  finite-difference Schredinger equation

abstract:
  A discrete version of the two-dimensional inverse scattering problem is
considered. On this basis, algebraic transformations for the two-dimensional
finite-difference Schredinger equation are elaborated.


title: Quantum Circuits: Fanout, Parity, and Counting

abstract:
  We propose definitions of QAC^0, the quantum analog of the classical class
AC^0 of constant-depth circuits with AND and OR gates of arbitrary fan-in, and
QACC^0[q], where n-ary Mod-q gates are also allowed. We show that it is
possible to make a `cat' state on n qubits in constant depth if and only if we
can construct a parity or Mod-2 gate in constant depth; therefore, any circuit
class that can fan out a qubit to n copies in constant depth also includes
QACC^0[2]. In addition, we prove the somewhat surprising result that parity or
fanout allows us to construct Mod-q gates in constant depth for any q, so
QACC^0[2] = QACC^0. Since ACC^0[p] != ACC^0[q] whenever p and q are mutually
prime, QACC^0[2] is strictly more powerful than its classical counterpart, as
is QAC^0 when fanout is allowed.


title: A Delayed Choice Quantum Eraser

abstract:
  This paper reports a "delayed choice quantum eraser" experiment proposed by
Scully and Dr\"{u}hl in 1982. The experimental results demonstrated the
possibility of simultaneously observing both particle-like and wave-like
behavior of a quantum via quantum entanglement. The which-path or both-path
information of a quantum can be erased or marked by its entangled twin even
after the registration of the quantum.


title: Quantum interference by two temporally distinguishable pulses

abstract:
  We report a two-photon interference effect, in which the entangled photon
pairs are generated from two laser pulses well-separated in time. In a single
pump pulse case, interference effects did not occur in our experimental scheme.
However, by introducing a second pump pulse delayed in time, quantum
interference was then observed. The visibility of the interference fringes
shows dependence on the delay time between two laser pulses. The results are
explained in terms of indistinguishability of biphoton amplitudes which
originated from two temporally separated laser pulses.


title: Landauer's erasure, error correction and entanglement

abstract:
  Classical and quantum error correction are presented in the form of Maxwell's
demon and their efficiency analyzed from the thermodynamic point of view. We
explain how Landauer's principle of information erasure applies to both cases.
By then extending this principle to entanglement manipulations we rederive
upper bounds on purification procedures thereby linking the ''no local increase
of entanglement'' principle to the Second Law of thermodynamics.


title:
Coherent states of the creation operator from fully developed
  Bose-Einstein condensates

abstract:
  A fully developed Bose-Einstein condensate, containing macroscopically large
number of bosons can under certain conditions be considered as a generalized
vacuum state. Applying the annihilation operator to the condensate, hole states
can be defined. Infinite ladders of such hole states can be considered as
generalized coherent states of the creation operator. Dedicated to the memory
of V. N. Gribov.


title: The Pondicherry interpretation of quantum mechanics

abstract:
  This article presents a novel interpretation of quantum mechanics. It extends
the meaning of ``measurement'' to include all property-indicating facts.
Intrinsically space is undifferentiated: there are no points on which a world
of locally instantiated physical properties could be built. Instead, reality is
built on facts, in the sense that the properties of things are extrinsic, or
supervenient on property-indicating facts. The actual extent to which the world
is spatially and temporally differentiated (that is, the extent to which
spatiotemporal relations and distinctions are warranted by the facts) is
necessarily limited. Notwithstanding that the state vector does nothing but
assign probabilities, quantum mechanics affords a complete understanding of the
actual world. If there is anything that is incomplete, it is the actual world,
but its incompleteness exists only in relation to a conceptual framework that
is more detailed than the actual world. Two deep-seated misconceptions are
responsible for the interpretational difficulties associated with quantum
mechanics: the notion that the spatial and temporal aspects of the world are
adequately represented by sets with the cardinality of the real numbers, and
the notion of an instantaneous state that evolves in time. The latter is an
unwarranted (in fact, incoherent) projection of our apparent ``motion in time''
into the world of physics. Equally unwarranted, at bottom, is the use of causal
concepts. There nevertheless exists a ``classical'' domain in which language
suggestive of nomological necessity may be used. Quantum mechanics not only is
strictly consistent with the existence of this domain but also presupposes it
in several ways.