title: The Importance of Boundary Conditions in Quantum Mechanics

abstract:
  We discuss the role of boundary conditions in determining the physical
content of the solutions of the Schrodinger equation. We study the
standing-wave, the ``in,'' the ``out,'' and the purely outgoing boundary
conditions. As well, we rephrase Feynman's $+i \epsilon$ prescription as a
time-asymmetric, causal boundary condition, and discuss the connection of
Feynman's $+i \epsilon$ prescription with the arrow of time of Quantum
Electrodynamics. A parallel of this arrow of time with that of Classical
Electrodynamics is made. We conclude that in general, the time evolution of a
closed quantum system has indeed an arrow of time built into the propagators.


title:
Robust creation of entanglement between ions in spatially separate
  cavities

abstract:
  We present a protocol that allows the generation of a maximally entangled
state between individual atoms held in spatially separate cavities. Assuming
perfect detectors and neglecting spontaneous emission from the atoms, the
resulting idealized scheme is deterministic. Under more realistic conditions,
when the the atom-cavity interaction departs from the strong coupling regime,
and considering imperfect detectors, we show that the scheme is robust against
experimental inefficiencies and yields probabilistic entanglement of very high
fidelity.


title: Direction Cryptography in Quantum Communications

abstract:
  We examine a situation in which an information-carrying signal is sent from
two sources to a common receiver. The radiation travels through free space in
the presence of noise. The information resides in a relationship between the
two beams. We inquire into whether itis possible, in principle, that the
locations of the transmitters can be concealed from a party who receives the
radiation and decodes the information. Direction finding entails making a set
of measurements on asignal and constructing an analytic continuation of the
time dependent fields from the results. The fact that this process is generally
different in quantum mechanics and in classical electrodynamics is the basis in
this investigation. We develop a model based upon encoding information into a
microscopic, transverse, non-local quantum image (whose dimensions are of the
order of a few wavelengths) and using a detector of a type recently proposed by
Strekalov et al. The optical system, which uses SPDC (Spontaneous Parametric
Down Conversion), functions like a Heisenberg microscope: the transverse
length, which encodes the signal information, is conjugate to the transverse
momentum of the light. In the model, reading the signal information spoils the
directional resolution of the detector, while determining the directions to the
sources spoils the information content. Each beam, when examined in isolation,
is random and indistinguishable from the background noise. We conclude that
quantum communications can, in principle, be made secure against
direction-finding, even from the party receiving the communication.


title:
Positive operator valued measures covariant with respect to an
  irreducible representation

abstract:
  Given an irreducible representation of a group G, we show that all the
covariant positive operator valued measures based on G/Z, where Z is a central
subgroup, are described by trace class, trace one positive operators.


title: Suppression of Rabi oscillations for moving atoms

abstract:
  The well-known laser-induced Rabi oscillations of a two-level atom are shown
to be suppressed under certain conditions when the atom is entering a
laser-illuminated region. For temporal Rabi oscillations the effect has two
regimes: classical-like, at intermediate atomic velocities, and quantum at low
velocities, associated respectively with the formation of incoherent or
coherent internal states of the atom in the laser region. In the low velocity
regime the laser projects the atom onto a pure internal state that can be
controlled by detuning. Spatial Rabi oscillations are only suppressed in this
low velocity, quantum regime.


title: On susy periodicity defects of the Lame Potentials

abstract:
  The supersymmetric Quantum Mechanics approach is applied to embed bound
states in the energy gaps of periodic potentials. The mechanism to generate
periodicity defects in the first Lame potential is analyzed. The related bound
states are explicitly derived.


title: Non-Hermitian SUSY Hydrogen-like Hamiltonians with real spectra

abstract:
  It is shown that the radial part of the Hydrogen Hamiltonian factorizes as
the product of two not mutually adjoint first order differential operators plus
a complex constant epsilon. The 1-susy approach is used to construct
non-hermitian Hamiltonians with hydrogen spectra. Other non-hermitian
Hamiltonians are shown to admit an extra `complex energy' at epsilon. New
self-adjoint hydrogen-like Hamiltonians are also derived by using a 2-susy
transformation with complex conjugate pairs epsilon, (c.c) epsilon.


title: Shape Invariant Potentials for Effective Mass Schrodinger Equation

abstract:
  Using the method of shape invariant potentials, a number of exact solutions
of one dimensional effective mass Schrodinger equation are obtained. The
solutions with equi-spaced spectrum are discussed in detail.


title: Semiclassical evaluation of quantum fidelity

abstract:
  We present a numerically feasible semiclassical (SC) method to evaluate
quantum fidelity decay (Loschmidt echo, FD) in a classically chaotic system. It
was thought that such evaluation would be intractable, but instead we show that
a uniform SC expression not only is tractable but it gives remarkably accurate
numerical results for the standard map in both the Fermi-golden-rule and
Lyapunov regimes. Because it allows Monte Carlo evaluation, the uniform
expression is accurate at times when there are 10^70 semiclassical
contributions. Remarkably, it also explicitly contains the ``building blocks''
of analytical theories of recent literature, and thus permits a direct test of
the approximations made by other authors in these regimes, rather than an a
posteriori comparison with numerical results. We explain in more detail the
extended validity of the classical perturbation approximation (CPA) and show
that within this approximation, the so-called ``diagonal approximation'' is
automatic and does not require ensemble averaging.


title: A random quantum key distribution by using Bell states

abstract:
  We proposed a new scheme for quantum key distribution based on entanglement
swapping. By this protocol \QTR{em}{Alice} can securely share a random quantum
key with \QTR{em}{Bob}, without transporting any particle.


title:
Reconstruction of quantum theory on the basis of the formula of total
  probability

abstract:
  The notion of context (complex of physical conditions) is basic in this
paper. We show that the main structures of quantum theory (interference of
probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state
space, representation of observables by operators) are present in a latent form
in the classical Kolmogorov probability model. However, this model should be
considered as a calculus of contextual probabilities. In our approach it is
forbidden to consider abstract context independent probabilities: ``first
context and then probability.'' We start with the conventional formula of total
probability for contextual (conditional) probabilities and then we rewrite it
by eliminating combinations of incompatible contexts from consideration. In
this way we obtain interference of probabilities without to appeal to the
Hilbert space formalism or wave mechanics. However, we did not just reconstruct
the probabilistic formalism of conventional quantum mechanics. Our contextual
probabilistic model is essentially more general and, besides the projection to
the complex Hilbert space, it has other projections. The most important new
prediction is the possibility (at least theoretical) of appearance of
hyperbolic interference.


title: New theory of periodical systems by finite interval inverse problem

abstract:
  We show that the mechanism of gap formation has a resonance nature. The
special real fundamental solutions were discovered which `paradoxically' have
knot distribution with a period coinciding with that of potential at all
energies of the whole lacuna interval. In terms of these solutions resonance
gap appearance gets the most direct explanation: ever repeating hits by the
potential result in exponential increase (decrease) of the wave amplitudes in
the forbidden zones. The analogous alternating hits from opposite sides are
responsible for the wave beatings in allowed zones. The inversion technique
gives rise to zone control algorithms - shifting chosen boundaries of spectral
bands, changing degree of zone forbiddenness. All this cannot be achieved by
the previous Bloch theory.


title: A Modified Wigner's Inequality for Secure Quantum Key Distribution

abstract:
  In this report we discuss the insecurity with present implementations of the
Ekert protocol for quantum-key distribution based on the Wigner Inequality. We
propose a modified version of this inequality which guarantees safe quantum-key
distribution.


title: Hilbert--Schmidt volume of the set of mixed quantum states

abstract:
  We compute the volume of the convex N^2-1 dimensional set M_N of density
matrices of size N with respect to the Hilbert-Schmidt measure. The hyper--area
of the boundary of this set is also found and its ratio to the volume provides
an information about the complex structure of M_N. Similar investigations are
also performed for the smaller set of all real density matrices. As an
intermediate step we analyze volumes of the unitary and orthogonal groups and
of the flag manifolds.


title: Quantum Computers and Decoherence: Exorcising the Demon from the Machine

abstract:
  Decoherence is the main obstacle to the realization of quantum computers.
Until recently it was thought that quantum error correcting codes are the only
complete solution to the decoherence problem. Here we present an alternative
that is based on a combination of a decoherence-free subspace encoding and the
application of strong and fast pulses: ``encoded recoupling and decoupling''
(ERD). This alternative has the advantage of lower encoding overhead (as few as
two physical qubits per logical qubit suffice), and direct application to a
number of promising proposals for the experimental realization of quantum
computers.


title:
The singular inverse square potential, limit cycles and self-adjoint
  extensions

abstract:
  We study the radial Schroedinger equation for a particle in the field of a
singular inverse square attractive potential. This potential is relevant to the
fabrication of nanoscale atom optical devices, is said to be the potential
describing the dipole-bound anions of polar molecules, and is the effective
potential underlying the universal behavior of three-body systems in nuclear
physics and atomic physics, including aspects of Bose-Einstein condensates,
first described by Efimov. New results in three-body physical systems motivate
the present investigation. Using the regularization method of Beane et al., we
show that the corresponding ``renormalization group flow'' equation can be
solved analytically. We find that it exhibits a limit cycle behavior and has
infinitely many branches. We show that a physical meaning for self-adjoint
extensions of the Hamiltonian arises naturally in this framework.


title:
Square integrable projective representations and square integrable
  representations modulo a relatively central subgroup (I): basic results

abstract:
  We introduce the notion of square integrable group representation modulo a
relatively central subgroup and, establishing a link with square integrable
projective representations, we prove a generalization of a classical theorem of
Duflo and Moore. As an example, we apply the results obtained to the
Weyl-Heisenberg group.


title: Atomic time-of-arrival measurements with a laser of finite beam width

abstract:
  A natural approach to measure the time of arrival of an atom at a spatial
region is to illuminate this region with a laser and detect the first
fluorescence photons produced by the excitation of the atom and subsequent
decay. We investigate the actual physical content of such a measurement in
terms of atomic dynamical variables, taking into account the finite width of
the laser beam. Different operation regimes are identified, in particular the
ones in which the quantum current density may be obtained.


title: Topological phase for entangled two-qubit states

abstract:
  We present an unambiguous characterization of the rotation group SO(3)
biconnectedness topology using two-qubit maximally entangled states. We show
how to generate cyclic evolutions of these states, which are in one-to-one
correspondence to closed paths in SO(3). The difference between the well known
two classes of such paths translates into the gain of a global phase of $\pi$
for one class and no phase change for the other. We propose a simple quantum
optics interference experiment to demonstrate this topological phase shift.


title: Entanglement teleportation using three-qubit entanglement

abstract:
  We investigate the teleportation of an entangled two-qubit state using
three-qubit GHZ and W channels. The effects of white noise on the average
teleportation fidelity and amount of entanglement transmitted are also studied.


title: The Phenomenon of Darboux Displacements

abstract:
  For a class of Schrodinger Hamiltonians the supersymmetry transformations can
degenerate to simple coordinate displacements. We examine this phenomenon and
show that it distinguishes the Weierstrass potentials including the one-soliton
wells and periodic Lame functions. A supersymmetric sense of the addition
formula for the Weierstrass functions is elucidated.


title: Decoherence in a Josephson junction qubit

abstract:
  The zero-voltage state of a Josephson junction biased with constant current
consists of a set of metastable quantum energy levels. We probe the spacings of
these levels by using microwave spectroscopy to enhance the escape rate to the
voltage state. The widths of the resonances give a measurement of the coherence
time of the two states involved in the transitions. We observe a decoherence
time shorter than that expected from dissipation alone in resonantly isolated
20 um x 5 um Al/AlOx/Al junctions at 60 mK. The data is well fit by a model
including dephasing effects of both low-frequency current noise and the escape
rate to the continuum voltage states. We discuss implications for quantum
computation using current-biased Josephson junction qubits, including the
minimum number of levels needed in the well to obtain an acceptable error limit
per gate.


title: Quantum logic gates for coupled superconducting phase qubits

abstract:
  Based on a quantum analysis of two capacitively coupled current-biased
Josephson junctions, we propose two fundamental two-qubit quantum logic gates.
Each of these gates, when supplemented by single-qubit operations, is
sufficient for universal quantum computation. Numerical solutions of the
time-dependent Schroedinger equation demonstrate that these operations can be
performed with good fidelity.


title: Concentration of higher dimensional entanglement

abstract:
  Enhancement of entanglement enhancement is necessary for most quantum
communication protocols many of which are defined in Hilbert spaces larger than
two. In this work we present the experimental realization of entanglement
concentration of orbital angular momentum entangled photons produced in the
spontaneous parametric down-conversion process which have been shown to provide
a source for higher dimensional entanglement. We investigate the specific case
of three dimensions and the possibility of generating different entangled
states out of an initial state. The results presented here are of importance
for pure states as well as for mixed states.


title: Linear optics substituting scheme for multi-mode operations

abstract:
  We propose a scheme allowing a conditional implementation of suitably
truncated general single- or multi-mode operators acting on states of traveling
optical signal modes. The scheme solely relies on single-photon and coherent
states and applies beam splitters and zero- and single-photon detections. The
signal flow of the setup resembles that of a multi-mode quantum teleportation
scheme thus allowing the individual signal modes to be spatially separated from
each other. Some examples such as the realization of cross-Kerr nonlinearities,
multi-mode mirrors, and the preparation of multi-photon entangled states are
considered.


title: A single particle uncertainty relation

abstract:
  We consider successive measurements of position and momentum of a single
particle. Let P be the conditional probability to measure the momentum k with
precision dk, given a previously successful position measurement q with
precision dq. Several upper bounds for the probability P are determined. For
arbitrary, but given precision dq, dk, these bounds refer to the variation of
q, k and the state vector of the particle. A weak bound is given by the
inequality P <= dkdq/h, where h is Planck's quantum of action. It is
non-trivial for all measurements with dkdq < h. A sharper bound is obtained by
applying the Hilbert-Schmidt-norm. As our main result the least upper bound of
P is determined. All bounds are independent of the order with which the
measuring of position and momentum is made.

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


title:
The non-deterministic quantum logic operation and teleportation of a
  vacuum and single photon superposition state via parametric amplifiers

abstract:
  We firstly present an all-optical scheme to implement the non-deterministic
quantum logic operation of Knill, Laflamme and Milburn (Nature, 409,
46-52(2001)). In our scheme, squeezed vacuum state is acted as auxiliary state
instead of single photon resources. Then we demonstrate that same setup can be
used to teleport a superposition of vacuum and single photon state of the form
$\alpha|0>+\beta|1>$ and a superposition of vacuum and single polarized photon
state of the form $\alpha|0>+\beta|H>+\gamma|V>$.


title: Optimal teleportation with a mixed state of two qubits

abstract:
  We consider a single copy of a mixed state of two qubits and derive the
optimal trace-preserving local operations assisted by classical communication
(LOCC) such as to maximize the fidelity of teleportation that can be achieved
with this state. These optimal local operations turn out to be implementable by
one-way communication, and always yields a teleportation fidelity larger than
2/3 if the original state is entangled. This maximal achievable fidelity is an
entanglement measure and turns out to quantify the minimal amount of mixing
required to destroy the entanglement in a quantum state.


title:
Deterministic linear optics quantum computation utilizing linked photon
  circuits

abstract:
  We suggest an efficient scheme for quantum computation with linear optical
elements utilizing "linked" photon states. The linked states are designed
according to the particular quantum circuit one wishes to process. Once a
linked-state has been successfully prepared, the computation is pursued
deterministically by a sequence of teleportation steps. The present scheme
enables a significant reduction of the average number of elementary gates per
logical gate to about 20-30 CZ_{9/16} gates.


title: Security bounds in Quantum Cryptography using d-level systems

abstract:
  We analyze the security of quantum cryptography schemes for $d$-level systems
using 2 or $d+1$ maximally conjugated bases, under individual eavesdropping
attacks based on cloning machines and measurement after the basis
reconciliation. We consider classical advantage distillation protocols, that
allow to extract a key even in situations where the mutual information between
the honest parties is smaller than the eavesdropper's information. In this
scenario, advantage distillation protocols are shown to be as powerful as
quantum distillation: key distillation is possible using classical techniques
if and only if the corresponding state in the entanglement based protocol is
distillable.


title: Quantum error rejection code with spontaneous parametric conversion

abstract:
  We propose a linear optics scheme with SPDC process to test the fault
tolerance property of quantum error correction code. To transmit an unknown
qubit robustly through the noisy channel, one may first encode it into a
certain quantum error correction code and then transmit it. The remote party
decodes it and stores it. Sending a qubit in such a way can significantly
reduces the error rate compared with directly sending the qubit itself. Here we
show how to realize such a scheme by linear optics.


title: Scheme for teleportation of quantum states onto a mechanical resonator

abstract:
  We propose an experimentally feasible scheme to teleport an unkown quantum
state onto the vibrational degree of freedom of a macroscopic mirror. The
quantum channel between the two parties is established by exploiting radiation
pressure effects.


title: Optomechanical detection of weak forces

abstract:
  Optomechanical systems are often used for the measurement of weak forces.
Feedback loops can be used in these systems for achieving noise reduction. Here
we show that even though feedback is not able to improve the signal to noise
ratio of the device in stationary conditions, it is possible to design a
nonstationary strategy able to improve the sensitivity.


title: Quantum Mechanical View of Mathematical Statistics

abstract:
  Multiparametric statistical model providing stable reconstruction of
parameters by observations is considered. The only general method of this kind
is the root model based on the representation of the probability density as a
squared absolute value of a certain function, which is referred to as a psi
function in analogy with quantum mechanics. The psi function is represented by
an expansion in terms of an orthonormal set of functions. It is shown that the
introduction of the psi function allows one to represent the Fisher information
matrix as well as statistical properties of the estimator of the state vector
(state estimator) in simple analytical forms.


title: Root Estimator of Quantum States

abstract:
  The root estimator of quantum states based on the expansion of the psi
function in terms of system eigenfunctions followed by estimating the expansion
coefficients by the maximum likelihood method is considered. In order to
provide statistical completeness of the analysis, it is necessary to perform
measurements in mutually complementing experiments (according to the Bohr
terminology). Estimation of quantum states by the results of coordinate,
momentum, and polarization (spin) measurements is considered.


title: Generation of entangled states of two three-level atoms in cavity QED

abstract:
  We present a scheme to generate maximally entangled states of two three-level
atoms with a nonresonant cavity by cavity-assisted collisions. Since the cavity
field is only virtually excited no quantum information will be transferred from
the atoms to the cavity.


title:
Two exactly-solvable problems in one-dimensional quantum mechanics on
  circle

abstract:
  In this note we establish a relation between two exactly-solvable problems on
circle, namely singular Coulomb and singular oscillator systems.


title: Embedding QM into an objective framework

abstract:
  An elementary model is given which shows how an objective (hence local and
noncontextual) picture of the microworld can be constructed without conflicting
with quantum mechanics (QM). This contradicts known no-go theorems, which
however do not hold in the model, and supplies some suggestions for a broader
theory in which QM can be embedded.


title:
Violation of Bell inequalities and Quantum Tomography with Pure-states,
  Werner-states and Maximally Entangled Mixed States created by a Universal
  Quantum Entangler

abstract:
  Entangled pure-states, Werner-states and generalized mixed-states of any
structure, spanning a 2x2 Hilbert space are created by a novel high-brilliance
universal source of polarization-entangled photon pairs. The violation of a
Bell inequality has been tested for the first time with a pure-state, indeed a
conceptually relevant ideal condition, and with Werner-states. The generalized
''maximally entangled mixed states'' (MEMS) were also synthetized for the first
time and their exotic properties investigated by means of a quantum tomographic
technique.


title:
Entanglement assisted alignment of reference frames using a dense
  covariant coding

abstract:
  We present a procedure inspired by dense coding, which enables a highly
efficient transmission of information of a continuous nature. The procedure
requires the sender and the recipient to share a maximally entangled state. We
deal with the concrete problem of aligning reference frames or trihedra by
means of a quantum system. We find the optimal covariant measurement and
compute the corresponding average error, which has a remarkably simple close
form. The connection of this procedure with that of estimating unitary
transformations on qubits is briefly discussed.


title: An invitation to quantum tomography

abstract:
  We describe quantum tomography as an inverse statistical problem and show how
entropy methods can be used to study the behaviour of sieved maximum likelihood
estimators. There remain many open problems, and a main purpose of the paper is
to bring these to the attention of the statistical community.


title:
Input-output relations at dispersing and absorbing planar multilayers
  for the quantized electromagnetic field containing evanescent components

abstract:
  By using the Green-function concept of quantization of the electromagnetic
field in dispersing and absorbing media, the quantized field in the presence of
a dispersing and absorbing dielectric multilayer plate is studied.
Three-dimensional input-output relations are derived for both amplitude
operators in the ${\bf k}$-space and the field operators in the coordinate
space. The conditions are discussed, under which the input-output relations can
be expressed in terms of bosonic operators. The theory applies to both
(effectively) free fields and fields, created by active atomic sources inside
and/or outside the plate, including also evanescent-field components.


title: Quantum states far from the energy eigenstates of any local Hamiltonian

abstract:
  What quantum states are possible energy eigenstates of a many-body
Hamiltonian? Suppose the Hamiltonian is non-trivial, i.e., not a multiple of
the identity, and L-local, in the sense of containing interaction terms
involving at most L bodies, for some fixed L. We construct quantum states \psi
which are ``far away'' from all the eigenstates E of any non-trivial L-local
Hamiltonian, in the sense that |\psi-E| is greater than some constant lower
bound, independent of the form of the Hamiltonian.


title:
Robust long-distance entanglement and a loophole-free Bell test with
  ions and photons

abstract:
  Two trapped ions that are kilometers apart can be entangled by the joint
detection of two photons, each coming from one of the ions, in a basis of
entangled states. Such a detection is possible with linear optical elements.
The use of two-photon interference allows entanglement distribution without
interferometric sensitivity to the path length of the photons. The present
method of creating entangled ions also opens up the possibility of a
loophole-free test of Bell's inequalities.


title: Coherence and the Clock

abstract:
  We discuss the notion of quantum mechanical coherence in its connection with
time evolution and stationarity. The transition from coherence to decoherence
is examined in terms of an equation for the time dependence of the density
matrix. It is explained how the decoherence rate parameter arising in this
description is related to the ``unitarity defect'' in interactions with the
environment as well as the growth in entropy of the system. Applications to the
``Zeno-Watched Pot Effect'' and gravitational interactions are given. Finally,
some recent results on applications to macroscopic coherence with the rf SQUID,
where the transition from quantum to classical behavior could be studied
experimentally, are shown.


title: Wavelet Quantum Search Algorithm with Partial Information

abstract:
  It is questionable that Grover algorithm may be more valuable than a
classical one, when a partial information is given in a unstructured database.
In this letter, to consider quantum search when a partial information is given,
we replace the Fourier transform in the Grover algorithm with the Haar wavelet
transform. We then, given a partial information $L$ to a unstructured database
of size $N$, show that there is the improved speedup, $O(\sqrt{N/L})$.


title: Entanglement with phase decoherence

abstract:
  The system of an atom couples to two distinct optical cavities with phase
decoherence is studied by making use of a dynamical algebraic method. We adopt
the concurrence to characterize the entanglement between atom and cavities or
between two optical cavities in the presence of the phase decoherence. It is
found that the entanglement between atom and cavities can be controlled by
adjusting the detuning parameter. Finally, we show that even if the atom is
initially prepared in a maximally mixed state, it can also entangle the two
mode cavity fields.


title: About non-positive evolutions in open system dynamics

abstract:
  The long-time evolution of a system in interaction with an external
environment is usually described by a family of linear maps g_t, generated by
master equations of Block-Redfield type. These maps are in general
non-positive; a widely adopted cure for this physical inconsistency is to
restrict the domain of definition of the dynamical maps to those states for
which g_t remains positive. We show that this prescription has to be modified
when two systems are immersed in the same environment and evolve with the
factorized dynamics g_t x g_t starting from an entangled initial state.


title:
Trap environment effects over quantum statistics and atom-photon
  correlations in the collective atomic-recoil laser

abstract:
  We consider the effects of the trap environment on the atomic and optical
quantum statistical properties and on the atom-photon correlations in the
Collective Atomic-Recoil Laser. Atomic and optical statistical properties, as
well as the atom-photon correlations are dependent on the optical field
intensity and phase. In particular, depending on the values of the optical
field intensity and phase, the fields statistics varies from coherent to
superchaotic.


title: Games with Quantum Analogues

abstract:
  A new class of stochastic variables, governed by a specifice set of rules, is
introduced. These rules force them to loose some properties usually assumed for
this kind of variables. We demonstrate that stochastic processes driven by
these random sources must be described using an probability amplitude formalism
in a close resemblance to Quantum Theory. This fact shows, for the first time,
that probability amplitudes are a general concept and is not exclusive to the
formalism of Quantum Theory. Application of these rules to a noisy,
one-dimensional motion, leds to a probability structure homomorphic to Quantum
Mechanics.


title: Dobinski-type relations and the Log-normal distribution

abstract:
  We consider sequences of generalized Bell numbers B(n), n=0,1,... for which
there exist Dobinski-type summation formulas; that is, where B(n) is
represented as an infinite sum over k of terms P(k)^n/D(k). These include the
standard Bell numbers and their generalizations appearing in the normal
ordering of powers of boson monomials, as well as variants of the "ordered"
Bell numbers. For any such B we demonstrate that every positive integral power
of B(m(n)), where m(n) is a quadratic function of n with positive integral
coefficients, is the n-th moment of a positive function on the positive real
axis, given by a weighted infinite sum of log-normal distributions.


title: Contractive Schroedinger cat states for a free mass

abstract:
  Contractive states for a free quantum particle were introduced by Yuen [Yuen
H P 1983 Phys. Rev. Lett. 51, 719] in an attempt to evade the standard quantum
limit for repeated position measurements. We show how appropriate families of
two- and three component ``Schroedinger cat states'' are able to support
non-trivial correlations between the position and momentum observables leading
to contractive behavior. The existence of contractive Schroedinger cat states
is suggestive of potential novel roles of non-classical states for precision
measurement schemes.


title: Multiple-photon resolving fiber-loop detector

abstract:
  We show first reconstructions of the photon-number distribution obtained with
a multi-channel fiber-loop detector. Apart from analyzing the statistics of
light pulses this device can serve as a sophisticated postselection device for
experiments in quantum optics and quantum information. We quantify its
efficiency by means of the Fisher information and compare it to the efficiency
of the ideal photodetector.


title:
Interplay of topology and quantization: topological energy quantization
  in a cavity

abstract:
  The interplay between quantization and topology is investigated in the frame
of a topological model of electromagnetism proposed by the author. In that
model, the energy of monochromatic electromagnetic radiation in a cubic cavity
is $E=(d/4)\hbar \omega$ where $d$ is a topological index equal to the degree
of a map between two orbifolds.


title: The Feynman Path Integral: An Historical Slice

abstract:
  Efforts to give an improved mathematical meaning to Feynman's path integral
formulation of quantum mechanics started soon after its introduction and
continue to this day. In the present paper, one common thread of development is
followed over many years, with contributions made by various authors. The
present version of this line of development involves a continuous-time
regularization for a general phase space path integral and provides, in the
author's opinion at least, perhaps the optimal formulation of the path
integral.


title: Unitary Gate Synthesis for Continuous Variable Systems

abstract:
  We investigate the synthesis of continuous-variable two-mode unitary gates in
the setting where two modes A and B are coupled by a fixed quadratic
Hamiltonian H. The gate synthesis consists of a sequence of evolutions governed
by Hamiltonian H interspaced by local phase shifts applied to A and B. We
concentrate on protocols that require the minimum necessary number of steps and
we show how to implement the beam splitter and the two-mode squeezer in just
three steps. Particular attention is paid to the Hamiltonian x_A p_B that
describes the effective off-resonant interaction of light with the collective
atomic spin.


title: A logical interpretation of a delayed-choice, quantum eraser experiment

abstract:
  This paper shows how one can construe the experimental results in a way that
does not involve effects that precede their causes.


title: Semiclassical Shor's Algorithm

abstract:
  We propose a semiclassical version of Shor's quantum algorithm to factorize
integer numbers, based on spin-1/2 SU(2) generalized coherent states.
Surprisingly, we find evidences that the algorithm's success probability is not
too severely modified by our semiclassical approximation. This suggests that it
is worth pursuing practical implementations of the algorithm on semiclassical
devices.


title: Ancilla-assisted quantum process tomography

abstract:
  Complete and precise characterization of a quantum dynamical process can be
achieved via the method of quantum process tomography. Using a source of
correlated photons, we have implemented several methods investigating a wide
range of processes, e.g., unitary, decohering, and polarizing. One of these
methods, ancilla-assisted process tomography (AAPT), makes use of an additional
``ancilla system,'' and we have theoretically determined the conditions when
AAPT is possible. All prior schemes for AAPT make use of entangled states. Our
results show that, surprisingly, entanglement is not required for AAPT, and we
present process tomography data obtained using an input state that has no
entanglement. However, the use of entanglement yields superior results.


title: Smaller Circuits for Arbitrary n-qubit Diagonal Computations

abstract:
  A unitary operator U=\sum u_{j,k} |k><j| is called diagonal when u_{j,k}=0
unless j=k. The definition extends to quantum computations, where j and k vary
over the 2^n binary expressions for integers 0,1 ..., 2^n-1, given n qubits.
Such operators do not affect outcomes of the projective measurement {<j| ; 0 <=
j <= 2^n-1} but rather create arbitrary relative phases among the computational
basis states {|j> ; 0 <= j <= 2^n-1}. These relative phases are often required
in applications.
  Constructing quantum circuits for diagonal computations using standard
techniques requires either O(n^2 2^n) controlled-not gates and one-qubit Bloch
sphere rotations or else O (n 2^n) such gates and a work qubit. This work
provides a recursive, constructive procedure which inputs the matrix
coefficients of U and outputs such a diagram containing 2^{n+1}-3 alternating
controlled-not gates and one-qubit z-axis Bloch sphere rotations. Up to a
factor of two, these circuits are the smallest possible. Moreover, should the
computation U be a tensor of diagonal one-qubit computations of the form
R_z(\alpha)=e^{-i \alpha/2}|0><0|+ e^{i \alpha/2} |1><1|, then a cancellation
of controlled-not gates reduces our circuit to that of an n-qubit tensor.


title: Taming Entanglement

abstract:
  Using a spontaneous parametric-downconversion source of photon pairs, we are
working towards the creation of arbitrary 2-qubit quantum states with high
fidelity. Currently, all physically allowable combinations of polarization
entanglement and mixture can be produced, including maximally-entangled mixed
states. The states are experimentally measured and refined via
computer-automated quantum-state tomography, and this system has also been used
to perform single-qubit and ancilla-assisted quantum process tomography.


title: Quantum Search of Spatial Regions

abstract:
  Can Grover's algorithm speed up search of a physical region - for example a
2-D grid of size sqrt(n) by sqrt(n)? The problem is that sqrt(n) time seems to
be needed for each query, just to move amplitude across the grid. Here we show
that this problem can be surmounted, refuting a claim to the contrary by
Benioff. In particular, we show how to search a d-dimensional hypercube in time
O(sqrt n) for d at least 3, or O((sqrt n)(log n)^(3/2)) for d=2. More
generally, we introduce a model of quantum query complexity on graphs,
motivated by fundamental physical limits on information storage, particularly
the holographic principle from black hole thermodynamics. Our results in this
model include almost-tight upper and lower bounds for many search tasks; a
generalized algorithm that works for any graph with good expansion properties,
not just hypercubes; and relationships among several notions of `locality' for
unitary matrices acting on graphs. As an application of our results, we give an
O(sqrt(n))-qubit communication protocol for the disjointness problem, which
improves an upper bound of Hoyer and de Wolf and matches a lower bound of
Razborov.


title: Testing integrability with a single bit of quantum information

abstract:
  We show that deterministic quantum computing with a single bit (DQC1) can
determine whether the classical limit of a quantum system is chaotic or
integrable using O(N) physical resources, where $N$ is the dimension of the
Hilbert space of the system under study. This is a square root improvement over
all known classical procedures. Our study relies strictly on the random matrix
conjecture. We also present numerical results for the nonlinear kicked top.


title:
Imperfection effects for multiple applications of the quantum wavelet
  transform

abstract:
  We study analytically and numerically the effects of various imperfections in
a quantum computation of a simple dynamical model based on the Quantum Wavelet
Transform (QWT). The results for fidelity timescales, obtained for a large
range of error amplitudes and number of qubits, imply that for static
imperfections the threshold for fault-tolerant quantum computation is decreased
by a few orders of magnitude compared to the case of random errors.


title:
Path integral treatment of a family of super-integrable systems in
  n-dimensional Euclidean space

abstract:
  The exact path integration for a family of maximally super-integrable systems
generalizing the hydrogen atom in the $n$-dimensional Euclidean space is
presented. The Green's function is calculated in parabolic rotational and
spherical coordinate systems. The energy spectrum and the correctly normalized
wave functions of the bound states are obtained from the poles of the Green's
function and their residues, respectively.


title: On Strong Superadditivity of the Entanglement of Formation

abstract:
  We employ a basic formalism from convex analysis to show a simple relation
between the entanglement of formation $E_F$ and the conjugate function $E^*$ of
the entanglement function $E(\rho)=S(\trace_A\rho)$. We then consider the
conjectured strong superadditivity of the entanglement of formation $E_F(\rho)
\ge E_F(\rho_I)+E_F(\rho_{II})$, where $\rho_I$ and $\rho_{II}$ are the
reductions of $\rho$ to the different Hilbert space copies, and prove that it
is equivalent with subadditivity of $E^*$. As an application, we show that
strong superadditivity would follow from multiplicativity of the maximal
channel output purity for all non-trace-preserving quantum channels, when
purity is measured by Schatten $p$-norms for $p$ tending to 1.


title:
The Quantum Four Stroke Heat Engine: Thermodynamic Observables in a
  Model with Intrinsic Friction

abstract:
  The fundamentals of a quantum heat engine are derived from first principles.
The study is based on the equation of motion of a minimum set of operators
which is then used to define the state of the system. The relation between the
quantum framework and thermodynamical observables is examined. A four stroke
heat engine model with a coupled two-level-system as a working fluid is used to
explore the fundamental relations. In the model used, the internal Hamiltonian
does not commute with the external control field which defines the two
adiabatic branches. Heat is transferred to the working fluid by coupling to hot
and cold reservoirs under constant field values. Explicit quantum equation of
motion for the relevant observables are derived on all branches. The dynamics
on the heat transfer constant field branches is solved in closed form. On the
adiabats, a general numerical solution is used and compared with a particular
analytic solution. These solutions are combined to construct the cycle of
operation. The engine is then analyzed in terms of frequency-entropy and
entropy-temperature graphs. The irreversible nature of the engine is the result
of finite heat transfer rates and friction-like behavior due to
noncommutability of the internal and external Hamiltonian.


title: Ensembles and experiments in classical and quantum physics

abstract:
  A philosophically consistent axiomatic approach to classical and quantum
mechanics is given. The approach realizes a strong formal implementation of
Bohr's correspondence principle. In all instances, classical and quantum
concepts are fully parallel: the same general theory has a classical
realization and a quantum realization.
  Extending the `probability via expectation' approach of Whittle to
noncommuting quantities, this paper defines quantities, ensembles, and
experiments as mathematical concepts and shows how to model complementarity,
uncertainty, probability, nonlocality and dynamics in these terms. The approach
carries no connotation of unlimited repeatability; hence it can be applied to
unique systems such as the universe.
  Consistent experiments provide an elegant solution to the reality problem,
confirming the insistence of the orthodox Copenhagen interpretation on that
there is nothing but ensembles, while avoiding its elusive reality picture. The
weak law of large numbers explains the emergence of classical properties for
macroscopic systems.


title: Universal quantum interfaces

abstract:
  To observe or control a quantum system, one must interact with it via an
interface. This letter exhibits simple universal quantum interfaces--quantum
input/output ports consisting of a single two-state system or quantum bit that
interacts with the system to be observed or controlled. It is shown that under
very general conditions the ability to observe and control the quantum bit on
its own implies the ability to observe and control the system itself. The
interface can also be used as a quantum communication channel, and multiple
quantum systems can be connected by interfaces to become an efficient universal
quantum computer. Experimental realizations are proposed, and implications for
controllability, observability, and quantum information processing are
explored.


title: Sharp Error Bounds on Quantum Boolean Summation in Various Settings

abstract:
  We study the quantum summation (QS) algorithm of Brassard, Hoyer, Mosca and
Tapp, that approximates the arithmetic mean of a Boolean function defined on N
elements. We improve error bounds presented in [1] in the worst-probabilistic
setting, and present new error bounds in the average-probabilistic setting. In
particular, in the worst-probabilistic setting, we prove that the error of the
QS algorithm using $M - 1$ queries is $3\pi /(4M)$ with probability $8/\pi^2$,
which improves the error bound $\pi M^{-1} + \pi^2 M^{-2}$ of Brassard et al.
We also present bounds with probabilities $p\in (1/2, 8/\pi^2]$ and show they
are sharp for large $M$ and $NM^{-1}$. In the average-probabilistic setting, we
prove that the QS algorithm has error of order $\min\{M^{-1}, N^{-1/2}\}$ if
$M$ is divisible by 4. This bound is optimal, as recently shown in [10]. For M
not divisible by 4, the QS algorithm is far from being optimal if $M \ll
N^{1/2}$ since its error is proportional to $M^{-1}^$.


title:
Everettian Rationality: defending Deutsch's approach to probability in
  the Everett interpretation

abstract:
  An analysis is made of Deutsch's recent claim to have derived the Born rule
from decision-theoretic assumptions. It is argued that Deutsch's proof must be
understood in the explicit context of the Everett interpretation, and that in
this context, it essentially succeeds. Some comments are made about the
criticism of Deutsch's proof by Barnum, Caves, Finkelstein, Fuchs, and Schack;
it is argued that the flaw which they point out in the proof does not apply if
the Everett interpretation is assumed.
  A longer version of this paper, entitled "Quantum Probability and Decision
Theory, Revisted", is also available online.


title: Nonlocal supersymmetric deformations of periodic potentials

abstract:
  Irreducible second-order Darboux transformations are applied to the periodic
Schrodinger's operators. It is shown that for the pairs of factorization
energies inside of the same forbidden band they can create new non-singular
potentials with periodicity defects and bound states embedded into the spectral
gaps. The method is applied to the Lame and periodic piece-wise transparent
potentials. An interesting phenomenon of translational Darboux invariance
reveals nonlocal aspects of the supersymmetric deformations.


title: Quantum cryptography with fewer random numbers

abstract:
  We prove that in the BB84 quantum cryptography protocol Alice and Bob do not
need to make random bases-choice for each qubit: they can keep the same bases
for entire blocks of qubits. It suffices that the raw key consists of many such
qubit-blocks. The practical advantage of reducing the need for random number is
emphasized.


title: Equivalence between two-qubit entanglement and secure key distribution

abstract:
  We study the problem of secret key distillation from bipartite states in the
scenario where Alice and Bob can only perform measurements at the single-copy
level and classically process the obtained outcomes. Even with these
limitations, secret bits can be asymptotically distilled by the honest parties
from any two-qubit entangled state, under any individual attack. Our results
point out a complete equivalence between two-qubit entanglement and secure key
distribution: a key can be established through a one-qubit channel if and only
if it allows to distribute entanglement. These results can be generalized to
higher dimension for all those states that are one-copy distillable.


title: Quantum Vacuum Heuristics

abstract:
  Didactic heuristic arguments, based on the quantum mechanics of the vacuum
and the structure of spacetime, are reviewed concerning particle creation from
the vacuum by an electric field, vacuum radiation in an accelerated frame,
black-hole radiation, minimum-mass black holes, spacetime breakdown, maximal
proper acceleration, the spacetime tangent bundle, and intrinsic Planck-scale
regularization of quantum fields.


title:
Classical deterministic complexity of Edmonds' problem and Quantum
  Entanglement

abstract:
  This paper continues research initiated in quant-ph/0201022 . The main
subject here is the so-called Edmonds' problem of deciding if a given linear
subspace of square matrices contains a nonsingular matrix . We present a
deterministic polynomial time algorithm to solve this problem for linear
subspaces satisfying a special matroids motivated property, called in the paper
the Edmonds-Rado property . This property is shown to be very closely related
to the separability of bipartite mixed states . One of the main tools used in
the paper is the Quantum Permanent introduced in quant-ph/0201022 .


title: Quantum Hamiltonians and Stochastic Jumps

abstract:
  With many Hamiltonians one can naturally associate a |Psi|^2-distributed
Markov process. For nonrelativistic quantum mechanics, this process is in fact
deterministic, and is known as Bohmian mechanics. For the Hamiltonian of a
quantum field theory, it is typically a jump process on the configuration space
of a variable number of particles. We define these processes for regularized
quantum field theories, thereby generalizing previous work of John S. Bell
[Phys. Rep. 137, 49 (1986)] and of ourselves [J. Phys. A: Math. Gen. 36, 4143
(2003)]. We introduce a formula expressing the jump rates in terms of the
interaction Hamiltonian, and establish a condition for finiteness of the rates.


title: Majorization criterion for distillability of a bipartite quantum state

abstract:
  Bipartite quantum states are classified into three categories: separable
states, bound entangled states, and free entangled states. It is of great
importance to characterize these families of states for the development of
quantum information science. In this paper, I show that the separable states
and the bound entangled states have a common spectral property. More precisely,
I prove that for undistillable -- separable and bound entangled -- states, the
eigenvalue vector of the global system is majorized by that of the local
system. This result constitutes a new sufficient condition for distillability
of bipartite quantum states. This is achieved by proving that if a bipartite
quantum state satisfies the reduction criterion for distillability, then it
satisfies the majorization criterion for separability.


title: Non-commutative Calculus and Discrete Physics

abstract:
  Sequences of actions do not commute.. For example, the tick of a clock and
the measurement of a position do not commute with one another, since the
position will have moved to the next position after the tick. We adopt
non-commutative calculus, with derivatives represented by commutators. In the
beginning distinct derivatives do not commute with one another, providing
curvature formalism so that the form of the curvature of a gauge field appears
almost as soon as the calculus is defined. This provides context for the
Feynman-Dyson derivation of electromagnetic formalism from commutators, and
generalizations including the early appearance of the form of the Levi-Civita
connection dervived from the Jacobi identity. In this version of
non-commutative physics bare quantum mechanics (its commutation relations)
appears as the flat background for all other constructions. Ascent to classical
physics is obtained by replacing commutators with Poisson brackets that satisfy
the Leibniz rule. An appendix on matrix algebra from a discrete point of view
(Iterants) is provided. This paper will appear in the proceedings of the ANPA
conference held in Cambridge, England in the summer of 2002.


title: Merging quantum theory into classical physics

abstract:
  The zero point field is an ordinary field existing in the dark, which cannot
be separated from the total electromagnetic field in an excited mode. The total
field is in equilibrium with matter that it polarizes temporarily and
reversibly. This polarisation is exceptionally large enough to allow the energy
of an atom reach and cross a pass between two minimums of potential,
stimulating an emission or an absorption.
  A paradox of quantum electrodynamics is explained classically: The nearly
plane wave generally used in stimulated emission experiments must be decomposed
into an efficient spherical wave and a scattered wave, so that the plane wave
is two times less efficient than the zero point component of the spherical
mode. The classical electromagnetism does not need the quantum postulate
"reduction of the wave packet" and it has no paradox such as EPR.
  De Broglie's waves may be the linear part of solitons of a field which may be
a high frequency electromagnetic field. These solitons may lead to a physical
interpretation of the superstrings theory.


title:
Asymmetric quantum telecloning of d-level systems and broadcasting of
  entanglement to different locations using the "many-to-many" communication
  protocol

abstract:
  We propose a generalization of quantum teleportation: the so-called
many-to-many quantum communication of the information of a d-level system from
N spatially separated senders to M>N receivers situated at different locations.
We extend the concept of asymmetric telecloning from qubits to d-dimensional
systems. We investigate the broadcasting of entanglement by using local 1->2
optimal universal asymmetric Pauli machines and show that the maximal
fidelities of the two final entangled states are obtained when symmetric
machines are applied. Cloning of entanglement is studied using a nonlocal
optimal universal asymmetric cloning machine and we show that the symmetric
machine optimally copies the entanglement. The "many-to-many" teleportation
scheme is applied in order to distribute entanglement shared between two
observers to two pairs of spatially separated observers.


abstract:
  We examine the validity of the Kraus representation in the presence of
initial correlations and show that it is assured only when a joint dynamics is
locally unitary.


title:
Polynomial deformations of sl(2,R) in a three-dimensional invariant
  subspace of monomials

abstract:
  New finite-dimensional representations of specific polynomial deformations of
sl(2,R) are constructed. The corresponding generators can be, in particular,
realized through linear differential operators preserving a finite-dimensional
subspace of monomials. We concentrate on three-dimensional spaces.


title: Programmable networks for quantum algorithms

abstract:
  The implementation of a quantum computer requires the realization of a large
number of N-qubit unitary operations which represent the possible oracles or
which are part of the quantum algorithm. Until now there are no standard ways
to uniformly generate whole classes of N-qubit gates. We have developed a
method to generate arbitrary controlled phase shift operations with a single
network of one-qubit and two-qubit operations. This kind of network can be
adapted to various physical implementations of quantum computing and is
suitable to realize the Deutsch-Jozsa algorithm as well as Grover's search
algorithm.


title: Quantum Brain States

abstract:
  If conscious observers are to be included in the quantum mechanical universe,
we need to find the rules that engage observers with quantum mechanical
systems. The author has proposed five rules that are discovered by insisting on
empirical completeness; that is, by requiring the rules to draw empirical
information from Schrodinger's solutions that is more complete than is
currently possible with the (Born) probability interpretation. I discard Born's
interpretation, introducing probability solely through probability current.
These rules tell us something about brains. They require the existence of
observer brain states that are neither conscious nor unconscious. I call them
'ready' brain states because they are on stand-by, ready to become conscious
the moment they are stochastically chosen. Two of the rules are selection rules
involving ready brain states. The place of these rules in a wider theoretical
context is discussed. Key Words: boundary conditions, consciousness,
decoherence, macroscopic superposition, Penrose, state reduction, von Neumann,
wave collapse.


title: Objective vs Observer Measurements

abstract:
  Post-inflationary boundary conditions are essential to the existence of our
highly structured universe, and these can only come about through quantum
mechanical state reductions - i.e., through measurements. The choice is
between: An 'objective' measurement that allows reduction to occur independent
of conscious observers, and an 'observer' based measurement that ties reduction
to the existence of a conscious observer. It is shown in this paper that that
choice cannot be determined empirically; so how we finally understand state
reduction will be decided by the way that reduction is used in a wider (future)
theoretical framework. Key Words: consciousness, decoherence, stochastic
choice, wave collapse.


title: Decoherence of a particle across a medium: a microscopic derivation

abstract:
  We deduce from a microscopic point of view the equation that describes how
the state of a particle crossing a medium decoheres. We apply our results to
the example of a particle crossing a gas, computing explicitly the Lindblad
operators in terms of the interaction potential between the particle and a
target of the medium. We interpret the imaginary part of the refraction index
as a loss of quantum coherence, that is reflected in the disappearance of
interference patterns in a Young experiment.


title: Timing of the Penrose R-Process

abstract:
  The Penrose reduction theory is applied to a particle/detector interaction
where the time that it takes for a particle capture (and reduction of the
original state) is constrained by the Heisenberg uncertainty between time and
energy . The usual interpretation of this equation is found to conflict with
the Hamiltonian dynamics of the interaction. Another interpretation of this
equation seems to solve that problem, but then another difficulty arises. We
conclude that the Penrose theory cannot reflect the timing implicit in the
Hamiltonian dynamics unless it can be amended to take account of the
probability current flow between competing states. Key Words: decoherence,
probability current, stochastic choice, wave collapse.


title:
Detecting N-particle interference patterns with linear balanced N-port
  analyzers

abstract:
  A standard two-path interferometer fed into a linear N-port analyzer with
coincidence detection of its output ports is analyzed. The N-port is assumed to
be implemented as a discrete Fourier transformation $\cal F$, i.e., to be
balanced. For unbound bosons it allows us to detect N-particle interference
patterns with an N-fold reduction of the observed de Broglie wavelength,
perfect visibility and minimal noise. Because the scheme involves heavy
filtering a lot of the signal is lost, yet, it is surprisingly robust against
common experimental imperfections, and can be implemented with current
technology.


title: Determination of the s-wave Scattering Length of Chromium

abstract:
  We have measured the deca-triplet s-wave scattering length of the bosonic
chromium isotopes $^{52}$Cr and $^{50}$Cr. From the time constants for
cross-dimensional thermalization in atomic samples we have determined the
magnitudes $|a(^{52}Cr)|=(170 \pm 39)a_0$ and $|a(^{50}Cr)|=(40 \pm 15)a_0$,
where $a_0=0.053nm$. By measuring the rethermalization rate of $^{52}$Cr over a
wide temperature range and comparing the temperature dependence with the
effective-range theory and single-channel calculations, we have obtained strong
evidence that the sign of $a(^{52}Cr)$ is positive. Rescaling our $^{52}$Cr
model potential to $^{50}$Cr strongly suggests that $a(^{50}Cr)$ is positive,
too.


title: On the practicality of time-optimal two-qubit Hamiltonian simulation

abstract:
  What is the time-optimal way of using a set of control Hamiltonians to obtain
a desired interaction? Vidal, Hammerer and Cirac [Phys. Rev. Lett. 88 (2002)
237902] have obtained a set of powerful results characterizing the time-optimal
simulation of a two-qubit quantum gate using a fixed interaction Hamiltonian
and fast local control over the individual qubits. How practically useful are
these results? We prove that there are two-qubit Hamiltonians such that
time-optimal simulation requires infinitely many steps of evolution, each
infinitesimally small, and thus is physically impractical. A procedure is given
to determine which two-qubit Hamiltonians have this property, and we show that
almost all Hamiltonians do. Finally, we determine some bounds on the penalty
that must be paid in the simulation time if the number of steps is fixed at a
finite number, and show that the cost in simulation time is not too great.


title: Unambiguous discrimination of mixed states

abstract:
  We present the conditions under which probabilistic error-free discrimination
of mixed states is possible, and provide upper and lower bounds on the maximum
probability of success for the case of two mixed states. We solve certain
special cases exactly, and demonstrate how the problems of state filtering and
state comparison can be recast as problems of mixed state unambiguous
discrimination.


title: Quantum tomography for Dirac spinors

abstract:
  We present a tomographic scheme, based on spacetime symmetries, for the
reconstruction of the internal degrees of freedom of a Dirac spinor. We discuss
the circumstances under which the tomographic group can be taken as SU(2), and
how this crucially depends on the choice of the gamma matrix representation. A
tomographic reconstruction process based on discrete rotations is considered,
as well as a continuous alternative.


title:
A unified approach to exact solutions of time-dependent Lie-algebraic
  quantum systems

abstract:
  By using the Lewis-Riesenfeld theory and the invariant-related unitary
transformation formulation, the exact solutions of the {\it time-dependent}
Schr\"{o}dinger equations which govern the various Lie-algebraic quantum
systems in atomic physics, quantum optics, nuclear physics and laser physics
are obtained. It is shown that the {\it explicit} solutions may also be
obtained by working in a sub-Hilbert-space corresponding to a particular
eigenvalue of the conserved generator ({\it i. e.}, the {\it time-independent}
invariant) for some quantum systems without quasi-algebraic structures. The
global and topological properties of geometric phases and their adiabatic limit
in time-dependent quantum systems/models are briefly discussed.


title: Probability Analysis of a Quantum Computer

abstract:
  The quantum computer algorithm by Peter Shor for factorization of integers is
studied. The quantum nature of a QC makes its outcome random. The output
probability distribution is investigated and the chances of a successful
operation is determined


title: Activation-like processes at zero temperature

abstract:
  We examine the possibility that a metastable quantum state could experiment a
phenomenon similar to thermal activation but at zero temperature. In order to
do that we study the real-time dynamics of the reduced Wigner function in a
simple open quantum system: an anharmonic oscillator with a cubic potential
linearly interacting with an environment of harmonic oscillators. Our results
suggest that this activation-like phenomenon exists indeed as a consequence of
the fluctuations induced by the environment and that its associated decay rate
is comparable to the tunneling rate as computed by the instanton method, at
least for the particular potential of the system and the distribution of
frequencies for the environment considered in this paper. However, we are not
able to properly deal with the term which leads to tunneling in closed quantum
systems, and a definite conclusion cannot be reached until tunneling and
activation-like effects are considered simultaneously.


title: Bell's theorem without inequalities and without alignments

abstract:
  A proof of Bell's theorem without inequalities is presented which exhibits
three remarkable properties: (a) reduced local states are immune to collective
decoherence; (b) distant local setups do not need to be aligned, since the
required perfect correlations are achieved for any local rotation of the local
setups; (c) local measurements require only individual measurements on the
qubits. Indeed, it is shown that this proof is essentially the only one which
fulfils (a), (b), and (c).


title: Relativistic BB84, relativistic errors, and how to correct them

abstract:
  The Bennett-Brassard cryptographic scheme (BB84) needs two bases, at least
one of them linearly polarized. The problem is that linear polarization
formulated in terms of helicities is not a relativistically covariant notion:
State which is linearly polarized in one reference frame becomes depolarized in
another one. We show that a relativistically moving receiver of information
should define linear polarization with respect to projection of
Pauli-Lubanski's vector in a principal null direction of the Lorentz
transformation which defines the motion, and not with respect to the helicity
basis. Such qubits do not depolarize.


title:
Exploring quantum dynamics in an open many-body system: Transition to
  superradiance

abstract:
  We study the dynamics of a complex open quantum many-body system. The
coupling to external degrees of freedom can be viewed as a coupling to a
radiation field, to continuum states or to a measuring apparatus. This
perturbation is treated in terms of an effective non-Hermitian Hamiltonian. The
influence of such coupling on the properties of the many-body dynamics is
discussed, with emphasis on new effects related to dynamical segregation of
fast and slow decays and the phase transition to Dicke superradiance. Relations
to quantum optics, continuum shell model, theory of measurement, quantum chaos,
percolation theory, and to quantum reactions are stressed.


title:
Connecting the geometric measure of entanglement and entanglement
  witnesses

abstract:
  The geometric measure of entanglement is an approach to quantifying
entanglement that is based on the Hilbert-space distance (or, equivalently,
angle) between pure states and their best unentangled approximants. An
entanglement witness is an operator that reveals entanglement for a given
entangled state. A connection is identified between entanglement witnesses and
the geometric measure of entanglement. This offers a new interpretation of the
geometric measure of entanglement of a state, and renders it experimentally
verifiable, doing so most readily for states that are pure.


title: Wigner Functions in High Energy Physics

abstract:
  Recent developments are (meta)reviewed in the applications of Wigner
functions to describe the observed single particle spectra and two-particle
Bose-Einstein (or Hanbury Brown -- Twiss) correlations in high energy particle
and nuclear physics, with examples from hadron-proton and Pb + Pb collisions at
CERN SPS.


title: Quantum random walks - an introductory overview

abstract:
  This article aims to provide an introductory survey on quantum random walks.
Starting from a physical effect to illustrate the main ideas we will introduce
quantum random walks, review some of their properties and outline their
striking differences to classical walks. We will touch upon both physical
effects and computer science applications, introducing some of the main
concepts and language of present day quantum information science in this
context. We will mention recent developments in this new area and outline some
open questions.


title:
Comment on ``Experimental Nonlocality Proof of Quantum Teleportation and
  Entanglement Swapping'' - by L.C. Ryff

abstract:
  It is shown that, concerning the experiment described by the authors, their
extension to the situation in which Alice's measurement occurs after Bob's is
unnecessary and their interpretation misleading.


title: Curvature induced toroidal bound states

abstract:
  Curvature induced bound state (E < 0) eigenvalues and eigenfunctions for a
particle constrained to move on the surface of a torus are calculated. A limit
on the number of bound states a torus with minor radius a and major radius R
can support is obtained. A condition for mapping constrained particle wave
functions on the torus into free particle wave functions is established.


title: Projection evolution in quantum mechanics

abstract:
  We propose a model of time evolution of quantum objects which unites the
unitary evolution and the measurement procedures. The model allows to treat the
time on equal footing with other dynamical variables.


title: The quantum speed limit

abstract:
  How fast can a quantum system evolve? We answer this question focusing on the
role of entanglement and interactions among subsystems. In particular, we
analyze how the order of the interactions shapes the dynamics.


title: Resource Limited Theories and their Extensions

abstract:
  This work is based on the idea that extension of physical and mathematical
theories to include the amount of space, time, momentum, and energy resources
required to determine properties of systems may influence what is true in
physics and mathematics at a foundational level. Background material, on the
dependence of region or system sizes on both the resources required to study
the regions or systems and the indirectness of the reality status of the
systems, suggests that one associate to each amount, r, of resources a domain,
D_{r}, a theory, T_{r}, and a language, L_{r}. D_{r} is limited in that all
statements in D_{r} require at most r resources to verify or refute. T_{r} is
limited in that any theorem of T_{r} must be provable using at most r
resources. Also any theorem of T_{r} must be true in D_{r}. L_{r} is limited in
that all expressions in L_{r} require at most r resources to create, display,
and maintain. A partial ordering of the resources is used to describe minimal
use of resources, a partial ordering of the T_{r}, and motion of an observer
using resources to acquire knowledge. Reflection principles are used to push
the effect of Godel's incompleteness theorem on consistency up in the partial
ordering. It is suggested that a coherent theory of physics and mathematics, or
theory of everything, is a common extension of all the T_{r}.


title: Multiparticle entanglement purification for graph states

abstract:
  We introduce a class of multiparticle entanglement purification protocols
that allow us to distill a large class of entangled states. These include
cluster states, GHZ states and various error correction codes all of which
belong to the class of two-colorable graph states. We analyze these schemes
under realistic conditions and observe that they are scalable, i.e. the
threshold value for imperfect local operations does not depend on the number of
parties for many of these states. When compared to schemes based on bipartite
entanglement purification, the protocol is more efficient and the achievable
quality of the purified states is larger. As an application we discuss an
experimental realization of the protocol in optical lattices which allows one
to purify cluster states.


title: Locking classical correlation in quantum states

abstract:
  We show that there exist bipartite quantum states which contain large hidden
classical correlation that can be unlocked by a disproportionately small amount
of classical communication. In particular, there are $(2n+1)$-qubit states for
which a one bit message doubles the optimal classical mutual information
between measurement results on the subsystems, from $n/2$ bits to $n$ bits.
States exhibiting this behavior need not be entangled. We study the range of
states exhibiting this phenomenon and bound its magnitude.


title: Set theoretical forcing in quantum mechanics and AdS/CFT correspondence

abstract:
  We show unexpected connection of Set Theoretical Forcing with Quantum
Mechanical lattice of projections over some separable Hilbert space. The basic
ingredient of the construction is the rule of indistinguishability of Standard
and some Nonstandard models of Peano Arithmetic. The ingeneric reals introduced
by M. Ozawa will correspond to simultaneous measurement of incompatible
observables. We also discuss some results concerning model theoretical analysis
of Small Exotic Smooth Structures on topological 4-space. Forcing appears
rather naturally in this context and the rule of indistinguishability is
crucial again. As an unexpected application we are able to approach Maldacena
Conjecture on $AdS/CFT$ correspondence in the case of AdS_5xS^5 and Super YM
Conformal Field Theory in 4 dimensions. We conjecture that there is possibility
of breaking Supersymetry via sources of gravity generated in 4 dimensions by
exotic smooth structures on R^4 emerging in this context.


title: Examples of Berezin-Toeplitz Quantization: Finite sets and Unit Interval

abstract:
  We present a quantization scheme of an arbitrary measure space based on
overcomplete families of states and generalizing the Klauder and the
Berezin-Toeplitz approaches. This scheme could reveal itself as an efficient
tool for quantizing physical systems for which more traditional methods like
geometric quantization are uneasy to implement. The procedure is illustrated by
(mostly two-dimensional) elementary examples in which the measure space is a
$N$-element set and the unit interval. Spaces of states for the $N$-element set
and the unit interval are the 2-dimensional euclidean $\R^2$ and hermitian
$\C^2$ planes.


title: Comment on "Probabilistic Quantum Memories"

abstract:
  This is a comment on two wrong Phys. Rev. Letters papers by C.A.
Trugenberger. Trugenberger claimed that quantum registers could be used as
exponentially large "associative" memories. We show that his scheme is no
better than one where the quantum register is replaced with a classical one of
equal size.
  We also point out that the Holevo bound and more recent bounds on "quantum
random access codes" pretty much rule out powerful memories (for classical
information) based on quantum states.


title:
Quantum-wave pattern recognition: From simulations towards
  implementation

abstract:
  A simulated Hopfield-type neural-net-like model, which is realizable using
quantum holography, is proposed for quantum associative memory and pattern
recognition.


title: Collisional decoherence observed in matter wave interferometry

abstract:
  We study the loss of spatial coherence in the extended wave function of
fullerenes due to collisions with background gases. From the gradual
suppression of quantum interference with increasing gas pressure we are able to
support quantitatively both the predictions of decoherence theory and our
picture of the interaction process. We thus explore the practical limits of
matter wave interferometry at finite gas pressures and estimate the required
experimental vacuum conditions for interferometry with even larger objects.


title: Collisional decoherence reexamined

abstract:
  We re-derive the quantum master equation for the decoherence of a massive
Brownian particle due to collisions with the lighter particles from a thermal
environment. Our careful treatment avoids the occurrence of squares of Dirac
delta functions. It leads to a decoherence rate which is smaller by a factor of
2 pi compared to previous findings. This result, which is in agreement with
recent experiments, is confirmed by both a physical analysis of the problem and
by a perturbative calculation in the weak coupling limit.


title:
Experimental Controlled-NOT Logic Gate for Single Photons in the
  Coincidence Basis

abstract:
  We report a proof-of-principle demonstration of a probabilistic
controlled-NOT gate for single photons. Single-photon control and target qubits
were mixed with a single ancilla photon in a device constructed using only
linear optical elements. The successful operation of the controlled-NOT gate
relied on post-selected three-photon interference effects which required the
detection of the photons in the output modes.


title: On continuous-variable entanglement with and without phase references

abstract:
  We discuss how continous-variable quantum states such as coherent states and
two-mode squeezed states can be encoded in phase-reference independent ways.


title: Reversible simulation of bipartite product Hamiltonians

abstract:
  Consider two quantum systems A and B interacting according to a product
Hamiltonian H = H_A x H_B. We show that any two such Hamiltonians can be used
to simulate each other reversibly (i.e., without efficiency losses) with the
help of local unitary operations and local ancillas. Accordingly, all non-local
features of a product Hamiltonian -- including the rate at which it can be used
to produce entanglement, transmit classical or quantum information, or simulate
other Hamiltonians -- depend only upon a single parameter. We identify this
parameter and use it to obtain an explicit expression for the entanglement
capacity of all product Hamiltonians. Finally, we show how the notion of
simulation leads to a natural formulation of measures of the strength of a
nonlocal Hamiltonian.


title: Alternative new notation for quantum information theory

abstract:
  A new notation has been introduced for the quantum information theory. By
this notation,some calculations became simple in quantum information theory
such as quantum swapping, quantum teleportation.


title: Retrodictive states and two-photon quantum imaging

abstract:
  We use retrodictive quantum theory to analyse two-photon quantum imaging
systems. The formalism is particularly suitable for calculating conditional
probability distributions.


title: Entanglement and spin squeezing in the two-atom Dicke model

abstract:
  We analyze the relation between the entanglement and spin-squeezing parameter
in the two-atom Dicke model and identify the source of the discrepancy recently
reported by Banerjee and Zhou et al that one can observe entanglement without
spin squeezing. Our calculations demonstrate that there are two criteria for
entanglement, one associated with the two-photon coherences that create
two-photon entangled states, and the other associated with populations of the
collective states. We find that the spin-squeezing parameter correctly predicts
entanglement in the two-atom Dicke system only if it is associated with
two-photon entangled states, but fails to predict entanglement when it is
associated with the entangled symmetric state. This explicitly identifies the
source of the discrepancy and explains why the system can be entangled without
spin-squeezing. We illustrate these findings in three examples of the
interaction of the system with thermal, classical squeezed vacuum and quantum
squeezed vacuum fields.


title:
Observation of an oscillatory correlation function of multimode
  two-photon pairs

abstract:
  An oscillatory correlation function has been observed by the coincidence
counting of multimode two-photon pairs produced with a degenerate optical
parametric oscillator far below threshold. The coherent superposition of the
multimode two-photon pairs provides the oscillation in the intensity
correlation function. The experimental data are well fitted to a theoretical
curve.


title: Limitations on building single-photon-resolution detection devices

abstract:
  Single-photon resolution (SPR) detectors can tell the difference between
incoming wave packets of n and n+1 photons. Such devices are especially
important for linear optical quantum computing with projective measurements.
However, in this paper I show that it is impossible to construct a
photodetector with single-photon resolution when we are restricted to
single-photon sources, linear optical elements and projective measurements with
standard (non-photon-number discriminating) photodetectors. These devices
include SPR detectors that sometimes fail to distinguish one- and two-photon
inputs, but at the same time indicate this failure.


title:
The survival probability and the local density of states for
  one-dimensional Hamiltonian systems

abstract:
  For chaotic systems there is a theory for the decay of the survival
probability, and for the parametric dependence of the local density of states.
This theory leads to the distinction between "perturbative" and
"non-perturbative" regimes, and to the observation that semiclassical tools are
useful in the latter case. We discuss what is "left" from this theory in the
case of one-dimensional systems. We demonstrate that the remarkably accurate
{\em uniform} semiclassical approximation captures the physics of {\em all} the
different regimes, though it cannot take into account the effect of strong
localization.


title:
Reply to Ryff's Comment on "Experimental Nonlocality Proof of Quantum
  Teleportation and Entanglement Swapping"

abstract:
  Ryff's Comment raises the question of the meaning of the quantum state. We
argue that the quantum state is just the representative of information
available to a given observer. Then Ryff's interpretation of one of our
experiments and our original one are both admissible.


title:
Three routes to the exact asymptotics for the one-dimensional quantum
  walk

abstract:
  We demonstrate an alternative method for calculating the asymptotic behaviour
of the discrete one-coin quantum walk on the infinite line, via the Jacobi
polynomials that arise in the path integral representation. This is
significantly easier to use than the Darboux method. It also provides a single
integral representation for the wavefunction that works over the full range of
positions, $n,$ including throughout the transitional range where the behaviour
changes from oscillatory to exponential. Previous analyses of this system have
run into difficulties in the transitional range, because the approximations on
which they were based break down here. The fact that there are two different
kinds of approach to this problem (Path Integral vs. Schr\"{o}dinger wave
mechanics) is ultimately a manifestation of the equivalence between the
path-integral formulation of quantum mechanics and the original formulation
developed in the 1920s. We discuss how and why our approach is related to the
two methods that have already been used to analyse these systems.


title: What could have we been missing while Pauli's Theorem was in force?

abstract:
  Pauli's theorem asserts that the canonical commutation relation $[T,H]=iI$
only admits Hilbert space solutions that form a system of imprimitivities on
the real line, so that only non-self-adjoint time operators exist in single
Hilbert quantum mechanics. This, however, is contrary to the fact that there is
a large class of solutions to $[T,H]=iI$, including self-adjoint time operator
solutions for semibounded and discrete Hamiltonians. Consequently the theorem
has brushed aside and downplayed the rest of the solution set of the
time-energy canonical commutation relation.


title: Quantum Bit Commitment Using Entangled States

abstract:
  Based on the fact that the entanglement can not be created locally, we
proposed a quantum bit commitment protocol, in which entangled states and
quantum algorithms is used. The bit is not encoded with the form of the quantum
states, and delaying the measurement is required. Therefore the protocol will
not be denied by the Mayers-Lo-Chau no-go theorem, and unconditional security
is achieved.


title: Weyl ordering rule and new Lie bracket of quantum mechanics

abstract:
  The product of quantum mechanics is defined as the ordinary multiplication
followed by the application of superoperator that orders involved operators.
The operator version of Poisson bracket is defined being the Lie bracket which
substitutes commutator in the von Neumann equation. These result in obstruction
free quantization, with the ordering rule which coincides with Weyl ordering
rule.


title: Experimental Vacuum Squeezing in Rubidium Vapor via Self-Rotation

abstract:
  We report the generation of optical squeezed vacuum states by means of
polarization self-rotation in rubidium vapor following a proposal by Matsko et
al. [Phys. Rev. A 66, 043815 (2002)]. The experimental setup, involving in
essence just a diode laser and a heated rubidium gas cell, is simple and easily
scalable. A squeezing of 0.85+-0.05 dB was achieved.


title: Scatterer that leaves "footprints" but no "fingerprints"

abstract:
  We calculate the exact transmission coefficient of a quantum wire in the
presence of a single point defect at the wire's cut-off frequencies. We show
that while the conductance pattern (i.e., the scattering) is strongly affected
by the presence of the defect, the pattern is totally independent of the
defect's characteristics (i.e., the defect that caused the scattering cannot be
identified from that pattern).


title:
Operationally Invariant Measure of the Distance between Quantum States
  by Complementary Measurements

abstract:
  We propose an operational measure of distance of two quantum states, which
conversely tells us their closeness. This is defined as a sum of differences in
partial knowledge over a complete set of mutually complementary measurements
for the two states. It is shown that the measure is operationally invariant and
it is equivalent to the Hilbert-Schmidt distance. The operational measure of
distance provides a remarkable interpretation of the information distance
between quantum states.


title: Quantum teleportation between multiparties

abstract:
  The paper presents general protocols for quantum teleportation between
multiparties. It is shown how N parties can teleport N unknown quantum states
to M other parties with the use of N+M qudits in the maximally entangled state.
It is also shown that a single pair of qudits in the maximally entangled state
can be used to teleport two qudits in opposite directions simultaneously.


title:
Heralded Two-Photon Entanglement from Probabilistic Quantum Logic
  Operations on Multiple Parametric Down-Conversion Sources

abstract:
  An ideal controlled-NOT gate followed by projective measurements can be used
to identify specific Bell states of its two input qubits. When the input qubits
are each members of independent Bell states, these projective measurements can
be used to swap the post-selected entanglement onto the remaining two qubits.
Here we apply this strategy to produce heralded two-photon polarization
entanglement using Bell states that originate from independent parametric
down-conversion sources, and a particular probabilistic controlled-NOT gate
that is constructed from linear optical elements. The resulting implementation
is closely related to an earlier proposal by Sliwa and Banaszek
[quant-ph/0207117], and can be intuitively understood in terms of familiar
quantum information protocols. The possibility of producing a ``pseudo-demand''
source of two-photon entanglement by storing and releasing these heralded pairs
from independent cyclical quantum memory devices is also discussed.


title: Drift-Diffusion in Mangled Worlds Quantum Mechanics

abstract:
  In Everett's many worlds interpretation, where quantum measurements are seen
as decoherence events, inexact decoherence may let large worlds mangle the
memories of observers in small worlds, creating a cutoff in observable world
size. I solve a growth-drift-diffusion-absorption model of such a mangled
worlds scenario, and show that it reproduces the Born probability rule closely,
though not exactly. Thus deviations from exact decoherence can allow the Born
rule to be derived in a many worlds approach via world counting, using a finite
number of worlds and no new fundamental physics.


title: A Method for Modeling Decoherence on a Quantum Information Processor

abstract:
  We develop and implement a method for modeling decoherence processes on an
N-dimensional quantum system that requires only an $N^2$-dimensional quantum
environment and random classical fields. This model offers the advantage that
it may be implemented on small quantum information processors in order to
explore the intermediate regime between semiclassical and fully quantum models.
We consider in particular $\sigma_z\sigma_z$ system-environment couplings which
induce coherence (phase) damping, though the model is directly extendable to
other coupling Hamiltonians. Effective, irreversible phase-damping of the
system is obtained by applying an additional stochastic Hamiltonian on the
environment alone, periodically redressing it and thereby irreversibliy
randomizing the system phase information that has leaked into the environment
as a result of the coupling. This model is exactly solvable in the case of
phase-damping, and we use this solution to describe the model's behavior in
some limiting cases. In the limit of small stochastic phase kicks the system's
coherence decays exponentially at a rate which increases linearly with the kick
frequency. In the case of strong kicks we observe an effective decoupling of
the system from the environment. We present a detailed implementation of the
method on an nuclear magnetic resonance quantum information processor.


title:
Optical coherence and teleportation: Why a laser is a clock, not a
  quantum channel

abstract:
  It has been argued [T. Rudolph and B.C. Sanders, Phys. Rev. Lett. {\bf 87},
077903 (2001)] that continuous-variable quantum teleportation at optical
frequencies has not been achieved because the source used (a laser) was not
`truly coherent'. Van Enk, and Fuchs [Phys. Rev. Lett, {\bf 88}, 027902
(2002)], while arguing against Rudolph and Sanders, also accept that an
`absolute phase' is achievable, even if it has not been achieved yet. I will
argue to the contrary that `true coherence' or `absolute phase' is always
illusory, as the concept of absolute time on a scale beyond direct human
experience is meaningless. All we can ever do is to use an agreed time
standard. In this context, a laser beam is fundamentally as good a `clock' as
any other. I explain in detail why this claim is true, and defend my argument
against various objections. In the process I discuss super-selection rules,
quantum channels, and the ultimate limits to the performance of a laser as a
clock. For this last topic I use some earlier work by myself [Phys. Rev. A {\bf
60}, 4083 (1999)] and Berry and myself [Phys. Rev. A {\bf 65}, 043803 (2002)]
to show that a Heisenberg-limited laser with a mean photon number $\mu$ can
synchronize $M$ independent clocks each with a mean-square error of
$\sqrt{M}/4\mu$ radians$^2$.


title: Accessible Information and Quantum operations

abstract:
  The accessible information decreases under quantum operations. We analyzed
the connection between quantum operations and accessible information. We show
that a general quantum process cannot be operated accurately. Futhermore, an
unknown state of a closed quantum system can not be operated arbitrarily by a
unitary quantum operation.


title:
A Generalized Hamiltonian Characterizing the Interaction of the
  Two-Level Atom and both the Single Radiation Mode and External Field

abstract:
  In this paper we propose some Hamiltonian characterizing the interaction of
the two-level atom and both the single radiation mode and external field, which
might be a generalization of that of Sch{\"o}n and Cirac (quant-ph/0212068). We
solve them in the strong coupling regime under some conditions (the rotating
wave approximation, resonance condition and etc), and obtain unitary
transformations of four types to perform Quantum Computation.


title:
Squeezing arbitrary cavity-field states through their interaction with a
  single driven atom

abstract:
  We propose an implementation of the parametric amplification of an arbitrary
radiation-field state previously prepared in a high-Q cavity. This nonlinear
process is accomplished through the dispersive interactions of a single
three-level atom (fundamental |g>, intermediate |i>, and excited |e> levels)
simultaneously with i) a classical driving field and ii) a previously prepared
cavity mode whose state we wish to squeeze. We show that, in the adiabatic
approximantion, the preparation of the initial atomic state in the intermediate
level |i> becomes crucial for obtaing the degenerated parametric amplification
process.


title: Maths-type q-deformed coherent states for q > 1

abstract:
  Maths-type q-deformed coherent states with $q > 1$ allow a resolution of
unity in the form of an ordinary integral. They are sub-Poissonian and
squeezed. They may be associated with a harmonic oscillator with minimal
uncertainties in both position and momentum and are intelligent coherent states
for the corresponding deformed Heisenberg algebra.


title: A thermodynamic approach to quantum measurement and quantum probability

abstract:
  A simple model of quantum particle is proposed in which the particle in a
{\it macroscopic} rest frame is represented by a {\it microscopic
d}-dimensional oscillator, {\it s=(d-1)/2} being the spin of the particle. The
state vectors are defined simply by complex combinations of coordinates and
momenta. It is argued that the observables of the system are Hermitian forms
(corresponding uniquely to Hermitian matrices). Quantum measurements transforms
the equilibrium state obtained after preparation into a family of equilibrium
states corresponding to the critical values of the measured observable
appearing as values of a random quantity associated with the observable. Our
main assumptions state that: i) in the process of measurement the measured
observable tends to minimum, and ii) the mean value of every random quantity
associated with an observable in some state is proportional to the value of the
corresponding observable at the same state. This allows to obtain in a very
simple manner the Born rule.


title:
Solvable simulation of a double-well problem in PT symmetric quantum
  mechanics

abstract:
  Within quantum mechanics which works with parity-pseudo-Hermitian
Hamiltonians we study the tunneling in a symmetric double well formed by two
delta functions with complex conjugate strengths. The model is exactly solvable
and exhibits several interesting features. Besides an amazingly robust absence
of any PT symmetry breaking, we observe a quasi-degeneracy of the levels which
occurs all over the energy range including the high-energy domain. This pattern
is interpreted as a manifestation of certain "quantum beats".


title: The confluent algorithm in second order supersymmetric quantum mechanics

abstract:
  The confluent algorithm, a degenerate case of the second order supersymmetric
quantum mechanics, is studied. It is shown that the transformation function
must asymptotically vanish to induce non-singular final potentials. The
technique can be used to create a single level above the initial ground state
energy. The method is applied to the free particle, one-soliton well and
harmonic oscillator.


title: Quantum mechanical Universal constructor

abstract:
  Arbitrary quantum states cannot be copied. In fact, to make a copy we must
provide complete information about the system. However, can a quantum system
self-replicate? This is not answered by the no-cloning theorem. In the
classical context, Von Neumann showed that a `universal constructor' can exist
which can self-replicate an arbitrary system, provided that it had access to
instructions for making copy of the system. We question the existence of a
universal constructor that may allow for the self-replication of an arbitrary
quantum system. We prove that there is no deterministic universal quantum
constructor which can operate with finite resources. Further, we delineate
conditions under which such a universal constructor can be designed to operate
dterministically and probabilistically.


title: Single-photon two-qubit "entangled'' states: preparation and measurement

abstract:
  We implement experimentally a deterministic method to prepare and measure so
called single-photon two-qubit entangled states or single-photon Bell-states,
in which the polarization and the spatial modes of a single-photon each
represent a quantum bit. All four single-photon Bell-states can be easily
prepared and measured deterministically using linear optical elements alone. We
also discuss how this method can be used for recently proposed single-photon
two-qubit quantum cryptography protocol.


title: Effective fiber-coupling of entangled photons for quantum communication

abstract:
  We report on theoretical and experimental demonstration of high-efficiency
coupling of two-photon entangled states produced in the nonlinear process of
spontaneous parametric down conversion into a single-mode fiber. We determine
constraints for the optimal coupling parameters. This result is crucial for
practical implementation of quantum key distribution protocols with entangled
states.