title: Wavefunction Collapse and Conservation Laws

abstract:
  It is emphasized that the collapse postulate of standard quantum theory can
violate conservation of energy-momentum and there is no indication from where
the energy-momentum comes or to where it goes. Likewise, in the Continuous
Spontaneous Localization (CSL) dynamical collapse model, particles gain energy
on average. In CSL, the usual Schr\"odinger dynamics is altered so that a
randomly fluctuating classical field interacts with quantized particles to
cause wavefunction collapse. In this paper it is shown how to define energy for
the classical field so that the average value of the energy of the field plus
the quantum system {\it is} conserved for the ensemble of collapsing
wavefunctions. While conservation of just the first moment of energy is, of
course, much less than complete conservation of energy, this does support the
idea that the field could provide the conservation law balance when events
occur.


title: Decoherence in a single trapped ion due to engineered reservoir

abstract:
  The decoherence in trapped ion induced by coupling the ion to the engineered
reservoir is studied in this paper. The engineered reservoir is simulated by
random variations in the trap frequency, and the trapped ion is treated as a
two-level system driven by a far off-resonant plane wave laser field. The
dependence of the decoherence rate on the amplitude of the superposition state
is given.


title: Entanglements and compound states in quantum information theory

abstract:
  Quantum entanglements, describing truly quantum couplings, are stu died and
classified from the point of view of quantum compound states. We show that c
lassical-quantum correspondences such as quantum encodings can be treated as
d-entanglements leading to a special class of the separable compound states.
The mutual information of the d-compound and entangled states lead to two di
fferent types of entropies for a given quantum state: the von Neumann entrop y,
which is achieved as the supremum of the information over all d-entanglem ents,
and the dimensional entropy, which is achieved at the standard entangl ement,
the true quantum entanglement, coinciding with a d-entanglement only in the
commutative case. The q-capacity of a quantum noiseless channel, defi ned as
the supremum over all entanglements, is given as the logarithm of the
dimensionality of the input von Neumann algebra. It can double the classical
capacity, achieved as the supremum over all semi-quantum couplings (d-entang
lements, or encodings), which is bounded by the logarithm of the dimensional
ity of a maximal Abelian subalgebra.


title: Quantum dynamics and statistics of two coupled down-conversion processes

abstract:
  In the framework of Heisenberg-Langevin theory the dynamical and statistical
effects arising from the linear interaction of two nondegenerate
down-conversion processes are investigated. Using the strong-pumping
approximation the analytical solution of equations of motion is calculated. The
phenomena reminiscent of Zeno and anti-Zeno effects are examined. The
possibility of phase-controlled and mismatch-controlled switching is
illustrated.


title: Does Anti-Parallel Spin Always Contain more Information ?

abstract:
  We show that the Bloch vectors lying on any great circle is the largest set
S(L) for which the parallel states |n,n> can always be transformed into the
anti-parallel states |n,-n>. Thus more information about the Bloch vector is
not extractable from |n,-n> than from |n,n> by any measuring strategy, for the
Bloch vector belonging to S(L). Surprisingly, the largest set of Bloch vectors
for which the corresponding qubits can be flipped is again S(L). We then show
that probabilistic exact parallel to anti-parallel transformation is not
possible if the corresponding anti-parallel spins span the whole Hilbert space
of the two qubits. These considerations allow us to generalise a conjecture of
Gisin and Popescu (Phys. Rev. Lett. 83 432 (1999)).


title: An Introduction to Quantum Error Correction

abstract:
  Quantum states are very delicate, so it is likely some sort of quantum error
correction will be necessary to build reliable quantum computers. The theory of
quantum error-correcting codes has some close ties to and some striking
differences from the theory of classical error-correcting codes. Many quantum
codes can be described in terms of the stabilizer of the codewords. The
stabilizer is a finite Abelian group, and allows a straightforward
characterization of the error-correcting properties of the code. The stabilizer
formalism for quantum codes also illustrates the relationships to classical
coding theory, particularly classical codes over GF(4), the finite field with
four elements.


title:
Nonclassical correlations between photon number and quadrature
  components of the light field

abstract:
  Finite resolution quantum nondemolition (QND) measurements allow a
determination of light field properties while preserving some of the original
quantum coherence of the input state. It is thus possible to measure
correlations between the photon number and a quadrature component of the same
light field mode. Nonclassical features emerge as photon number quantization is
resolved. In particular, a strong anti-correlation of quantization and
coherence is observable in QND measurements of photon number, and a correlation
between measurement induced quantum jumps and quadrature component measurement
results is obtained in QND measurements of quadrature fluctuations in the
photon vacuum. Such nonclassical correlations represent fundamental quantum
properties of the light field and may provide new insights into the nature of
quantization itself.


title:
Defect Mass in Gravitational Field and Red Shift of Atomic and Nuclear
  Radiation Spectra

abstract:
  It is shown, that radiation spectrum of atoms (or nuclei) in the
gravitational field has a red shift since the effective mass of radiating
electrons (or nucleons) changes in this field. This red shift is equal to the
red shift of radiation spectrum in the gravitational field measured in
existence experiments. The same shift must arise when the photon (or $ \gamma $
quantum) is passing through the gravitational field if it participates in
gravitational interactions (photon has no rest mass). The absence of the double
effect in the experiments, probably, means that photons (or $ \gamma $ quanta)
are passing through the gravitational field without interactions.


title: Decoherence and thermalization dynamics of a quantum oscillator

abstract:
  We introduce the quantitative measures characterizing the rates of
decoherence and thermalization of quantum systems. We study the time evolution
of these measures in the case of a quantum harmonic oscillator whose relaxation
is described in the framework of the standard master equation, for various
initial states (coherent, `cat', squeezed and number). We establish the
conditions under which the true decoherence measure can be approximated by the
linear entropy $1-{Tr}\hat\rho^2$. We show that at low temperatures and for
highly excited initial states the decoherence process consists of three
distinct stages with quite different time scales. In particular, the `cat'
states preserve 50% of the initial coherence for a long time interval which
increases logarithmically with increase of the initial energy.


title: Quantum Games

abstract:
  In these lecture notes we investigate the implications of the identification
of strategies with quantum operations in game theory beyond the results
presented in [J. Eisert, M. Wilkens, and M. Lewenstein, Phys. Rev. Lett. 83,
3077 (1999)]. After introducing a general framework, we study quantum games
with a classical analogue in order to flesh out the peculiarities of game
theoretical settings in the quantum domain. Special emphasis is given to a
detailed investigation of different sets of quantum strategies.


title:
Probability in Orthodox Quantum Mechanics: Probability as a Postulate
  Versus Probability as an Emergent Phenomenon

abstract:
  The role of probability in quantum mechanics is reviewed, with a discussion
of the ``orthodox'' versus the statistical interpretive frameworks, and of a
number of related issues. After a brief summary of sources of unease with
quantum mechanics, a survey is given of attempts either to give a new
interpretive framework assuming quantum mechanics is exact, or to modify
quantum mechanics assuming it is a very accurate approximation to a more
fundamental theory. This survey focuses particularly on the issues of whether
probabilities in quantum mechanics are postulated or emergent.


title: A spin-coherent semiconductor photo-detector for quantum communication

abstract:
  We describe how quantum information may be transferred from photon
polarization to electron spin in a semiconductor device. The transfer of
quantum information relies on selection rules for optical transitions, such
that two superposed photon polarizations excite two superposed spin states.
Entanglement of the electron spin state with the spin state of the remaining
hole is prevented by using a single, non-degenerate initial valence band. The
degeneracy of the valence band is lifted by the combination of strain and a
static magnetic field. We give a detailed description of a semiconductor
structure that transfers photon polarization to electron spin coherently, and
allows electron spins to be stored and to be made available for quantum
information processing.


title: High Frequency Acousto-electric Single Photon Source

abstract:
  We propose a single optical photon source for quantum cryptography based on
the acousto-electric effect. Surface acoustic waves (SAWs) propagating through
a quasi-one-dimensional channel have been shown to produce packets of electrons
which reside in the SAW minima and travel at the velocity of sound. In our
scheme these electron packets are injected into a p-type region, resulting in
photon emission. Since the number of electrons in each packet can be controlled
down to a single electron, a stream of single (or N) photon states, with a
creation time strongly correlated with the driving acoustic field, should be
generated.


title: Vibrational Superposition States Without Rotating Wave Approximation

abstract:
  We propose a scheme to generate superpositions of coherent states for the
vibrational motion of a laser cooled trapped-ion. It is based on the
interaction with a standing wave making use of the counter-rotating terms, i.e.
not applying the rotating wave approximation. We also show that the same scheme
can be exploited for quantum state measurement, i.e. with the same scheme
non-classical states may be reconstructed


title: A Quantum Approach To Static Games Of Complete Information

abstract:
  We extend the concept of a classical two-person static game to the quantum
domain, by giving an Hilbert structure to the space of classical strategies and
studying the Battle of the Sexes game. We show that the introduction of
entangled strategies leads to a unique solution of this game.


title: Special collision dynamics of massless fermions leading to confinement

abstract:
  This is a theory for the fundamental structure of nature based on spinors as
unique building blocks. Confinement of the spinors in particles is due uniquely
to the dynamics of the collisions between them. The interaction operator
contains only spin and momentum operators. The eigenfunctions of the
interaction operator have negative as well as positive eigenvalues, limited in
magnitude to the Planck energy. Interactions in one-center particles between
spinors with eigenvalues of different sign tend to bring the energy of the
particle closer to zero.
  At the origin of the energy reduction through interaction is the spin
precession, taking place when two spinors of different type come together. The
model can explain the existence of stable particles and all the known forces,
including gravitation.


title: Generating entangled atom-photon pairs from Bose-Einstein condensates

abstract:
  We propose using spontaneous Raman scattering from an optically driven
Bose-Einstein condensate as a source of atom-photon pairs whose internal states
are maximally entangled. Generating entanglement between a particle which is
easily transmitted (the photon) and one which is easily trapped and coherently
manipulated (an ultracold atom) will prove useful for a variety of
quantum-information related applications. We analyze the type of entangled
states generated by spontaneous Raman scattering and construct a geometry which
results in maximum entanglement.


title:
Dynamic generation of maximally entangled photon multiplets by adiabatic
  passage

abstract:
  The adiabatic passage scheme for quantum state synthesis, in which atomic
Zeeman coherences are mapped to photon states in an optical cavity, is extended
to the general case of two degenerate cavity modes with orthogonal
polarization. Analytical calculations of the dressed-state structure and Monte
Carlo wave-function simulations of the system dynamics show that, for a
suitably chosen cavity detuning, it is possible to generate states of photon
multiplets that are maximally entangled in polarization. These states display
nonclassical correlations of the type described by Greenberger, Horne, and
Zeilinger (GHZ). An experimental scheme to realize a GHZ measurement using
coincidence detection of the photons escaping from the cavity is proposed. The
correlations are found to originate in the dynamics of the adiabatic passage
and persist even if cavity decay and GHZ state synthesis compete on the same
time scale. Beyond entangled field states, it is also possible to generate
entanglement between photons and the atom by using a different atomic
transition and initial Zeeman state.


title: Mixed-state twin observables

abstract:
  Twin observables, i.e. opposite subsystem observables A+ and A- that are
indistinguishable in measurement in a given mixed or pure state W, are
investigated in detail algebraicly and geometrically. It is shown that there is
a far-reaching correspondence between the detectable (in W) spectral entities
of the two operators. Twin observables are state-dependently quantum-logically
equivalent, and direct subsystem measurement of one of them ipso facto gives
rise to the indirect (i.e. distant) measurement of the other. Existence of
nontrivial twins requires singularity of W. Systems in thermodynamic
equilibrium do not admit subsystem twins. These observables may enable one to
simplify the matrix representing W.


title: "Velocities" in Quantum Mechanics

abstract:
  The present paper deals with some kind of quantum ``velocity'' which is
introduced by the method of hydrodynamical analogy. It is found that this
``velocity'' is in general irrotational, namely, a vorticity vanishes, and then
a velocity potential must exist in quantum mechanics. In some elementary
examples of stable systems we will see what the ``velocities'' are. In
particular, the two-dimensional flows of these examples can be expressed by
complex velocity potentials whose real and imaginary parts are the velocity
potentials and stream functions, respectively.


title: Generalized coherent states for SU(n) systems

abstract:
  Generalized coherent states are developed for SU(n) systems for arbitrary
$n$. This is done by first iteratively determining explicit representations for
the SU(n) coherent states, and then determining parametric representations
useful for applications. For SU(n), the set of coherent states is isomorphic to
a coset space $SU(n)/SU(n-1)$, and thus shows the geometrical structure of the
coset space. These results provide a convenient $(2n - 1)$--dimensional space
for the description of arbitrary SU(n) systems. We further obtain the metric
and measure on the coset space, and show some properties of the SU(n) coherent
states.


title:
Reversing quantum dynamics with near-optimal quantum and classical
  fidelity

abstract:
  We consider the problem of reversing quantum dynamics, with the goal of
preserving an initial state's quantum entanglement or classical correlation
with a reference system. We exhibit an approximate reversal operation, adapted
to the initial density operator and the ``noise'' dynamics to be reversed. We
show that its error in preserving either quantum or classical information is no
more than twice that of the optimal reversal operation. Applications to quantum
algorithms and information transmission are discussed.


title: Three-particle GHZ correlations without nonlocality

abstract:
  The formalism employing local complex amplitudes that resolved the
Einstein-Podolsky-Rosen puzzle (C. S. Unnikrishnan, quant-ph/0001112) is
applied to the three-particle GHZ correlations. We show that the GHZ quantum
correlations can be reproduced without nonlocality.


title: Path Integral Methods and Applications

abstract:
  These lectures are intended as an introduction to the technique of path
integrals and their applications in physics. The audience is mainly first-year
graduate students, and it is assumed that the reader has a good foundation in
quantum mechanics. No prior exposure to path integrals is assumed, however.
  The path integral is a formulation of quantum mechanics equivalent to the
standard formulations, offering a new way of looking at the subject which is,
arguably, more intuitive than the usual approaches. Applications of path
integrals are as vast as those of quantum mechanics itself, including the
quantum mechanics of a single particle, statistical mechanics, condensed matter
physics and quantum field theory.
  After an introduction including a very brief historical overview of the
subject, we derive a path integral expression for the propagator in quantum
mechanics, including the free particle and harmonic oscillator as examples. We
then discuss a variety of applications, including path integrals in
multiply-connected spaces, Euclidean path integrals and statistical mechanics,
perturbation theory in quantum mechanics and in quantum field theory, and
instantons via path integrals.
  For the most part, the emphasis is on explicit calculations in the familiar
setting of quantum mechanics, with some discussion (often brief and schematic)
of how these ideas can be applied to more complicated situations such as field
theory.


title: An intuitive Hamiltonian for quantum search

abstract:
  We present new intuition behind Grover's quantum search algorithm by means of
a Hamiltonian. Given a black-box Boolean function f mapping strings of length n
into {0,1} such that f(w) = 1 for exactly one string w, L. K. Grover describes
a quantum algorithm that finds w in O(2^{n/2}) time. Farhi & Gutmann show that
w can also be found in the same amount time by letting the quantum system
evolve according to a simple Hamiltonian depending only on f. Their system
evolves along a path far from that taken by Grover's original algorithm,
however. The current paper presents an equally simple Hamiltonian matching
Grover's algorithm step for step. The new Hamiltonian is similar in appearance
from that of Farhi & Gutmann, but has some important differences, and provides
new intuition for Grover's algorithm itself. This intuition both contrasts with
and supplements other explanations of Grover's algorithm as a rotation in two
dimensions, and suggests that the Hamiltonian-based approach to quantum
algorithms can provide a useful heuristic for discovering new quantum
algorithms.


title: Quantum games and quantum algorithms

abstract:
  A quantum algorithm for an oracle problem can be understood as a quantum
strategy for a player in a two-player zero-sum game in which the other player
is constrained to play classically. I formalize this correspondence and give
examples of games (and hence oracle problems) for which the quantum player can
do better than would be possible classically. The most remarkable example is
the Bernstein-Vazirani quantum search algorithm which I show creates no
entanglement at any timestep.


title: Teleportation Criteria: Form and Significance

abstract:
  Our criteria for continuous variable quantum teleportation [T.C.Ralph and
P.K.Lam, Phys.Rev.Lett. {\bf 81}, 5668 (1998)] take the form of sums, rather
than products, of conjugate quadrature measurements of the signal transfer
coefficients and the covariances between the input and output states. We
discuss why they have this form. We also discuss the physical significance of
the covariance inequality.


title:
Estimation of Buttiker-Landauer traversal time based on the visibility
  of transmission current

abstract:
  We present a proposal for the estimation of B\"uttiker-Landauer traversal
time based on the visibility of transmission current. We analyze the tunneling
phenomena with a time-dependent potential and obtain the time-dependent
transmission current. We found that the visibility is directly connected to the
traversal time. Furthermore, this result is valid not only for rectangular
potential barrier but also for general form of potential to which the WKB
approximation is applicable . We compared these results with the numerical
values obtained from the simulation of Nelson's quantum mechanics. Both of them
fit together and it shows our method is very effective to measure
experimentally the traversal time.


title: Teleportation Scheme of S-level Quantum Pure States by Two-level EPRs

abstract:
  Unknown quantum pure states of arbitrary but definite S-level of a particle
can be transferred onto a group of remote two-level particles through two-level
EPRs as many as the number of those particles in this group. We construct such
a kind of teleportation, the realization of which need a nonlocal unitary
transformation to the quantum system that is made up of the s-level particle
and all the two-level particles at one end of the EPRs, and measurements to all
the single particles in this system. The unitary transformation to more than
two particles is also written into the product form of two-body unitary
transformations.


title: Enhanced Quantum Estimation via Purification

abstract:
  We analyze the estimation of a finite ensemble of quantum bits which have
been sent through a depolarizing channel. Instead of using the depolarized
qubits directly, we first apply a purification step and show that this improves
the fidelity of subsequent quantum estimation. Even though we lose some qubits
of our finite ensemble the information is concentrated in the remaining
purified ones.


title: An Upper Bound on the Number of States in an Unextendible Product Basis

abstract: This paper has been withdrawn as the result is not correct.


title: Partitioning optical solitons for generating entangled light beams

abstract:
  It is shown that bipartition of optical solitons can be used to generate
entangled light beams. The achievable amount of entanglement can be
substantially larger for N-bound solitons N=2,3 than for the fundamental
soliton (N=1). An analysis of the mode structure of the entangled beams shows
that just N modes are essentially entangled. In particular, partitioning of the
fundamental soliton effectively produces 2-mode squeezed light.


title: Recurrence relation for relativistic atomic matrix elements

abstract:
  Recurrence formulae for arbitrary hydrogenic radial matrix elements are
obtained in the Dirac form of relativistic quantum mechanics. Our approach is
inspired on the relativistic extension of the second hypervirial method that
has been succesfully employed to deduce an analogous relationship in non
relativistic quantum mechanics. We obtain first the relativistic extension of
the second hypervirial and then the relativistic recurrence relation.
Furthermore, we use such relation to deduce relativistic versions of the
Pasternack-Sternheimer rule and of the virial theorem.

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


title: On rounds in quantum communication

abstract:
  We investigate the power of interaction in two player quantum communication
protocols. Our main result is a rounds-communication hierarchy for the pointer
jumping function $f_k$. We show that $f_k$ needs quantum communication
$\Omega(n)$ if Bob starts the communication and the number of rounds is limited
to $k$ (for any constant $k$). Trivially, if Alice starts, $O(k\log n)$
communication in $k$ rounds suffices. The lower bound employs a result relating
the relative von Neumann entropy between density matrices to their trace
distance and uses a new measure of information. We also describe a classical
probabilistic $k$ round protocol with communication
$O(n/k\cdot(\log^{(k/2)}n+\log k)+k\log n)$ in which Bob starts the
communication. Furthermore as a consequence of the lower bound for pointer
jumping we show that any $k$ round quantum protocol for the disjointness
problem needs communication $\Omega(n^{1/k})$ for $k=O(1)$.


title: Effects of Local Fields on Spontaneous Emission in Dielectric Media

abstract:
  The local-field renormalization of the spontaneous emission rate in a
dielectric is explicitly obtained from a fully microscopic
quantum-electrodynamical, many-body derivation of Langevin-Bloch operator
equations for two-level atoms embedded in an absorptive and dispersive, linear
dielectric host. We find that the dielectric local-field enhancement of the
spontaneous emission rate is smaller than indicated by previous studies.


title: Mathematical Foundations of Holonomic Quantum Computer

abstract:
  We make a brief review of (optical) Holonomic Quantum Computer (or
Computation) proposed by Zanardi and Rasetti (quant-ph/9904011) and Pachos and
Chountasis (quant-ph/9912093), and give a mathematical reinforcement to their
works.


title:
Renormalization Group Computation of Correlation Functions and Particle
  Densities

abstract:
  We show that the Renormalization Group formalism allows to compute with
accuracy the zero temperature correlation functions and particle densities of
quantum systems.


title: NMR Based Quantum Information Processing: Achievements and Prospects

abstract:
  Nuclear magnetic resonance (NMR) provides an experimental setting to explore
physical implementations of quantum information processing (QIP). Here we
introduce the basic background for understanding applications of NMR to QIP and
explain their current successes, limitations and potential. NMR spectroscopy is
well known for its wealth of diverse coherent manipulations of spin dynamics.
Ideas and instrumentation from liquid state NMR spectroscopy have been used to
experiment with QIP. This approach has carried the field to a complexity of
about 10 qubits, a small number for quantum computation but large enough for
observing and better understanding the complexity of the quantum world. While
liquid state NMR is the only present-day technology about to reach this number
of qubits, further increases in complexity will require new methods. We sketch
one direction leading towards a scalable quantum computer using spin 1/2
particles. The next step of which is a solid state NMR-based QIP capable of
reaching 10-30 qubits.


title: Quantum Clock Synchronization Based on Shared Prior Entanglement

abstract:
  We demonstrate that two spatially separated parties (Alice and Bob) can
utilize shared prior quantum entanglement, and classical communications, to
establish a synchronized pair of atomic clocks. In contrast to classical
synchronization schemes, the accuracy of our protocol is independent of Alice
or Bob's knowledge of their relative locations or of the properties of the
intervening medium.


title:
Fluctuation, Dissipation, and Entanglement: the Classical and Quantum
  Theory of Thermal Magnetic Noise

abstract:
  A general theory of thermal magnetic fluctuations near conductive materials
is developed; such fluctuations are the magnetic analog of Johnson noise. For
realistic experiments in quantum computing and magnetic resonance force
microscopy, the predicted relaxation can be rapid enough that substantial
experimental care should be taken to minimize it. The same Hamiltonian matrix
elements that govern fluctuation and dissipation are shown to also govern
entanglement and renormalization, and a specific example of a
fluctuation-dissipation-entanglement theorem is constructed.


title: Toward scalable quantum computation with cavity QED systems

abstract:
  We propose a scheme for quantum computing using high-Q cavities in which the
qubits are represented by single cavity modes restricted in the space spanned
by the two lowest Fock states. We show that single qubit operations and
universal multiple qubit gates can be implemented using atoms sequentially
crossing the cavities.


title: Exclusion Statistics in Classical Mechanics

abstract:
  We present a general method to derive the classical mechanics of a system of
identical particles in a way that retains information about quantum statistics.
The resulting statistical mechanics can be interpreted as a classical version
of Haldane's exclusion statistics.


title: Hidden Variables or Positive Probabilities?

abstract:
  Despite claims that Bell's inequalities are based on the Einstein locality
condition, or equivalent, all derivations make an identical mathematical
assumption: that local hidden-variable theories produce a set of
positive-definite probabilities for detecting a particle with a given spin
orientation. The standard argument is that because quantum mechanics assumes
that particles are emitted in a superposition of states the theory cannot
produce such a set of probabilities. We examine a paper by Eberhard, and
several similar papers, which claim to show that a generalized Bell inequality,
the CHSH inequality, can be derived solely on the basis of the locality
condition, without recourse to hidden variables. We point out that these
authors nonetheless assumes a set of positive-definite probabilities, which
supports the claim that hidden variables or "locality" is not at issue here,
positive-definite probabilities are. We demonstrate that quantum mechanics does
predict a set of probabilities that violate the CHSH inequality; however these
probabilities are not positive-definite. Nevertheless, they are physically
meaningful in that they give the usual quantum-mechanical predictions in
physical situations. We discuss in what sense our results are related to the
Wigner distribution.


title: Bell's inequalities III. Logical loophole in their formulation

abstract:
  In a remarkably insightful pair of papers recently, Sica demonstrated that:
dichotomic data taken in any experiment that violates Bell's inequalities
``cannot represent any data streams that could possibly exist or be imagined''
if it is to be consistent with the derivation of the inequalities.\cite{sica}
The present writer maintains, however, that corrections in the formulation of
Bell's analysis loosen restrictions imposed by Bell inequalities. Moreover, it
is argued that the resolution proposed by Sica for the conflict arising from
the fact that real data does violate Bell inequalities, namely that the
functional form of the correlations considered by Bell must be amended, is
untenable on physical grounds. Finally, an alternate resolution is proposed.


title: Preparation of GHZ states via Grover's quantum searching algorithm

abstract:
  In this paper we propose an approach to prepare GHZ states of an arbitrary
multi-particle system in terms of Grover's fast quantum searching algorithm.
  This approach can be regarded as an extension of the Grover's algorithm to
find one or more items in an unsorted database.


title: Introduction to Quantum Algorithms

abstract:
  These notes discuss the quantum algorithms we know of that can solve problems
significantly faster than the corresponding classical algorithms. So far, we
have only discovered a few techniques which can produce speed up versus
classical algorithms. It is not clear yet whether the reason for this is that
we do not have enough intuition to discover more techniques, or that there are
only a few problems for which quantum computers can significantly speed up the
solution.


title:
A Characterization of Completely-Positive Trace-Preserving Maps on 2x2
  Matrices

abstract: This paper has been superseded by quant-ph/0101003.

categories: quant-ph math-ph math.MP math.OA math.RA


title: Basic limitations for entanglement catalysis

abstract:
  In this paper we summarize the necessary condition for incomparable states
which can be catalyzed under entanglement-assisted LQCC (ELQCC). When we apply
an extended condition for entanglement transformation to entanglement-assisted
local manipulation we obtain a fundamental limit for entanglement catalysts.
Some relative questions are also discussed.


title: A Critique on `Quantum No-Deleting Principle'

abstract:
  The argument used, in a recent letter to Nature (Nature 130 vol 404, 2000) to
arrive at the `quantum-no-deleting principle' is erroneous. It is pointed out
here that there may not be anything like such a principle. In any case, the
claims made in the letter are beyond its working premise.


title:
Contact between laboratory instruments and equations of quantum
  mechanics

abstract:
  Ambiguity in the contact between laboratory instruments and equations of
quantum mechanics is formulated in terms of responses of the instruments to
commands transmitted to them by a Classical digital Process-control Computer
(CPC); in this way instruments are distinguished from quantum-mechanical models
(sets of equations) that specify what is desired of the instruments. Results
include: (1) a formulation of quantum mechanics adapted to computer-controlled
instruments; (2) a lower bound on the precision of unitary transforms required
for quantum searching and a lower bound on sample size needed to show that
instruments implement a desired model at that precision; (3) a lower bound on
precision of timing required of a CPC in directing instruments; (4) a
demonstration that guesswork is necessary in ratcheting up the precision of
commands.


title: Nonbinary Quantum Stabilizer Codes

abstract:
  We define and show how to construct nonbinary quantum stabilizer codes. Our
approach is based on nonbinary error bases. It generalizes the relationship
between selforthogonal codes over $GF_{4}$ and binary quantum codes to one
between selforthogonal codes over $GF_{q^2}$ and $q$-ary quantum codes for any
prime power $q$.


title:
Ground state laser cooling using electromagnetically induced
  transparency

abstract:
  A laser cooling method for trapped atoms is described which achieves ground
state cooling by exploiting quantum interference in a driven Lambda-shaped
arrangement of atomic levels. The scheme is technically simpler than existing
methods of sideband cooling, yet it can be significantly more efficient, in
particular when several motional modes are involved, and it does not impose
restrictions on the transition linewidth. We study the full quantum mechanical
model of the cooling process for one motional degree of freedom and show that a
rate equation provides a good approximation.


title: Contextuality of Approximate Measurements

abstract:
  The claim of Meyer, Kent and Clifton (MKC) that finite precision measurement
nullifies the Kochen-Specker theorem is criticised. It is argued that, although
MKC have nullified the Kochen-Specker theorem strictly so-called, there are
other, related propositions which are not nullified. The argument given is an
elaboration of some of Mermin's critical remarks. Although MKC allow for the
fact that the observables to be measured cannot be precisely specified, they
continue to assume that the observables which are actually measured are
strictly commuting. As Mermin points out, this assumption is unjustified.
Consequently, the analysis of MKC is incomplete. To make it complete one needs
to investigate the predictions their models make regarding approximate joint
measurements of non-commuting observables. Such an investigation is carried
out, using methods previously developed in connection with approximate joint
measurements of position and momentum. It is shown that a form of contextuality
then re-emerges.


title: Collapse-revivals and population trapping in the m-photon mazer

abstract:
  We present a study of collapse-revival patterns that appear in the changes of
atomic populations induced by the interaction of ultracold two-level atoms with
electromagnetic cavities in resonance with an $m$-photon transition of the
atoms ($m$-photon mazer). In particular, sech$^2$ and gaussian cavity mode
profiles are considered and differences in the collapse-revival patterns are
reported. The quantum theory of the $m$-photon mazer is written in the
framework of the dressed-state coordinate formalism. Simple expressions for the
atomic populations, the cavity photon statistics, and the reflection and
transmission probabilities are given for any initial state of the atom-field
system. Evidence for the population trapping phenomenon which suppress the
collapse-revivals in the $m$-photon mazer is given.


title:
Manipulating motional states by selective vibronic interaction in two
  trapped ions

abstract:
  We present a selective vibronic interaction for manipulating motional states
in two trapped ions, acting resonantly on a previously chosen vibronic subspace
and dispersively on all others. This is done respecting technical limitations
on ionic laser individual addressing. We discuss the generation of Fock states
and entanglement in the ionic collective motional degrees of freedom, among
other applications.


title: How entangled can two couples get?

abstract:
  We describe a pure state of four qubits whose single-qubit density matrices
are all maximally mixed and whose average entanglement as a system of two pairs
of qubits appears to be maximal.


title: Optimization of entanglement witnesses

abstract:
  An entanglement witness (EW) is an operator that allows to detect entangled
states. We give necessary and sufficient conditions for such operators to be
optimal, i.e. to detect entangled states in an optimal way. We show how to
optimize general EW, and then we particularize our results to the
non-decomposable ones; the latter are those that can detect positive partial
transpose entangled states (PPTES). We also present a method to systematically
construct and optimize this last class of operators based on the existence of
``edge'' PPTES, i.e. states that violate the range separability criterion
[Phys. Lett. A{\bf 232}, 333 (1997)] in an extreme manner. This method also
permits the systematic construction of non-decomposable positive maps (PM). Our
results lead to a novel sufficient condition for entanglement in terms of
non-decomposable EW and PM. Finally, we illustrate our results by constructing
optimal EW acting on $H=\C^2\otimes \C^4$. The corresponding PM constitute the
first examples of PM with minimal ``qubit'' domain, or - equivalently - minimal
hermitian conjugate codomain.


title: Emergence of Quantum Chaos in Quantum Computer Core and How to Manage It

abstract:
  We study the standard generic quantum computer model, which describes a
realistic isolated quantum computer with fluctuations in individual qubit
energies and residual short-range inter-qubit couplings. It is shown that in
the limit where the fluctuations and couplings are small compared to one-qubit
energy spacing the spectrum has a band structure and a renormalized Hamiltonian
is obtained which describes the eigenstate properties inside one band. The
studies are concentrated on the central band of the computer (``core'') with
the highest density of states. We show that above a critical inter-qubit
coupling strength, quantum chaos sets in, leading to quantum ergodicity of the
computer eigenstates. In this regime the ideal qubit structure disappears, the
eigenstates become complex and the operability of the computer is quickly
destroyed. We confirm that the quantum chaos border decreases only linearly
with the number of qubits n, although the spacing between multi-qubit states
drops exponentially with n. The investigation of time-evolution in the quantum
computer shows that in the quantum chaos regime, an ideal (noninteracting)
state quickly disappears and exponentially many states become mixed after a
short chaotic time scale for which the dependence on system parameters is
determined. Below the quantum chaos border an ideal state can survive for long
times and be used for computation. The results show that a broad parameter
region does exist where the efficient operation of a quantum computer is
possible.


title: Control of tunneling by adapted signals

abstract:
  Process of quantum tunneling of particles in various physical systems can be
effectively controlled even by a weak and slow varying in time electromagnetic
signal if to adapt specially its shape to a particular system. During an
under-barrier motion of a particle such signal provides a "coherent" assistance
of tunneling by the multi-quanta absorption resulting in a strong enhancement
of the tunneling probability. The semiclassical approach based on trajectories
in the complex time is developed for tunneling in a non-stationary field.
Enhancement of tunneling occurs when a singularity of the signal coincides in
position at the complex time plane with a singularity of the classical
Newtonian trajectory of the particle. The developed theory is also applicable
to the over-barrier reflection of particles and to reflection of classical
waves (electromagnetic, hydrodynamic, etc.) from a spatially-smooth medium.


title:
A study of the consistency between noncommutative quantum mechanics and
  Galilean isotropy

abstract:
  A demonstration is given that the simplest model of quantum mechanics
formulated on a plane non-commutative geometry endowed with a Galilean symmetry
group in which the position and linear momentum-variable commutators are first
order in the dynamical variables (and thus constitute a true Lie algebra) is
incompatible with the hypothesis of spacial isotropy.


title: Quantum Kolmogorov Complexity

abstract:
  In this paper we give a definition for quantum Kolmogorov complexity. In the
classical setting, the Kolmogorov complexity of a string is the length of the
shortest program that can produce this string as its output. It is a measure of
the amount of innate randomness (or information) contained in the string.
  We define the quantum Kolmogorov complexity of a qubit string as the length
of the shortest quantum input to a universal quantum Turing machine that
produces the initial qubit string with high fidelity. The definition of Vitanyi
(Proceedings of the 15th IEEE Annual Conference on Computational Complexity,
2000) measures the amount of classical information, whereas we consider the
amount of quantum information in a qubit string. We argue that our definition
is natural and is an accurate representation of the amount of quantum
information contained in a quantum state.


title:
Symmetric Hybrid Dynamics: A canonical formulation of coupled
  classical-quantum dynamics

abstract:
  A canonical formulation of coupled classical-quantum dynamics is presented.
The theory is named symmetric hybrid dynamics. It is proved that under some
general conditions its predictions are consistent with the full quantum ones.
Moreover symmetric hybrid dynamics displays a fully consistent canonical
structure. Namely, it is formulated over a Lie algebra of observables, time
evolution is unitary and the solution of a hybrid type Schr\"odinger equation.
A quantization prescription from classical mechanics to hybrid dynamics is
presented. The quantization map is a Lie algebra isomorphism. Finally some
possible applications of the theory are succinctly suggested.


title:
Singlet aided infinite resource reduction in the comparison of distant
  fields

abstract:
  We present a task which can be faithfully solved with finite resources only
when aided by particles prepared in a particular entangled state: the singlet
state. The task consists of identifying the mutual parallelity or orthogonality
of weak distant magnetic fields whose absolute directions are completely
unknown.


title:
Entanglement, thermalisation and stationarity: The computational
  foundations of quantum mechanics

abstract:
  'Tis said, to know others is to be learned, to know oneself, wise - I
demonstrate that it could be more fundamental than knowing the rest of nature,
by applying classical computational principles and engineering hindsight to
derive and explain quantum entanglement, state space formalism and the
statistical nature of quantum mechanics. I show that an entangled photon pair
is literally no more than a 1-bit hologram, that the quantum state formalism is
completely derivable from general considerations of representation of physical
information, and that both the probabilistic aspects of quantum theory and the
constancy of h are exactly predicted by the thermodynamics of representation,
without precluding a fundamental, relative difference in spatial scale between
non-colocated observers, leading to logical foundations of relativity and
cosmology that show the current thinking in that field to be simplistic and
erroneous.


title: Asymmetric quantum channel for quantum teleportation

abstract:
  There are a few obstacles, which bring about imperfect quantum teleportation
of a continuous variable state, such as unavailability of maximally entangled
two-mode squeezed states, inefficient detection and imperfect unitary
transformation at the receiving station. We show that all those obstacles can
be understood by a combination of an {\it asymmetrically-decohered} quantum
channel and perfect apparatuses for other operations. For the
asymmetrically-decohered quantum channel, we find some counter-intuitive
results; one is that teleportation does not necessarily get better as the
channel is initially squeezed more and another is when one branch of the
quantum channel is unavoidably subject to some imperfect operations, blindly
making the other branch as clean as possible may not result in the best
teleportation result. We find the optimum strategy to teleport an unknown field
for a given environment or for a given initial squeezing of the channel.


title: Optomechanical tailoring of quantum fluctuations

abstract:
  We propose the use of feedback mechanism to control the level of quantum
noise in a radiation field emerging from a pendular Fabry-Perot cavity. It is
based on the possibility to perform quantum nondemolition measurements by means
of optomechanical coupling.


title: Time symmetry in Rigged Hilbert Spaces

abstract:
  Despite the fact that the fundamental physical laws are symmetric in time,
most observed processes do not show this symmetry. Especially the phenomenon of
decay seems to involve a kind of irreversibility that makes the definition of a
microscopic arrow of time possible. Such an intrinsic irreversibility is
incorporated within the Rigged Hilbert Space quantum mechanics of the Brussels
School, contrasting to the statements of standard quantum mechanics. As shown
in this paper, the formalism bears significant advantages in the description of
decaying systems, however the breaking of time symmetry can be avoided.


title:
Quantum Computation in Brain Microtubules? Decoherence and Biological
  Feasibility

abstract:
  The Penrose-Hameroff (`Orch OR') model of quantum computation in brain
microtubules has been criticized as regards the issue of environmental
decoherence. A recent report by Tegmark finds that microtubules can maintain
quantum coherence for only $10^{-13}$ s, far too short to be
neurophysiologically relevant. Here, we critically examine the assumptions
behind Tegmark's calculation and find that: 1) Tegmark's commentary is not
aimed at an existing model in the literature but rather at a hybrid that
replaces the superposed protein conformations of the `Orch OR' theory with a
soliton in superposition along the microtubule, 2) Tegmark predicts decreasing
decoherence times at lower temperature, in direct contradiction of the observed
behavior of quantum states, 3) recalculation after correcting Tegmark's
equation for differences between his model and the `Orch OR' model
(superposition separation, charge vs. dipole, dielectric constant) lengthens
the decoherence time to $10^{-5} - 10^{-4}$ s and invalidates a critical
assumption of Tegmark's derivation, 4) incoherent metabolic energy supplied to
the collective dynamics ordering water in the vicinity of microtubules at a
rate exceeding that of decoherence can counter decoherence effects (in the same
way that lasers avoid decoherence at room temperature), and 5) phases of actin
gelation may enhance the ordering of water around microtubule bundles, further
increasing the decoherence-free zone by an order of magnitude and the
decoherence time to $10^{-2} - 10^{-1}$ s. These revisions bring microtubule
decoherence into a regime in which quantum gravity can interact with
neurophysiology.


title: Schrodinger revisited: an algebraic approach

abstract:
  Starting with the quantum Liouville equation, we write the density operator
as the product of elements respectively in the left and right ideals of an
operator algebra and find that the Schrodinger picture may be expressed through
two representation independent algebraic forms in terms of the density and
phase operators. These forms are respectively the continuity equation, which
involves the commutator of the Hamiltonian with the density operator, and an
equation for the time development of the phase operator that involves the
anti-commutator of the Hamiltonian with this density operator. We show that
this latter equation plays two important roles: (i) it expresses the
conservation of energy in a system where energy is well defined and (ii) it
provides a simple way to evaluate the gauge changes that occur in the
Aharonov-Bohm, the Aharonov-Casher, and Berry phase effects. Both these
operator (i.e. purely algebraic) equations also allow us to re-examine the Bohm
interpretation, showing that it is in fact possible to construct Bohm
interpretations in representations other than the x-representation. We discuss
the meaning of the Bohm interpretation in the light of these new results in
terms of non-commutative structures and this enables us to clarify its relation
to standard quantum mechanics.


title: p-Adic and Adelic Harmonic Oscillator with Time-Dependent Frequency

abstract:
  The classical and quantum formalism for a p-adic and adelic harmonic
oscillator with time-dependent frequency is developed, and general formulae for
main theoretical quantities are obtained. In particular, the p-adic propagator
is calculated, and the existence of a simple vacuum state as well as adelic
quantum dynamics is shown. Space discreteness and p-adic quantum-mechanical
phase are noted.


title:
Violations of local realism by two entangled quNits are stronger than
  for two qubits

abstract:
  Tests of local realism vs quantum mechanics based on Bell's inequality employ
two entangled qubits. We investigate the general case of two entangled quNits,
i.e. quantum systems defined in an N-dimensional Hilbert space. Via a numerical
linear optimization method we show that violations of local realism are
stronger for two maximally entangled quNits (N=3,4,...,9), than for two qubits
and that they increase with N. The two quNit measurements can be experimentally
realized using entangled photons and unbiased multiport beamsplitters.


title: Quantum decoherence and the Glauber dynamics from the Stochastic limit

abstract:
  The effects of decoherence for quantum system coupled with a bosonic field
are investigated. An application of the stochastic golden rule shows that in
the stochastic limit the dynamics of such a system is described by a quantum
stochastic differential equation. The corresponding master equation describes
convergence of a system to equilibrium. In particular it predicts exponential
damping for off-diagonal matrix elements of the system density matrix, moreover
these elements for a generic system will decay at least as
\exp(-tN{kT\over\hbar}), where N is a number of particles in the system. As an
application of the described technique a derivation from first principles (i.e.
starting from a Hamiltonian description) of a quantum extension of the Glauber
dynamics for systems of spins is given.


title: Darboux-integration of id\rho/dt=[H,f(\rho)]

abstract:
  A Darboux-type method of solving the nonlinear von Neumann equation $i\dot
\rho=[H,f(\rho)]$, with functions $f(\rho)$ commuting with $\rho$, is
developed. The technique is based on a representation of the nonlinear equation
by a compatibility condition for an overdetermined linear system. von Neumann
equations with various nonlinearities $f(\rho)$ are found to possess the
so-called self-scattering solutions. To illustrate the result we consider the
Hamiltonian $H$ of a one-dimensional harmonic oscillator and
$f(\rho)=\rho^q-2\rho^{q-1}$ with arbitary real $q$. It is shown that
self-scattering solutions possess the same asymptotics for all $q$ and that
different nonlinearities may lead to effectively indistinguishable evolutions.
The result may have implications for nonextensive statistics and experimental
tests of linearity of quantum mechanics.


title: On the Entangling Power of Quantum Evolutions

abstract:
  We analyze the entangling capabilities of unitary transformations $U$ acting
on a bipartite $d_1\times d_2$-dimensional quantum system. To this aim we
introduce an entangling power measure $e(U)$ given by the mean linear entropy
produced acting with $U$ on a given distribution of pure product states. This
measure admits a natural interpretation in terms of quantum operations. For a
uniform distribution explicit analytical results are obtained using
group-theoretic arguments. The behaviour of the features of $e(U)$ as the
subsystem dimensions $d_1$ and $d_2$ are varied is studied both analytically
and numerically. The two-qubit case $d_1=d_2=2$ is argued to be peculiar.


title: Quantum Communication Complexity

abstract:
  This paper surveys the field of quantum communication complexity. Some
interesting recent results are collected concerning relations to classical
communication, lower bound methods, one-way communication, and applications of
quantum communication complexity.


title:
Group Theoretical Quantization of Phase and Modulus Related to
  Interferences

abstract:
  Following a recent group theoretical quantization of the symplectic space
S={(phi in R mod 2pi, p>0)} in terms of irreducible unitary representations of
the group SO(1,2) the present paper proposes an application of those results to
the old problem of quantizing modulus and phase in interference phenomena: The
self-adjoint Lie algebra generators K_1, K_2 and K_3 of that group correspond
to the classical observables p cos(phi), -p sin(phi) and p > 0 the Poisson
brackets of which obey that Lie algebra, too. For the irreducible unitary
representations of the positive series the modulus operator K_3 has the
positive discrete spectrum {n+k, n=0,1,2,...; k > 0}. Self-adjoint operators
for cos(phi) and sin(phi) can then be defined as (K_3^{-1}K_1 + K_1 K_3^{-1})/2
and - (K_3^{-1} K_2 + K_2 K_3^{-1})/2 which have the theoretically desired
properties for k >0.32. Some matrix elements with respect to number eigenstates
and with respect to coherent states are calculated. One conclusion is that
group theoretical quantization may be tested by quantum optical experiments.

categories: quant-ph hep-th math-ph math.MP physics.optics


title: Symmetry and Covariance of Non-relativistic Quantum Mechanics

abstract:
  On the basis of a 5-dimensional form of space-time transformations
non-relativistic quantum mechanics is reformulated in a manifestly covariant
manner. The resulting covariance resembles that of the conventional
relativistic quantum mechanics.


title: Inertial Force, Equivalence Principle and Quantum Mechanics

abstract:
  On the basis of a manifestly covariant formalism of non-relativistic quantum
mechanics in general coordinate systems, proposed by us recently, we derive
general expressions for inertial forces. The results enable us further to
discuss, and to explain the validity of, the equivalence principle in
non-relativistic quantum mechanics.


title:
Efficient State Preparation via Ion Trap Quantum Computing and Quantum
  Searching Algorithm

abstract:
  We present a scheme to prepare a quantum state in a ion trap with probability
approaching to one by means of ion trap quantum computing and Grover's quantum
search algorithm acting on trapped ions.


title:
Berry phase for a potential well transported in a homogeneous magnetic
  field

abstract:
  We consider a two-dimensional particle of charge $e$ interacting with a
homogeneous magnetic field perpendicular to the plane and a potential well
which is transported along a closed loop in the plane. We show that a bound
state corresponding to a simple isolated eigenvalue acquires at that Berry's
phase equal to $2\pi {\rm sgn} e$ times the number of flux quanta through the
oriented area encircled by the loop. We also argue that this is a purely
quantum effect since the corresponding Hannay angle is zero.


title: Heating of trapped particles close to surfaces - Blackbody and beyond

abstract:
  We discuss heating and decoherence in traps for ions and neutral particles
close to metallic surfaces. We focus on simple trap geometries and compute
noise spectra of thermally excited electromagnetic fields. If the trap is
located in the near field of the substrate, the field fluctuations are largely
increased compared to the level of the blackbody field, leading to much shorter
coherence and life times of the trapped atoms. The corresponding time constants
are computed for ion traps and magnetic traps. Analytical estimates for the
size dependence of the noise spectrum are given. We finally discuss prospects
for the coherent transport of matter waves in integrated surface waveguides.


title:
A New Method to Derive Low-Lying N-dimensional Quantum Wave Functions by
  Quadratures Along a Single Trajectory

abstract:
  We present a new method to derive low-lying N-dimensional quantum wave
functions by quadrature along a single trajectory. The N-dimensional
Schroedinger equation is cast into a series of readily integrable first order
ordinary differential equations. Our approach resembles the familiar W.K.B.
approximation in one dimension, but is designed to explore the classically
forbidden region and has a much wider applicability than W.K.B.. The method
also provides a perturbation series expansion and the Green's functions of the
wave equation in N-dimension, all by quadratures along a single trajectory. A
number of examples are given for illustration, including a simple algorithm to
evaluate the Stark effect in closed form to any finite order of the electric
field.


title: Quantum Teleportation and Beam Splitting

abstract:
  Following the previous paper in which quantum teleportation is rig orously
discussed with coherent entangled states given by beam splittings, we further
discuss two types of models, perfect teleportation model and non-perfect
teleportation model, in general scheme. Then the difference among several
models, i.e., the perfect models and the non-perfect models, is studied. Our
teleportation models are constructed by means of coherent states in some Fock
space with counting measures, so that our model can be treated in the frame of
usual optical communication.


title: Minimal irreversible quantum mechanics. The decay of unstable states

abstract:
  Brownian motion is modelled by a harmonic oscillator (Brownian particle)
interacting with a continuous set of uncoupled harmonic oscillators. The
interaction is linear in the coordinates and the momenta. The model has an
analytical solution that is used to study the time evolution of the reduced
density operator. It is derived in a closed form, in the one-particle sector of
the model. The irreversible behavior of the Brownian particle is described by a
reduced density matrix.


title:
Linking Classical and Quantum Key Agreement: Is There "Bound
  Information"?

abstract:
  After carrying out a protocol for quantum key agreement over a noisy quantum
channel, the parties Alice and Bob must process the raw key in order to end up
with identical keys about which the adversary has virtually no information. In
principle, both classical and quantum protocols can be used for this
processing. It is a natural question which type of protocols is more powerful.
We prove for general states but under the assumption of incoherent
eavesdropping that Alice and Bob share some so-called intrinsic information in
their classical random variables, resulting from optimal measurements, if and
only if the parties' quantum systems are entangled. In addition, we provide
evidence that the potentials of classical and of quantum protocols are equal in
every situation. Consequently, many techniques and results from quantum
information theory directly apply to problems in classical information theory,
and vice versa. For instance, it was previously believed that two parties can
carry out unconditionally secure key agreement as long as they share some
intrinsic information in the adversary's view. The analysis of this purely
classical problem from the quantum information-theoretic viewpoint shows that
this is true in the binary case, but false in general. More explicitly, bound
entanglement, i.e., entanglement that cannot be purified by any quantum
protocol, has a classical counterpart. This "bound intrinsic information"
cannot be distilled to a secret key by any classical protocol. As another
application we propose a measure for entanglement based on classical
information-theoretic quantities.


title: Isotropic phase squeezing and the arrow of time

abstract:
  We prove that isotropic squeezing of the phase is equivalent to reversing the
arrow of time.


title: Optimal N-to-M Cloning of Quantum Coherent States

abstract:
  The cloning of continuous quantum variables is analyzed based on the concept
of Gaussian cloning machines, i.e., transformations that yield copies that are
Gaussian mixtures centered on the state to be copied. The optimality of
Gaussian cloning machines that transform N identical input states into M output
states is investigated, and bounds on the fidelity of the process are derived
via a connection with quantum estimation theory. In particular, the optimal
N-to-M cloning fidelity for coherent states is found to be equal to
MN/(MN+M-N).


title:
Supersymmetric and Shape-Invariant Generalization for Non-resonant
  Jaynes-Cummings Systems

abstract:
  A class of shape-invariant bound-state problems which represent transitions
in a two-level system introduced earlier are generalized to include arbitrary
energy splittings between the two levels. We show that the coupled-channel
Hamiltonians obtained correspond to the generalization of the non-resonant
Jaynes-Cummings Hamiltonian, widely used in quantized theories of laser. In
this general context, we determine the eigenstates, eigenvalues, the time
evolution matrix and the population inversion matrix factor.


title:
Generalized Jaynes-Cummings Model with Intensity-Dependent and
  Non-resonant Coupling

abstract:
  We study the intensity-dependent and nonresonant Jaynes-Cummings Hamiltonian
when the field is described by an arbitrary shape-invariant system. We
determine the eigenstates, eigenvalues, time evolution matrix and the
population inversion matrix factor.


title: Effect of resonance radiative processes on the amplification factor

abstract:
  Optimal conditions to acomplish amplification without inversion in
three-level schemes based on quantum nonlinear interference effects are
analyzed. Specific features of relaxation processes in optical transitions
seting these conditions apart from those in microwave schemes are outlined.
Numerical evaluations related to neon 2s_2-2p_4-3s_2 transitions are given.


title:
On a SUSY QM scheme for any linear homogeneous differential equation of
  the second order

abstract:
  A formal SUSY QM procedure for any linear homogeneous second-order
differential equation is briefly sketched up and applied to a simple exactly
solvable case


title:
Shape of the amplification line corresponding to an adjacent transition
  in a strong field

abstract:
  An analysis is made of the effect of a strong field on the shape of the
amplification spectral line for mono-velocity V-type three-level atoms. There
are three strong-field contributions, differing in their dependence on the set
of relaxation parameters of the medium and on the differences among the
populations corresponding to the Raman transitions. An analysis is made of the
conditions under which each of the contributions is predominant. The change in
the line shape by an intensified external field is found for each case. Neon
atoms are discussed as an example. The results are compared with those
corresponding to a Maxwellian velocity distribution.


title: Transient interference of transmission and incidence

abstract:
  Due to a transient quantum interference during a wavepacket collision with a
potential barrier, a particular momentum, that depends on the potential
parameters but is close to the initial average momentum, becomes suppressed.
The hole left pushes the momentum distribution outwards leading to a
significant constructive enhancement of lower and higher momenta. This is
explained in the momentum complex-plane language in terms of a saddle point and
two contiguous ``structural'' poles, which are not associated with resonances
but with incident and transmitted components of the wavefunction.


title:
Position eigenstates, symmetries, and the redundant hermiticity of
  free-particle Hamiltonians

abstract:
  The quantum state of a particle can be completely specified by a position at
one instant of time. This implies a lack of information, hence a symmetry, as
to where the particle will move. We here study the consequences for free
particles of spin 0 and spin 1/2. On a cubic spatial lattice a hopping equation
is derived, and the continuum limit taken. Spin 0 leads to the Schroedinger
equation, and spin 1/2 to the Weyl equation. Both Hamiltonians are hermitian
automatically, if time-reversal symmetry is assumed. Hopping amplitudes with a
"slight" inhomogeneity lead to the Weyl equation in a metric-affine space-time.


title: Quasi exactly solvable matrix Schroedinger operators

abstract:
  Two families of quasi exactly solvable 2*2 matrix Schroedinger operators are
constructed. The first one is based on a polynomial matrix potential and
depends on three parameters. The second is a one-parameter generalisation of
the scalar Lame equation. The relationship between these operators and QES
Hamiltonians already considered in the literature is pointed out.


title: Dynamics of multiply charged ions in intense laser fields

abstract:
  We numerically investigate the dynamics of multiply charged hydrogenic ions
in near-optical linearly polarized laser fields with intensities of order 10^16
to 10^17 W/cm^2. Depending on the charge state Z of the ion the relation of
strength between laser field and ionic core changes. We find around Z=12
typical multiphoton dynamics and for Z=3 tunneling behaviour, however with
clear relativistic signatures. In first order in v/c the magnetic field
component of the laser field induces a Z-dependent drift in the laser
propagation direction and a substantial Z-dependent angular momentum with
repect to the ionic core. While spin oscillations occur already in first order
in v/c as described by the Pauli equation, spin induced forces via spin orbit
coupling only appear in the parameter regime where (v/c)^2 corrections are
significant. In this regime for Z=12 ions we show strong splittings of resonant
spectral lines due to spin-orbit coupling and substantial corrections to the
conventional Stark shift due to the relativistic mass shift while those to the
Darwin term are shown to be small. For smaller charges or higher laser
intensities, parts of the electronic wavepacket may tunnel through the
potential barrier of the ionic core, and when recombining are shown to give
rise to keV harmonics in the radiation spectrum. Some parts of the wavepacket
do not recombine after ionisation and we find very energetic electrons in the
weakly relativistic regime of above threshold ionization.


title: Operations, Disturbance, and Simultaneous Measurability

abstract:
  Quantum mechanics predicts the joint probability distributions of the
outcomes of simultaneous measurements of commuting observables, but the current
formulation lacks the operational definition of simultaneous measurements. In
order to provide foundations of joint statistics of local general measurements
on entangled systems in a general theoretical framework, the question is
answered as to under what condition the outputs of two measuring apparatuses
satisfy the joint probability formula for simultaneous measurements of their
observables. For this purpose, all the possible state changes caused by
measurements of an observable are characterized and the notion of disturbance
in measurement is formalized in terms of operations derived by the measuring
interaction.


title: Quantum Amplitude Amplification and Estimation

abstract:
  Consider a Boolean function $\chi: X \to \{0,1\}$ that partitions set $X$
between its good and bad elements, where $x$ is good if $\chi(x)=1$ and bad
otherwise. Consider also a quantum algorithm $\mathcal A$ such that $A
|0\rangle= \sum_{x\in X} \alpha_x |x\rangle$ is a quantum superposition of the
elements of $X$, and let $a$ denote the probability that a good element is
produced if $A |0\rangle$ is measured. If we repeat the process of running $A$,
measuring the output, and using $\chi$ to check the validity of the result, we
shall expect to repeat $1/a$ times on the average before a solution is found.
*Amplitude amplification* is a process that allows to find a good $x$ after an
expected number of applications of $A$ and its inverse which is proportional to
$1/\sqrt{a}$, assuming algorithm $A$ makes no measurements. This is a
generalization of Grover's searching algorithm in which $A$ was restricted to
producing an equal superposition of all members of $X$ and we had a promise
that a single $x$ existed such that $\chi(x)=1$. Our algorithm works whether or
not the value of $a$ is known ahead of time. In case the value of $a$ is known,
we can find a good $x$ after a number of applications of $A$ and its inverse
which is proportional to $1/\sqrt{a}$ even in the worst case. We show that this
quadratic speedup can also be obtained for a large family of search problems
for which good classical heuristics exist. Finally, as our main result, we
combine ideas from Grover's and Shor's quantum algorithms to perform amplitude
estimation, a process that allows to estimate the value of $a$. We apply
amplitude estimation to the problem of *approximate counting*, in which we wish
to estimate the number of $x\in X$ such that $\chi(x)=1$. We obtain optimal
quantum algorithms in a variety of settings.


title: Existential Contextuality and the Models of Meyer, Kent and Clifton

abstract:
  It is shown that the models recently proposed by Meyer, Kent and Clifton
(MKC) exhibit a novel kind of contextuality, which we term existential
contextuality. In this phenomenon it is not simply the pre-existing value but
the actual existence of an observable which is context dependent. This result
confirms the point made elsewhere, that the MKC models do not, as the authors
claim, ``nullify'' the Kochen-Specker theorem. It may also be of some
independent interest.


title: Optically Driven Qubits in Artificial Molecules

abstract:
  We present novel models of quantum gates based on coupled quantum dots in
which a qubit is regarded as the superposition of ground states in each dot.
Coherent control on the qubit is performed by both a frequency and a
polarization of a monochromatic light pulse illuminated on the quantum dots. We
also show that a simple combination of two single qubit gates functions as a
controlled NOT gate resulting from an electron-electron interaction. To examine
the decoherence of quantum states, we discuss electronic relaxation contributed
mainly by LA phonon processes.


title: The Pauli Equation for Probability Distributions

abstract:
  The "marginal" distributions for measurable coordinate and spin projection is
introduced. Then, the analog of the Pauli equation for spin-1/2 particle is
obtained for such probability distributions instead of the usual wave
functions. That allows a classical-like approach to quantum mechanics. Some
illuminating examples are presented.


title: Quantum Algorithm for Generalized Deutsch-Jozsa Problem

abstract:
  We generalize the Deutsch-Jozsa problem and present a quantum algorithm that
can solve the generalized Deutsch-Jozsa problem by a single evaluation of a
given function. We discuss the initialization of an auxiliary register and
present a generalized Deutsch-Jozsa algorithm that requires no initialization
of an auxiliary register.


title: Time Evolution of Quantum Fractals

abstract:
  We propose a general construction of wave functions of arbitrary prescribed
fractal dimension, for a wide class of quantum problems, including the infinite
potential well, harmonic oscillator, linear potential and free particle. The
box-counting dimension of the probability density $P_t(x)=|\Psi(x,t)|^2$ is
shown not to change during the time evolution. We prove a universal relation
$D_t=1+D_x/2$ linking the dimensions of space cross-sections $D_x$ and time
cross-sections $D_t$ of the fractal quantum carpets.


title: Quantum remote control: Teleportation of unitary operations

abstract:
  We consider the implementation of an arbitrary unitary operation U upon a
distant quantum system. This teleportation of U can be viewed as a quantum
remote control. We investigate protocols which achieve this using local
operations, classical communication and shared entanglement (LOCCSE). Lower
bounds on the necessary entanglement and classical communication are determined
using causality and the linearity of quantum mechanics. We examine in
particular detail the resources required if the remote control is to be
implemented as a classical black box. Under these circumstances, we prove that
the required resources are, necessarily, those needed for implementation by
bidirectional state teleportation.


title: The Entanglement of Formation for Isotropic States

abstract:
  We give an explicit expression for the entanglement of formation for
isotropic density matrices in arbitrary dimensions in terms of the convex hull
of a simple function. For two qutrit isotropic states we determine the convex
hull and we have strong evidence for its exact form for arbitrary dimension.
Unlike for two qubits, the entanglement of formation for two qutrits or more is
found to be a nonanalytic function of the maximally entangled fraction in the
regime where the density matrix is entangled.


title:
Comment on "Experimental realization of Popper's experiment: Violation
  of the uncertainty principle?"

abstract:
  Application of the uncertainty principle to conditional measurements is
investigated, and found to be valid for measurements on separated sub-systems.
In light of this, an apparent violation of the uncertainty principle obtained
by Kim and Shih in their realization of Popper's experiment (quant-ph/9905039)
is explained through analogy with a simple optical system.


title:
Exploiting exciton-exciton interactions in semiconductor quantum dots
  for quantum-information processing

abstract:
  We propose an all-optical implementation of quantum-information processing in
semiconductor quantum dots, where electron-hole excitations (excitons) serve as
the computational degrees of freedom (qubits). We show that the strong dot
confinement leads to an overall enhancement of Coulomb correlations and to a
strong renormalization of the excitonic states, which can be exploited for
performing conditional and unconditional qubit operations.


title:
Manipulating the frequency entangled states by
  acoustic-optical-modulator

abstract:
  In this paper, we describe how to realize conditional frequency entanglement
swapping and to produce probabilisticly a three-photon frequency entangled
state from two pairs of frequency entangled states by using an
Acoustic-Optical-Modulator. Both schemes are very simple and may be
implementable in practice.


title: Radiation Pressure Induced Einstein-Podolsky-Rosen Paradox

abstract:
  We demonstrate the appearance of Einstein-Podolsky-Rosen (EPR) paradox when a
radiation field impinges on a movable mirror. The, the possibility of a local
realism test within a pendular Fabry-Perot cavity is shown to be feasible.


title: Teleportation of the Relativistic Quantum Field

abstract:
  The process of teleportation of a completely unknown one-particle state of a
free relativistic quantum field is considered. In contrast to the
non-relativistic quantum mechanics, the teleportation of an unknown state of
the quantum field cannot be in principle described in terms of a measurement in
a tensor product of two Hilbert spaces to which the unknown state and the state
of the EPR-pair belong. The reason is of the existence of a cyclic (vacuum)
state common to both the unknown state and the EPR-pair. Due to the common
vacuum vector and the microcausality principle (commutation relations for the
field operators), the teleportation amplitude contains inevitably contributions
which are irrelevant to the teleportation process. Hence in the relativistic
theory the teleportation in the sense it is understood in the non-relativistic
quantum mechanics proves to be impossible because of the impossibility of the
realization of the appropriate measurement as a tensor product of the
measurements related to the individual subsystems so that one can only speak of
the amplitude of the propagation of the field as a whole.


title: On Teleportation of a Completely Unknown State of Relativistic Photon

abstract:
  The process of teleportation of a completely unknown single-photon
relativistic state is considered. Analysis of the relativistic case reveals
that the teleportation as it is understood in the non-relativistic quantum
mechanics is impossible if no {\it a priori} information on the state to be
teleported is available. It is only possible to speak of the amplitude of the
propagation of the field (taking into account the measurement procedure) since
the existence of a common vacuum state together with the microcausality
principle (the field operators commutation relations) make the concept of the
propagation amplitude for the individual subsystems physically meaningless.
When partial {\it a priori} information is available (for example, only the
polarization state of the photon is unknown while its spatial state is
specified beforehand), the teleportation does become possible in the
relativistic case. In that case the {\it a priori} information can be used to
``label'' the identical particles to make them effectively distinguishable.


title:
Performing Quantum Measurement in Suitably Entangled States Originates
  the Quantum Computation Speed Up

abstract:
  We introduce a local concept of speed-up applicable to intermediate stages of
a quantum algorithm. We use it to analyse the complementary roles played by
quantum parallel computation and quantum measurement in yielding the speed-up.
A severe conflict between there being a speed-up and the many worlds
interpretation is highlighted.


title:
Broadcasting of entanglement in three-particle GHZ state via quantum
  copying

abstract:
  We introduce entanglement measures to describe entanglement in a
three-particle system and apply it to studying broadcasting of entanglement in
three-particle GHZ state. We show that entanglement of three-qubit GHZ state
can be partially broadcasted with the help of local or non-local copying
processes. It is found that non-local cloning is much more efficient than local
cloning for the broadcasting of entanglement.


title: Robustness and diffusion of pointer states

abstract:
  Classical properties of an open quantum system emerge through its interaction
with other degrees of freedom (decoherence). We treat the case where this
interaction produces a Markovian master equation for the system. We derive the
corresponding distinguished local basis (pointer basis) by three methods. The
first demands that the pointer states mimic as close as possible the local
non-unitary evolution. The second demands that the local entropy production be
minimal. The third imposes robustness on the inherent quantum and emerging
classical uncertainties. All three methods lead to localized Gaussian pointer
states, their formation and diffusion being governed by well-defined quantum
Langevin equations.


title: Geometric phases for mixed states in interferometry

abstract:
  We provide a physical prescription based on interferometry for introducing
the total phase of a mixed state undergoing unitary evolution, which has been
an elusive concept in the past. We define the parallel transport condition that
provides a connection-form for obtaining the geometric phase for mixed states.
The expression for the geometric phase for mixed state reduces to well known
formulas in the pure state case when a system undergoes noncyclic and unitary
quantum evolution.


title: Perturbative method for generalized spectral decompositions

abstract:
  Imposing analytic properties to states and observables we construct a
perturbative method to obtain a generalized biorthogonal system of eigenvalues
and eigenvectors for quantum unstable systems. A decay process can be described
using this generalized spectral decomposition, and the final generalized state
is obtained.


title:
Variational Approach to Hydrogen Atom in Uniform Magnetic Field of
  Arbitrary Strength

abstract:
  Extending the Feynman-Kleinert variational approach, we calculate the
temperature-dependent effective classical potential governing the quantum
statistics of a hydrogen atom in a uniform magnetic at all temperatures. The
zero-temperature limit yields the binding energy of the electron which is quite
accurate for all magnetic field strengths and exhibits, in particular, the
correct logarithmic growth at large fields.


title: Macroscopic Interference Effects in Resonant Cavities

abstract:
  We investigate the possibility of interference effects induced by macroscopic
quantum-mechanical superpositions of almost othogonal coherent states - a
Schroedinger cats state - in a resonant microcavity. Despite the fact that a
single atom, used as a probe of the cat state, on the average only change the
mean number of photons by one unit, we show that this single atom can change
the system drastically. Interference between the initial and almost orthogonal
macroscopic quantum states of the radiation field can now take place.
Dissipation under current experimental conditions is taken into account and it
is found that this does not necessarily change the intereference effects
dramatically.


title:
Spatially Encoded Pseudo-Pure States for NMR Quantum Information
  Processing

abstract:
  Quantum information processing by liquid-state NMR spectroscopy uses
pseudo-pure states to mimic the evolution and observations on true pure states.
A new method of preparing pseudo-pure states is described, which involves the
selection of the spatially labeled states of an ancilla spin with which the
spin system of interest is correlated. This permits a general procedure to be
given for the preparation of pseudo-pure states on any number of spins, subject
to the limitations imposed by the loss of signal from the selected subensemble.
The preparation of a single pseudo-pure state is demonstrated by carbon and
proton NMR on 13C-labeled alanine. With a judicious choice of magnetic field
gradients, the method further allows encoding of up to 2^N pseudo-pure states
in independent spatial modes in an N+1 spin system. Fast encoding and decoding
schemes are demonstrated for the preparation of four such spatially labeled
pseudo-pure states.


title: The Global Nature of the Arrow of Time and the Bohm-Reichenbach diagram

abstract:
  The importance of the global nature of the arrow of time is shown. Classical
Reichenbach diagram and quantum Bohm-Reichenbach diagram, for the universe are
introduced. They are used to show the increase of entropy in closed systems,
the global nature of the quantum measurement, and the relation among the
different arrows of time.


title: Minimal Irreversible Quantum Mechanics: An Axiomatic Formalism

abstract:
  An axiomatic formalism for a minimal irreversible quantum mechanics is
introduced. It is shown that a quantum equilibrium and the decoherence
phenomenon are consequences of the axioms and that Lyapunov variables,
exponential survival probabilities, and a classisal conditional
never-decreasing entropy can be defined.


title:
Spatiotemporal Chaos of Soliton in a Generalized Skyrme Model with the
  Modified Symmetrybreaking Term

abstract:
  The chiral symmetry-breaking term of the Skyrme model with massive pion is
modified to obtain the hedgehog profile function which is in best coincidence
with the kink-like profile function. For the modified Lagrangian, the minimum
of the energy of the B=2 twisty skyrmion configuration is lower than the values
for both the cases of the Skyrme Lagrangian with and without the non-modified
symmetry-breaking term. The equations of motion for the time-dependent hedgehog
of this model and for a generalizated Skyrme model including sixth-order
stabilizing term are derived and integrated nummerically. The time evolution of
soliton is obtained. We have observed the seft-exitation of soliton because of
the fast developement of fluctuation.


title: On oscillatorlike Hamiltonians and squeezing

abstract:
  Generalizing a recent proposal leading to one-parameter families of
Hamiltonians and to new sets of squeezed states, we construct larger classes of
physically admissible Hamiltonians permitting new developments in squeezing.
Coherence is also discussed.


title: Resonant radiative processes

abstract:
  The frequency correlation properties of the radiation from an atom in a
strong field in resonance with neighboring transitions are considered. It is
shown that the difference in frequency correlation in two-photon and stepwise
processes decreases with increase of the external field. The spectral
compositions of the Doppler-broadened resonance scattering and fluorescence are
analyzed. It is shown that in these cases the Doppler line width is
anisotropic.


title:
Low temperature dynamics and laser-cooling of two-species Coulomb chains
  for quantum logic

abstract:
  We study from the point of view of quantum logic the properties of the
collective oscillations of a linear chain of ions trapped in a linear Paul trap
and composed of two ion species. We discuss extensively sympathetic cooling of
the chain and the effect of anharmonicity on laser-cooling and
quantum-information processing.


title: On the generation and identification of optical Schr\"odinger cats

abstract:
  We discuss the possibility of generating and detecting, by a tomographic
reconstruction of the Wigner function, a macroscopic superposition of two
coherent states. The superposition state is created using a conditioned
measurement on the polarisation of a probe photon entangled to a coherent
state. The entanglement is obtained using a Kerr cell inserted in a Mach-Zender
interferometer. Some hint about generation of GHZ states is given as well.


title: Operationally Invariant Information in Quantum Measurements

abstract:
  A new measure of information in quantum mechanics is proposed which takes
into account that for quantum systems the only feature known before an
experiment is performed are the probabilities for various events to occur. The
sum of the individual measures of information for mutually complementary
observations is invariant under the choice of the particular set of
complementary observations and conserved if there is no information exchange
with an environment. That operational quantum information invariant results in
N bits of information for a system consisting of N qubits.


title: Fulfillment of expectations of precise measurements of the Casimir force

abstract:
  We compare theoretical expectations for the Casimir force with the results of
precise measurements. The force is calculated at finite temperature for
multilayered covering of the bodies using the Lifshitz theory. We argue that
the dielectric function of the metallization has to be directly measured to
reach the necessary precision in the force calculation. Without knowledge of
this function one can establish a well defined upper limit on the force using
parameters of perfect single-crystal materials. The force measured in the
torsion pendulum experiment does not contradict to the upper limit. Importance
of a thin Au/Pd layer in the atomic force microscope experiments is stressed.
The force measured with the microscope is larger than the upper limit at small
separations between bodies. The discrepancy is significant and reproduced for
both performed measurements. The origin of the discrepancy is discussed. The
simplest modification of the experiment is proposed allowing to make its
results more reliable and answer the question if the discrepancy has any
relation with the existence of a new force.


title: State Extended Uncertainty Relations

abstract:
  A scheme for construction of uncertainty relations (UR) for n observables and
m states is presented. Several lowest order UR are displayed and briefly
discussed. For two states |\psi> and |\phi> and canonical observables the
(entangled) extension of Heisenberg UR reads [\Delta p(\psi)]^2[\Delta
q(\phi)]^2 + [\Delta p(\phi)]^2[\Delta q(\psi)]^2 \geq 1/2. Some possible
applications of the new inequalities are noted.


title: Polarized distances between quantum states and observables

abstract:
  The proposition 1 is incomplete. In some of the examples D(a,b) may not obey
the triangle inequality. The paper is withdrawn for further elaboration.


title: Improved Precision Measurement of the Casimir Force Using Gold Surfaces

abstract:
  We report an improved precision measurement of the Casimir force using
metallic gold surfaces. The force is measured between a large gold coated
sphere and flat plate using an Atomic Force Microscope. The use of gold
surfaces removes some theoretical uncertainties in the interpretation of the
measurement. The forces are also measured at smaller surface separations. The
complete dielectric spectrum of the metal is used in the comparison of theory
to the experiment. The average statistical precision remains at the same 1% of
the forces measured at the closest separation. These results should lead to the
development of stronger constraints on hypothetical forces.


title:
Enhanced four-wave mixing via elimination of inhomogeneous broadening by
  coherent driving of quantum transition with control fields

abstract:
  We show that atoms from wide velocity interval can be concurrently involved
in Doppler-free two-photon resonant far from frequency degenerate four-wave
mixing with the aid of auxiliary electromagnetic field. This gives rise to
substantial enhancement of the output radiation generated in optically thick
medium. Numerical illustrations addressed to typical experimental conditions
are given.


title: Estimating mixed quantum states

abstract:
  We discuss single adaptive measurements for the estimation of mixed quantum
states of qubits. The results are compared to the optimal estimation schemes
using collective measurements. We also demonstrate that the advantage of
collective measurements increases when the degree of mixing of the quantum
states increases.


title: Mesoscopic quantum coherence in an optical lattice

abstract:
  We observe the quantum coherent dynamics of atomic spinor wavepackets in the
double well potentials of a far-off-resonance optical lattice. With appropriate
initial conditions the system Rabi oscillates between the left and right
localized states of the ground doublet, and at certain times the wavepacket
corresponds to a coherent superposition of these mesoscopically distinguishable
quantum states. The atom/optical double well potential is a flexible and
powerful system for further study of mesoscopic quantum coherence, quantum
control and the quantum/classical transition.


title: Quantum algorithm for distributed clock synchronization

abstract:
  The clock synchronization problem is to determine the time difference
$\Delta$ between two spatially separated clocks. When message delivery times
between the two clocks are uncertain, $O(2^{2n})$ classical messages must be
exchanged between the clocks to determine $n$ digits of $\Delta$. On the other
hand, as we show, there exists a quantum algorithm to obtain $n$ digits of
$\Delta$ while communicating only O(n) quantum messages.


title: Anisotropic Vacuum Induced Interference in Decay Channels

abstract:
  We demonstrate how the anisotropy of the vacuum of the electromagnetic field
can lead to quantum interferences among the decay channels of close lying
states. Our key result is that interferences are given by the {\em scalar}
formed from the antinormally ordered electric field correlation tensor for the
anisotropic vacuum and the dipole matirx elements for the two transitions. We
present results for emission between two conducting plates as well as for a two
photon process involving fluorescence produced under coherent cw excitation


title:
Nonlinear interference effects in emission, absorption, and generation
  spectra

abstract:
  Nonlinear effects in emission and absorption spectra of gaseous systems are
considered. It is shown that level splitting can be detected spectroscopically
even if it is below the Doppler width. Conditions for distinguishing
interference effects from those due to nonequilibrium velocity distribution are
determined. In the case of large Doppler broadening the correction for atomic
motion is equivalent to the substitution of an "effective immobile atom" for
the moving atom ensemble. The spectral manifestation of nonlinear effects is
analyzed in detail. The influence of nonlinear interference effects on the
generation characteristics in the presence of external field is investigated.


title: Is the Universe a Quantum System?

abstract:
  In order to relate the probabilistic predictions of quantum theory uniquely
to measurement results, one has to conceive of an ensemble of identically
prepared copies of the quantum system under study. Since the universe is the
total domain of physical experience, it cannot be copied, not even in a thought
experiment. Therefore, a quantum state of the whole universe can never be made
accessible to empirical test. Hence the existence of such a state is only a
metaphysical idea. Despite prominent claims to the contrary, recent
developments in the quantum-interpretation debate do not invalidate this
conclusion.


title:
Polarization dependence of four-wave mixing in a degenerate two-level
  system

abstract:
  Nearly degenerate four-wave mixing (NDFWM) within a closed degenerate
two-level atomic transition is theoretically and experimentally examined. Using
the model presented by A. Lezama et al [Phys. Rev. A 61, 013801 (2000)] the
NDFWM spectra corresponding to different pump and probe polarization cases are
calculated and discussed. The calculated spectra are compared to the
observation of NDFWM within the $6S_{1/2}(F=4)\to 6P_{3/2}(F=5)$ transition of
cesium in a phase conjugation experiment using magneto optically cooled atoms


title: Cooling of a small sample of Bose atoms with accidental degeneracy

abstract:
  A system of bosons in a harmonic trap is cooled via their interactions with a
thermal reservoir. We derive the master equation that governs the evolution of
the system and may describe diverse physical situations: laser cooling,
symphatetic cooling, etc. We investigate in detail the dynamics of the gas in
the Lamb-Dicke limit, whereby the size of the trap is small in comparison to
the de Broglie wavelength of the reservoir quanta. In this case, the dynamics
is characterized by two time scales. First, an equilibrium is reached on a fast
time scale within the degenerated subspaces of the system. Then, an equilibrium
between these subspaces is reached on a slow time scale.


title: Decoherence and the Final Pointer Basis

abstract:
  Using a functional method it is demonstrated that a generic quantum system
evolves to a decohered state in a final pointer basis.


title: Functional Approach to Quantum Decoherence and the Classical Final Limit

abstract:
  For a wide set of quantum systems it is demonstrated that the quantum regime
can be considered as the transient phase while the final classical statistical
regime is a permanent state. A basis where exact matrix decoherence appears for
these final states is found. The relation with the decoherence of histories
formalism is studied. A set of final intrinsically consistent histories is
found.


title: Quantum Statistics of Hydrogen in Strong Magnetic Fields

abstract:
  By an extension of the Feynman-Kleinert variational approach, we calculate
the temperature-dependent effective classical potential governing the quantum
statistical properties of a hydrogen atom in a uniform magnetic field. In the
zero-temperature limit, we obtain ground state energies which are accurate for
all magnetic field strengths from weak to strong fields.


title: Optimal local implementation of non-local quantum gates

abstract:
  We investigate the minimal resources that are required in the local
implementation of non-local quantum gates in a distributed quantum computer.
Both classical communication requirements and entanglement consumption are
investigated. We present general statements on the minimal resource
requirements and present optimal procedures for a number of important gates,
including CNOT and Toffoli gates. We show that one bit of classical
communication in each direction is both necessary and sufficient for the
non-local implementation of the quantum CNOT, while in general two bits in each
direction is required for the implementation of a general two bit quantum gate.
In particular, the state-swapper requires this maximum classical communication
overhead. Extensions of these ideas to multi-party gates are presented.


title: The non-local content of quantum operations

abstract:
  We show that quantum operations on multi-particle systems have a non-local
content; this mirrors the non-local content of quantum states. We introduce a
general framework for discussing the non-local content of quantum operations,
and give a number of examples. Quantitative relations between quantum actions
and the entanglement and classical communication resources needed to implement
these actions are also described. We also show how entanglement can catalyse
classical communication from a quantum action.