title: Probabilistic Quantum Logic Operations Using Polarizing Beam Splitters

abstract:
  It has previously been shown that probabilistic quantum logic operations can
be performed using linear optical elements, additional photons (ancilla), and
post-selection based on the output of single-photon detectors. Here we describe
the operation of several quantum logic operations of an elementary nature,
including a quantum parity check and a quantum encoder, and we show how they
can be combined to implement a controlled-NOT (CNOT) gate. All of these gates
can be constructed using polarizing beam splitters that completely transmit one
state of polarization and totally reflect the orthogonal state of polarization,
which allows a simple explanation of each operation. We also describe a
polarizing beam splitter implementation of a CNOT gate that is closely
analogous to the quantum teleportation technique previously suggested by
Gottesman and Chuang [Nature 402, p.390 (1999)]. Finally, our approach has the
interesting feature that it makes practical use of a quantum-eraser technique.


title: Explicitly solvable cases of one-dimensional quantum chaos

abstract:
  We identify a set of quantum graphs with unique and precisely defined
spectral properties called {\it regular quantum graphs}. Although chaotic in
their classical limit with positive topological entropy, regular quantum graphs
are explicitly solvable. The proof is constructive: we present exact periodic
orbit expansions for individual energy levels, thus obtaining an analytical
solution for the spectrum of regular quantum graphs that is complete, explicit
and exact.


title: Bell inequalities and Entanglement

abstract:
  We discuss general Bell inequalities for bipartite and multipartite systems,
emphasizing the connection with convex geometry on the mathematical side, and
the communication aspects on the physical side. Known results on families of
generalized Bell inequalities are summarized. We investigate maximal violations
of Bell inequalities as well as states not violating (certain) Bell
inequalities. Finally, we discuss the relation between Bell inequality
violations and entanglement properties currently discussed in quantum
information theory.


title:
Exact trace formulae for a class of one-dimensional ray-splitting
  systems

abstract:
  Based on quantum graph theory we establish that the ray-splitting trace
formula proposed by Couchman {\it et al.} (Phys. Rev. A {\bf 46}, 6193 (1992))
is exact for a class of one-dimensional ray-splitting systems. Important
applications in combinatorics are suggested.


title:
A PT Symmetric QES Partner to the Khare Mandal Potential With Real Eigen
  Values

abstract:
  We consider a PT Symmetric Partner to Khare Mandal's recently proposed
non-Hermitian potential with complex eigen values. Our potential is
Quasi-Exactly solvable and is shown to possess only real eigen values.


title:
Formal and Precise Derivation of the Green Functions for a Simple
  Potential

abstract:
  In formal scattering theory, Green functions are obtained as solutions of a
distributional equation. In this paper, we use the Sturm-Liouville theory to
compute Green functions within a rigorous mathematical theory. We shall show
that both the Sturm-Liouville theory and the formal treatment yield the same
Green functions. We shall also show how the analyticity of the Green functions
as functions of the energy keeps track of the so-called ``incoming'' and
``outgoing'' boundary conditions.


title: Line shape narrowing in carbon dioxide at high pressures

abstract:
  The description of the narrowing effect at high pressures is demonstrated on
the example of CO2-He absorption for Q-, P-, and R-branches and for the head of
the R-branch. The problem is focused on the physical meaning of this phenomenon
that should be associated with the angular and translation momentum transfer to
matter from the photon absorbed. The effect is described in the approximation
of the single line without the conventional line mixing. A narrowing function
is introduced that links the absorption in the resonance region with the one in
far wings. This function enlarges the absorption of a single line approximately
in two times in the resonance region at high pressures and decreases the one
approximately in 20 times in far wings in comparison with the Lorentzian,
independently of the type of molecule and pressures. The halfwidth of a single
line is assumed to have a nonlinear pressure dependence and approaches to a
saturated value at high pressures.


title: A delayed-choice thought-experiment with later-time entanglement

abstract:
  It is possible to find the nonlocality type of correlations between particle
pairs retrospectively, matched with the outcomes of a future entangling
measurement. But this does not imply nonlocality in subensembles of product
pairs, nor does it imply an influence propagating backwards in time.


title:
Semiclassical Explanation of the Matteucci-Pozzi and Aharonov-Bohm Phase
  Shifts

abstract:
  Classical electromagnetic forces can account for the experimentally observed
phase shifts seen in an electron interference pattern when a line of electric
dipoles or a line of magnetic dipoles (a solenoid) is placed between the
electron beams forming the interference pattern.


title: Teleportation of rotations and receiver-encoded secret sharing

abstract:
  We show how an arbitrary qubit rotation can be teleported, albeit
probabilistically, using 1 e-bit of entanglement and one classical bit. We use
this to present a scheme for implementing quantum secret sharing. The scheme
operates essentially by sending a "secret" rotated qubit of information to
several users, who need to cooperate in order to recover the original qubit.


title: Supercatalysis

abstract:
  We show that entanglement-assisted transformations of bipartite entangled
states can be more efficient than catalysis [D. Jonathan and M. B. Plenio,
Phys. Rev. Lett. 83, 3566 (1999)}, i.e., given two incomparable bipartite
states not only can the transformation be enabled by performing collective
operations with an auxiliary entangled state, but the entanglement of the
auxiliary state itself can be enhanced. We refer to this phenomenon as
supercatalysis. We provide results on the properties of supercatalysis and its
relationship with catalysis. In particular, we obtain a useful necessary and
sufficient condition for catalysis, provide several sufficient conditions for
supercatalysis and study the extent to which entanglement of the auxiliary
state can be enhanced via supercatalysis.


title: Some Good Error-Correcting Codes from Algebraic-Geometric Codes

abstract:
  Algebraic-geometric codes on Garcia-Stichtenoth family of curves are used to
construct the asymptotically good quantum codes.


title: A New Laser Cooling Concept for Molecular Translational Motion

abstract:
  We propose a laser cooling concept for the translational motion of molecules
which does not require repeated spontaneous emission by each molecule. The
cooling works by repetition of three main steps: velocity selection of a narrow
momentum width, deceleration of velocity selected molecules and accumulation of
the decelerated molecules by an irreversible process, namely by single
spontaneous emission. We develop a cooling model which enables analytical
description of the transient populations and entropies for the total molecular
system, the center of mass degree of freedom and the internal degrees of
freedom. Simulation shows that the cooling process can reduce a large momentum
width to a final width which in principle can be arbitrarily small. Center of
mass entropy is reduced while the internal entropy is increased after cooling.
We show that translational cooling can occur during coherent laser
interactions. The entropies change in consistency with the Araki-Lieb
inequality.


title:
Quantum versus classical descriptions of sub-Poissonian light generation
  in three-wave mixing

abstract:
  Sub-Poissonian light generation in the non-degenerate three-wave mixing is
studied numerically and analytically within quantum and classical approaches.
Husimi Q-functions and their classical trajectory simulations are analysed to
reveal a special regime corresponding to the time-stable sub-Poissonian
photocount statistics of the sum-frequency mode. Conditions for observation of
this regime are discussed. Theoretical predictions of the Fano factor and
explanation of the extraordinary stabilization of the sub-Poissonian photocount
behavior are obtained analytically by applying the classical trajectories.
Scaling laws for the maximum sub-Poissonian behavior are found. Noise
suppression levels in the non-degenerate vs degenerate three-wave mixing are
discussed on different time scales compared to the revival times. It is shown
that the non-degenerate conversion offers much better stabilization of the
suppressed noise in comparison to that of degenerate process.


title:
Comment on "Experimental observation of the topological structure of
  exceptional points" [Phys.Rev.Lett. 86, 787 (2001]

abstract:
  It is shown that the two experiments Dembowski et al., PRL 86, 787 (2001),
and Lauber et al., PRL 72, 1004 (1994), prove the same topological singularity.
The phase changes found in both experiments are related to a second order
branch point in the complex plane.


title: The Quantum Entanglement of Binary and Bipolar Sequences

abstract:
  Classification of different forms of quantum entanglement is an active area
of research, central to development of effective quantum computers, and similar
to classification of error-correction codes, where code duality is broadened to
equivalence under all 'local' unitary transforms. We explore links between
entanglement, coding theory, and sequence design, by examining multi-spectra of
quantum states under local unitary action, and show that optimal
error-correcting codes and sequences represent states with high multiparticle
entanglement.


title:
Wehrl information entropy and phase distributions of Schrodinger cat and
  cat-like states

abstract:
  The Wehrl information entropy and its phase density, the so-called Wehrl
phase distribution, are applied to describe Schr\"odinger cat and cat-like
(kitten) states. The advantages of the Wehrl phase distribution over the Wehrl
entropy in a description of the superposition principle are presented. The
entropic measures are compared with a conventional phase distribution from the
Husimi Q-function. Compact-form formulae for the entropic measures are found
for superpositions of well-separated states. Examples of Schr\"odinger cats
(including even, odd and Yurke-Stoler coherent states), as well as the cat-like
states generated in Kerr medium are analyzed in detail. It is shown that, in
contrast to the Wehrl entropy, the Wehrl phase distribution properly
distinguishes between different superpositions of unequally-weighted states in
respect to their number and phase-space configuration.


title: A fidelity measure for quantum channels

abstract:
  We propose a fidelity measure for quantum channels in a straightforward
analogy to the corresponding mixed-state fidelity of Jozsa. We describe
properties of this fidelity measure and discuss some applications of it to
quantum information science.


title: J-matrix method and Bargmann potentials

abstract:
  By applying the J-matrix method [1] to neutral particles scattering we have
discovered that there is a one-to-one correspondence between the nonlocal
separable potential with the Laguerre form factors and a Bargmann potential.
Thus this discrete approach to direct and inverse scattering problem can be
considered as a tool of the S-matrix rational parametrization. As an
application, the Bargmann potentials, phase-equivalent to the np $^1S_0$
Yamaguchi potential [7] and to the np potential from inverse scattering in the
J-matrix approach [6] have been obtained.


title: Remote control of restricted sets of operations: Teleportation of Angles

abstract:
  We study the remote implementation of a unitary transformation on a qubit. We
show the existence of non-trivial protocols (i.e., using less resources than
bidirectional state teleportation) which allow the perfect remote
implementation of certain continuous sets of quantum operations. We prove that,
up to a local change of basis, only two subsets exist that can be implemented
remotely with a non-trivial protocol: Arbitrary rotations around a fixed
direction $\vec{n}$ and rotations by a fixed angle around an arbitrary
direction lying in a plane orthogonal to $\vec{n}$. The overall classical
information and distributed entanglement cost required for the remote
implementation depends on whether it is a priori known to which of the two
teleportable subsets the transformation belongs to. If it is so, the optimal
protocol consumes one e-bit of entanglement and one c-bit in each direction. If
the subset is not known, two e-bits of entanglement need to be consumed while
the classical channel becomes asymmetric, two c-bits are conveyed from Alice to
Bob but only one from Bob to Alice.


title:
New Invariants and Separability criterion of the Mixed States: Bipartite
  Case

abstract:
  We introduce algebraic sets in the complex projective spaces for the mixed
states in bipartite quantum systems as their invariants under local unitary
operations. The algebraic sets of the mixed state have to be the union of the
linear subspaces if the mixed state is separable. Some examples are given and
studied based on our criterion


title:
New Invariants and Separability Criterion of the Mixed States:
  Multipartite Case

abstract:
  We introduce algebraic sets in the products of complex projective spaces for
the mixed states in multipartite quantum systems as their invariants under
local unitary operations. The algebraic sets have to be the union of the linear
subspaces if the state is separable. Some examples are studied based on our
criterion


title:
A universal cloner allowing the input to be arbitrary states in
  symmetric subspace

abstract:
  A generalized universal quantum cloning machine is proposed which allows the
input to be arbitrary states in symmetric subspace. And it reduces to the
universal quantum cloning machine (UQCM) if the input are identical pure
states. The generalized cloner is optimal in the sense we compare the input and
output reduced density operators at a single qubit. The result for qubits is
extended to arbitrary-dimensional states.


title: Covariant quantum measurements may not be optimal

abstract:
  Quantum particles, such as spins, can be used for communicating spatial
directions to observers who share no common coordinate frame. We show that if
the emitter's signals are the orbit of a group, then the optimal detection
method may not be a covariant measurement (contrary to widespread belief). It
may be advantageous for the receiver to use a different group and an indirect
estimation method: first, an ordinary measurement supplies redundant numerical
parameters; the latter are then used for a nonlinear optimal identification of
the signal.


title:
Supersymmetric approach for generating quasi-exactly solvable potentials
  with arbitrary two known eigenstates

abstract:
  Using supersymmetric quantum mechanics we construct the quasi-exactly
solvable (QES) potentials with arbitrary two known eigenstates. The QES
potential and the wave functions of the two energy levels are expressed by some
generating function the properties of which determine the state numbers of
these levels. Choosing different generating functions we present a few explicit
examples of the QES potentials.


title: Alternative Hamiltonian Desciptions and Statistical Mechanics

abstract:
  We argue here that, as it happens in Classical and Quantum Mechanics, where
it has been proven that alternative Hamiltonian descriptions can be compatible
with a given set of equations of motion, the same holds true in the realm of
Statistical Mechanics, i.e. that alternative Hamiltonian descriptions do lead
to the same thermodynamical description of any physical system.


title: The New Interpretation of Quantum Mechanics and Hidden Parameters

abstract:
  The new interpretation of Quantum Mechanics is based on a complex probability
theory. An interpretation postulate specifies events which can be observed and
it follows that the complex probability of such event is, in fact, a real
positive number. The two-slit experiment, the mathematical formulation of the
complex probability theory, the density matrix, Born's law and a possibility of
hidden variables are discussed.


title: Double entanglement and quantum cryptography

abstract:
  We propose a quantum transmission based on bi-photons which are
doubly-entangled both in polarisation and phase. This scheme finds a natural
application in quantum cryptography, where we show that an eventual
eavesdropper is bound to introduce a larger error on the quantum communication
than for a single entangled bi-photon communication, when steeling the same
information.


title: Discrimination of the Bell states of qudits by means of linear optics

abstract:
  The question of the discrimination of the Bell states of two qudits (i.e.,
d-dimensional quantum systems) by means of passive linear optical elements and
conditional measurements is discussed. A qudit is supposed to be represented by
d optical modes containing exactly one photon altogether. From recent results
of Calsamiglia it follows that there is no way how to distinguish the Bell
states of two qudits for d>2 - not even with the probability of success lower
than one - without any auxiliary photons in ancillary modes. Following the
results of Carollo and Palma it is proved that it is impossible to distinguish
even only one such a Bell state with certainty (i.e., with the probability of
success equal to one), irrespective of how many auxiliary photons are involved.
However, it is shown that auxiliary photons can help to discriminate the Bell
states of qudits with the high probability of success: A Bell-state analyzer
based on the idea of linear optics quantum computation that can achieve the
probability of success arbitrarily close to one is described. It requires many
auxiliary photons that must be first "combined" into entangled states.


title: Deterministic entanglement concentration

abstract:
  Deterministic extraction of Bell pairs from a finite number of partially
entangled pairs is discussed. We derive the maximum number of Bell pairs that
can be obtained with probability 1 by local operations and classical
communication. It is proved that the optimal deterministic concentration needs
only a two-pair collective manipulation in each step, and that a collective
manipulation of all entangled pairs is not necessary. Finally, this scheme
reveals an entanglement measure for the deterministic concentration.


title: Restoration of Entanglement by Spectral Filters

abstract:
  We experimentally demonstrate that entanglement of bi-photon polarization
state can be restored by spectral filters. This restoration procedure can be
viewed as a new class of quantum eraser, which retrieves entanglement rather
than just interference by manipulating an ancillary degree of freedom.


title: The quantum phase problem: steps toward a resolution

abstract:
  Defining the observable ${\bf \phi}$ canonically conjugate to the number
observable ${\bf N}$ has long been an open problem in quantum theory. The
problem stems from the fact that ${\bf N}$ is bounded from below. In a previous
work we have shown how to define the absolute phase observable ${\bf
\Phi}\equiv |{\bf\phi}|$ by suitably restricting the Hilbert space of $x$ and
$p$ like variables. Here we show that also from the classical point of view,
there is no rigorous definition for the phase even though it's absolute value
is well defined.


title:
A Topos Perspective on the Kochen-Specker Theorem: IV. Interval
  Valuations

abstract:
  We extend the topos-theoretic treatment given in previous papers of assigning
values to quantities in quantum theory. In those papers, the main idea was to
assign a sieve as a partial and contextual truth value to a proposition that
the value of a quantity lies in a certain set $\Delta \subseteq \mathR$. Here
we relate such sieve-valued valuations to valuations that assign to quantities
subsets, rather than single elements, of their spectra (we call these
`interval' valuations). There are two main results. First, there is a natural
correspondence between these two kinds of valuation, which uses the notion of a
state's support for a quantity (Section 3). Second, if one starts with a more
general notion of interval valuation, one sees that our interval valuations
based on the notion of support (and correspondingly, our sieve-valued
valuations) are a simple way to secure certain natural properties of
valuations, such as monotonicity (Section 4).


title: Multi Mode Interferometer for Guided Matter Waves

abstract:
  We describe the fundamental features of an interferometer for guided matter
waves based on Y-beam splitters and show that, in a quasi two-dimensional
regime, such a device exhibits high contrast fringes even in a multi mode
regime and fed from a thermal source.


title: PPLN Waveguide for Quantum Communication

abstract:
  We report on energy-time and time-bin entangled photon-pair sources based on
a periodically poled lithium niobate (PPLN) waveguide. Degenerate twin photons
at 1314 nm wavelength are created by spontaneous parametric down-conversion and
coupled into standard telecom fibers. Our PPLN waveguide features a very high
conversion efficiency of about 10^(-6), roughly 4 orders of magnitude more than
that obtained employing bulk crystals. Even if using low power laser diodes,
this engenders a significant probability for creating two pairs at a time - an
important advantage for some quantum communication protocols. We point out a
simple means to characterize the pair creation probability in case of a pulsed
pump. To investigate the quality of the entangled states, we perform
photon-pair interference experiments, leading to visibilities of 97% for the
case of energy-time entanglement and of 84% for the case of time-bin
entanglement. Although the last figure must still be improved, these tests
demonstrate the high potential of PPLN waveguide based sources to become a key
element for future quantum communication schemes


title:
Coherent population trapping in two-electron three-level systems with
  aligned spins

abstract:
  The possibility of coherent population trapping in two electron states with
aligned spins (ortho-system) is evidenced. From the analysis of a three-level
atomic system containing two electrons, and driven by the two laser fields
needed for coherent population trapping, a conceptually new kind of
two-electron dark state appears. The properties of this trapping are studied
and are physically interpreted in terms of a dark hole, instead of a dark
two-electron state. This technique, among many other applications, offers the
possibility of measuring, with subnatural resolution, some superposition-state
matrix-elements of the electron-electron correlation that due to their time
dependent nature are inaccesible by standard measuring procedures.


title: A Quantum solution to the Byzantine agreement problem

abstract:
  We present a solution to an old and timely problem in distributed computing.
Like Quantum Key Distribution (QKD), quantum channels make it possible to
achieve taks classically impossible. However, unlike QKD, here the goal is not
secrecy but agreement, and the adversary is not outside but inside the game,
and the resources require qutrits.


title: From Geometry to Quantum Computation

abstract:
  The aim of this paper is to introduce our idea of Holonomic Quantum
Computation (Computer). Our model is based on both harmonic oscillators and
non-linear quantum optics, not on spins of usual quantum computation and our
method is moreover completely geometrical. We hope that therefore our model may
be strong for decoherence.


title: Algebraic geometric construction of a quantum stabilizer code

abstract:
  The stabilizer code is the most general algebraic construction of quantum
error-correcting codes proposed so far. A stabilizer code can be constructed
from a self-orthogonal subspace of a symplectic space over a finite field. We
propose a construction method of such a self-orthogonal space using an
algebraic curve. By using the proposed method we construct an asymptotically
good sequence of binary stabilizer codes. As a byproduct we improve the
Ashikhmin-Litsyn-Tsfasman bound of quantum codes. The main results in this
paper can be understood without knowledge of quantum mechanics.


title: Security of quantum key distribution using d-level systems

abstract:
  We consider two quantum cryptographic schemes relying on encoding the key
into qudits, i.e. quantum states in a d-dimensional Hilbert space. The first
cryptosystem uses two mutually unbiased bases (thereby extending the BB84
scheme), while the second exploits all the d+1 available such bases (extending
the six-state protocol for qubits). We derive the information gained by a
potential eavesdropper applying a cloning-based individual attack, along with
an upper bound on the error rate that ensures unconditional security against
coherent attacks.


title: Separability of Two-Party Gaussian States

abstract:
  We investigate the separability properties of quantum two-party Gaussian
states in the framework of the operator formalism for the density operator.
Such states arise as natural generalizations of the entangled state originally
introduced by Einstein, Podolsky, and Rosen. We present explicit forms of
separable and nonseparable Gaussian states.


title:
Teleportation as a Depolarizing Quantum Channel, Relative Entropy and
  Classical Capacity

abstract:
  We show that standard teleportation with an arbitrary mixed state resource is
equivalent to a generalized depolarizing channel with probabilities given by
the maximally entangled components of the resource. This enables the usage of
any quantum channel as a generalized depolarizing channel without additional
twirling operations. It also provides a nontrivial upper bound on the
entanglement of a class of mixed states. Our result allows a consistent and
statistically motivated quantification of teleportation success in terms of the
relative entropy and this quantification can be related to a classical
capacity.


title: Dynamics with unitary phase operator:implications for Wigner's problem

abstract:
  We show that for general deformations of SU(2) algebra, the dynamics in terms
of ladder operators is preserved. This is done for a system of precessing
magnetic dipole in magnetic field, using the unitary phase operator which
arises in the polar decomposition of SU(2) operators. It is pointed out that
there is a single phase operator dynamics underlying the dynamics of usual and
deformed ladder operators.


title: A fresh look at 3D microwave ionization curves of hydrogen Rydberg atoms

abstract:
  Analytical arguments and numerical simulations suggest that the shapes of 3D
microwave ionization curves measured by Koch and collaborators (see P. M. Koch
and K. A. H. van Leeuwen, Phys. Rep. {\bf 255}, 289 (1995)) depend only weakly
on the angular momentum of the atoms in the initial microcanonical ensemble,
but strongly on the principal quantum number and the magnetic quantum number.
Based on this insight, coupled with the computational power of a high-end
60-node Beowulf PC cluster, we present the first 3D quantum calculations of
microwave ionization curves in the experimentally relevant parameter regime.


title:
Interference of probabilities and number field structure of quantum
  models

abstract:
  We study the probabilistic consequences of the choice of the basic number
field in quantum formalism. We demonstrate that by choosing a number field for
a linear space representation of quantum model it is possible to describe
various interference phenomena. We analyse interference of probabilistic
alternatives induced by real, complex, hyperbolic (Clifford) and p-adic
representations.


title: Quantum Logic for Trapped Atoms via Molecular Hyperfine Interactions

abstract:
  We study the deterministic entanglement of a pair of neutral atoms trapped in
an optical lattice by coupling to excited-state molecular hyperfine potentials.
Information can be encoded in the ground-state hyperfine levels and processed
by bringing atoms together pair-wise to perform quantum logical operations
through induced electric dipole-dipole interactions. The possibility of
executing both diagonal and exchange type entangling gates is demonstrated for
two three-level atoms and a figure of merit is derived for the fidelity of
entanglement. The fidelity for executing a CPHASE gate is calculated for two
87Rb atoms, including hyperfine structure and finite atomic localization. The
main source of decoherence is spontaneous emission, which can be minimized for
interaction times fast compared to the scattering rate and for sufficiently
separated atomic wavepackets. Additionally, coherent couplings to states
outside the logical basis can be constrained by the state dependent trapping
potential.


title:
Some Consequences of the Law of Local Energy Conservation in
  Electromagnetic field

abstract:
  At electromagnetic interactions of particles there arises defect of masses,
i.e. the energy is liberated since the particles of the different charges are
attracted. It is shown that this change of the effective mass of a particle in
the external electrical field (of a nucleus) results in displacement of atomic
levels of electrons. The expressions describing these velocity changes and
displacement of energy levels of electrons in the atom are obtained.


title: Quantum limits of cold damping with optomechanical coupling

abstract:
  Thermal noise of a mirror can be reduced by cold damping. The displacement is
measured with a high-finesse cavity and controlled with the radiation pressure
of a modulated light beam. We establish the general quantum limits of noise in
cold damping mechanisms and we show that the optomechanical system allows to
reach these limits. Displacement noise can be arbitrarily reduced in a narrow
frequency band. In a wide-band analysis we show that thermal fluctuations are
reduced as with classical damping whereas quantum zero-point fluctuations are
left unchanged. The only limit of cold damping is then due to zero-point energy
of the mirror


title: Master Equation for Retrodiction of Quantum Communication Signals

abstract:
  We derive the master equation that governs the evolution of the measured
state backwards in time in an open system. This allows us to determine
probabilities for a given set of preparation events from the results of
subsequent measurements, which has particular relevance to quantum
communication.


title: Positioning and clock synchronization through entanglement

abstract:
  A method is proposed to employ entangled and squeezed light for determining
the position of a party and for synchronizing distant clocks. An accuracy gain
over analogous protocols that employ classical resources is demonstrated and a
quantum-cryptographic positioning application is given, which allows only
trusted parties to learn the position of whatever must be localized. The
presence of a lossy channel and imperfect photodetection is considered. The
advantages in using partially entangled states is discussed.


title:
Electrical control of superposed quantum states evolution in quantum dot
  molecule by pulsed field

abstract:
  Quantum computing (or generally, quantum information processing) is of prime
interest for it potentially has a significant impact on present electronics and
computations1-5. Essence of quantum computing is a direct usage of the
superposition and entanglement of quantum mechanical states that are pronounced
in nanoscopic particles such as atoms and molecules6, 7. On the other hand,
many proposals regarding the realization of semiconductor quantum dot (QD)
qubits8,9 and QD quantum gates10 were reported and several experimental clues
were successfully found11-16. While these pioneering experiments opened up the
basis of semiconductor QD quantum computing, direct electrical control of
superposed states in time domain17 has not been realized yet. Here, we
demonstrate the coherent control of the superposed quantum states evolution in
the QD molecule. Short electrical pulses are shown to inject single electron
into the QD molecule and the current collected at the substrate exhibits
oscillations as a function of the pulse width. The oscillations are originated
from different decay rates of the symmetric (S) and the anti-symmetric (AS)
state of the QD molecule and the evolution of the occupation probabilities
controlled by the injection pulse width


title: Raman subrecoil spectroscopy of cold cesium atoms

abstract:
  We describe and characterize a setup for subrecoil stimulated Raman
spectroscopy of cold cesium atoms. We study in particular the performances of a
method designed to active control and stabilization of the magnetic fields
across a cold-atom cloud inside a small vacuum cell. The performance of the
setup is monitored by {\em copropagative-beam} stimulated Raman spectroscopy of
a cold cesium sample. The root mean-square value of the residual magnetic field
is 300 $\mu G$, with a compensation bandwidth of 500 Hz. The shape of the
observed spectra is theoretically interpreted and compares very well to
numerically generated spectra.


title:
Remote operations and interactions for systems of arbitrary dimensional
  Hilbert space: a state-operator approach

abstract:
  We present a systematic simple method for constructing deterministic remote
operations on single and multiple systems of arbitrary discrete dimensionality.
These operations include remote rotations, remote interactions and
measurements. The resources needed for an operation on a two-level system are
one ebit and a bidirectional communication of two cbits, and for an n-level
system, a pair of entangled n-level particles and two classical ``nits''. In
the latter case, there are $n-1$ possible distinct operations per one n-level
entangled pair. Similar results apply for generating interaction between a pair
of remote systems and for remote measurements. We further consider remote
operations on $N$ spatially distributed systems, and show that the number of
possible distinct operations increases here exponentially, with the available
number of entangled pairs that are initial distributed between the systems. Our
results follow from the properties of a hybrid state-operator object
(``stator''), which describes quantum correlations between states and
operations.


title: Everett and Structure

abstract:
  I address the problem of indefiniteness in quantum mechanics: the problem
that the theory, without changes to its formalism, seems to predict that
macroscopic quantities have no definite values. The Everett interpretation is
often criticised along these lines and I shall argue that much of this
criticism rests on a false dichotomy: that the macroworld must either be
written directly into the formalism or be regarded as somehow illusory. By
means of analogy with other areas of physics, I develop the view that the
macroworld is instead to be understood in terms of certain structures and
patterns which emerge from quantum theory (given appropriate dynamics, in
particular decoherence). I extend this view to the observer, and in doing so
make contact with functionalist theories of mind.


title: Preparation of polarization entangled mixed states of two photons

abstract:
  We propose a scheme for preparing arbitrary two photons polarization
entangled mixed states via controlled location decoherence. The scheme uses
only linear optical devices and single-mode optical fibers, and may be feasible
in experiment within current optical technology.


title:
Bell's theorem with and without inequalities for the three-qubit
  Greenberger-Horne-Zeilinger and W states

abstract:
  A proof of Bell's theorem without inequalities valid for both inequivalent
classes of three-qubit entangled states under local operations assisted by
classical communication, namely Greenberger-Horne-Zeilinger (GHZ) and W, is
described. This proof leads to a Bell inequality that allows more conclusive
tests of Bell's theorem for three-qubit systems. Another Bell inequality
involving both tri- and bipartite correlations is introduced which illustrates
the different violations of local realism exhibited by the GHZ and W states.


title: Concurrence in arbitrary dimensions

abstract:
  We argue that a complete characterisation of quantum correlations in
bipartite systems of many dimensions may require a quantity which, even for
pure states, does not reduce to a single number. Subsequently, we introduce
multi-dimensional generalizations of concurrence and find evidence that they
may provide useful tools for the analysis of quantum correlations in mixed
bipartite states. We also introudce {\it biconcurrence} that leads to a
necessary and sufficient condition for separability.


title: Conditional beam splitting attack on quantum key distribution

abstract:
  We present a novel attack on quantum key distribution based on the idea of
adaptive absorption [calsam01]. The conditional beam splitting attack is shown
to be much more efficient than the conventional beam spitting attack, achieving
a performance similar to the, powerful but currently unfeasible, photon number
splitting attack. The implementation of the conditional beam splitting attack,
based solely on linear optical elements, is well within reach of current
technology.


title: Exact uncertainty relations: physical significance

abstract:
  The Heisenberg inequality \Delta X \Delta P \geq \hbar/2 can be replaced by
an exact equality, for suitably chosen measures of position and momentum
uncertainty, which is valid for all wavefunctions. The statistics of
complementary observables are thus connected by an ``exact'' uncertainty
relation.


title:
Intermolecular energy transfer in the presence of dispersing and
  absorbing media

abstract:
  By making use of the Green function concept of quantization of the
electromagnetic field in Kramers--Kronig consistent media, a rigorous quantum
mechanical derivation of the rate of intermolecular energy transfer in the
presence of arbitrarily shaped, dispersing, and absorbing material bodies is
given. Applications to bulk material, multi-slab planar structures, and
microspheres are studied. It is shown that when the two molecules are near a
planar interface, then surface-guided waves can strongly affect the energy
transfer and essentially modify both the (F\"{o}rster) short-range $R^{-6}$
dependence of the transfer rate and the long-range $R^{-2}$ dependence, which
are typically observed in free space. In particular, enhancement (inhibition)
of energy transfer can be accompanied by inhibition (enhancement) of donor
decay. Results for four- and five-layered planar structures are given and
compared with experimental results. Finally, the energy transfer between two
molecules located at diametrically opposite positions outside a microsphere is
briefly discussed.


title: Whose Knowledge?

abstract:
  Sir Rudolph Peierls, in a reply to John Bell's last critique of the state of
our understanding of quantum mechanics, maintained that it is easy to give an
acceptable account of the physical significance of the quantum theory. The key
is to recognize that all the density matrix characterizing a physical system
ever represents is knowledge about that system. In answer to Bell's implicit
rejoinder "Whose knowledge?" Peierls offered two simple consistency conditions
that must be satisfied by density matrices that convey the knowledge different
people might have about one and the same physical system: their density
matrices must commute and must have a non-zero product. I describe a simple
counterexample to his first condition, but show that his second condition,
which holds trivially if the first does, continues to be valid in its absence.
It is an open question whether any other conditions must be imposed.


title: Total Absorption in Finite Time in an $i\delta$ Potential

abstract:
  We consider the evolution of Green's function of the one-dimensional
Schr\"odinger equation in the presence of the complex potential $-ik\delta(x)$.
Our result is the construction of an explicit time-dependent solution which we
use to calculate the time-dependent survival probability of a quantum particle.
The survival probability decays to zero in finite time, which means that the
complex delta potential well is a total absorber for quantum particles. This
potential can be interpreted as a killing measure with infinite killing rate
concentrated at the origin.


title: Martingale Models for Quantum State Reduction

abstract:
  Stochastic models for quantum state reduction give rise to statistical laws
that are in most respects in agreement with those of quantum measurement
theory. Here we examine the correspondence of the two theories in detail,
making a systematic use of the methods of martingale theory. An analysis is
carried out to determine the magnitude of the fluctuations experienced by the
expectation of the observable during the course of the reduction process and an
upper bound is established for the ensemble average of the greatest
fluctuations incurred. We consider the general projection postulate of L\"uders
applicable in the case of a possibly degenerate eigenvalue spectrum, and derive
this result rigorously from the underlying stochastic dynamics for state
reduction in the case of both a pure and a mixed initial state. We also analyse
the associated Lindblad equation for the evolution of the density matrix, and
obtain an exact time-dependent solution for the state reduction that explicitly
exhibits the transition from a general initial density matrix to the L\"uders
density matrix. Finally, we apply Girsanov's theorem to derive a set of simple
formulae for the dynamics of the state in terms of a family of geometric
Brownian motions, thereby constructing an explicit unravelling of the Lindblad
equation.


title: A note on bound entanglement and local realism

abstract:
  We show using a numerical approach that gives necessary and sufficient
conditions for the existence of local realism, that the bound entangled state
presented in Bennett et. al. Phys. Rev. Lett. 82, 5385 (1999) admits a local
and realistic description. We also find the lowest possible amount of some
appropriate entangled state that must be ad-mixed to the bound entangled state
so that the resulting density operator has no local and realistic description
and as such can be useful in quantum communication and quantum computation.


title: On the geometry of entangled states

abstract:
  The basic question that is addressed in this paper is finding the closest
separable state for a given entangled state, measured with the Hilbert Schmidt
distance. While this problem is in general very hard, we show that the
following strongly related problem can be solved: find the Hilbert Schmidt
distance of an entangled state to the set of all partially transposed states.
We prove that this latter distance can be expressed as a function of the
negative eigenvalues of the partial transpose of the entangled state, and show
how it is related to the distance of a state to the set of positive partially
transposed states (PPT-states). We illustrate this by calculating the closest
biseparable state to the W-state, and give a simple and very general proof for
the fact that the set of W-type states is not of measure zero. Next we show
that all surfaces with states whose partial transposes have constant minimal
negative eigenvalue are similar to the boundary of PPT states. We illustrate
this with some examples on bipartite qubit states, where contours of constant
negativity are plotted on two-dimensional intersections of the complete state
space.


title: Photonic Entanglement for Fundamental Tests and Quantum Communication

abstract:
  Entanglement is at the heart of fundamental tests of quantum mechanics like
tests of Bell-inequalities and, as discovered lately, of quantum computation
and communication. Their technological advance made entangled photons play an
outstanding role in entanglement physics. We give a generalized concept of
qubit entanglement and review the state of the art of photonic experiments.


title: Franson-type experiment realizes two-qubit quantum logic gate

abstract:
  Quantum computers promise great improvements in solving problems such as
factoring large integers, simulating quantum systems, and database searching.
Using a photon as a quantum bit (qubit) is one of the most promising ways to
realize a universal quantum computer because the coherent superposition state
of a photon is very robust against various sources of decoherence. However, it
is too difficult to realize two-qubit (photon) gates because it requires huge
nonlinearity between photons. Here we show the realization of a controlled-NOT
(CNOT) gate, the most important and elemental two-qubit gate for quantum
computation, by extending our previous research. The heart of our experiment is
the conditional measurement of two-photon coincidences in the Franson-type
experiment[7]. The photon counting measurement plays the same role as the
nonlinearity required for the two-qubit gate, and our system reproduces the
truth table of the CNOT gate. Furthermore, we create an entangled state from
the superposition state by our gate, which is clear evidence that our gate
works as a quantum logic gate. Our results make it possible to manipulate the
quantum state of photons including entanglement and represent significant
progress in the operation of various algorithms in quantum computation.


title: Two theories of decoherence

abstract:
  Theories of decoherence come in two flavors---Platonic and Aristotelian.
Platonists grant ontological primacy to the concepts and mathematical symbols
by which we describe or comprehend the physical world. Aristotelians grant it
to the physical world. The significance one attaches to the phenomenon of
decoherence depends on the school to which one belongs. The debate about the
significance of quantum states has for the most part been carried on between
Platonists and Kantians, who advocate an epistemic interpretation, with
Aristotelians caught in the crossfire. For the latter, quantum states are
neither states of Nature nor states of knowledge. The real issue is not the
kind of reality that we should attribute to quantum states but the reality of
the spatial and temporal distinctions that we make. Once this is recognized,
the necessity of attributing ontological primacy to facts becomes obvious, the
Platonic stance becomes inconsistent, and the Kantian point of view becomes
unnecessarily restrictive and unilluminating.


title:
Diffusion Resonances in Action Space for an Atom Optics Kicked Rotor
  with Decoherence

abstract:
  We numerically investigate momentum diffusion rates for the pulse kicked
rotor across the quantum to classical transition as the dynamics are made more
macroscopic by increasing the total system action. For initial and late time
rates we observe an enhanced diffusion peak which shifts and scales with
changing kick strength, and we also observe distinctive peaks around quantum
resonances. Our investigations take place in the context of a system of
ultracold atoms which is coupled to its environment via spontaneous emission
decoherence, and the effects should be realisable in ongoing experiments.


title: Quantum walks in higher dimensions

abstract:
  We analyze the quantum walk in higher spatial dimensions and compare
classical and quantum spreading as a function of time. Tensor products of
Hadamard transformations and the discrete Fourier transform arise as natural
extensions of the quantum coin toss in the one-dimensional walk simulation, and
other illustrative transformations are also investigated. We find that
entanglement between the dimensions serves to reduce the rate of spread of the
quantum walk. The classical limit is obtained by introducing a random phase
variable.


title: Decoherence-induced wave packet splitting

abstract:
  We provide an intuitive interpretation of the optical Stern-Gerlach effect
(OSGE) in the dressed-state point of view. We also analyze the effect of atomic
damping in an experiment on the OSGE. We show that the atomic damping also
causes the wave packet splitting, in a non-mechanical fashion, as opposed to
the coherent process that is mechanical.


title: Giant light shift of atoms near optical microstructures

abstract:
  Atoms coupled to optical fields confined in one and two spatial dimensions in
solid state microstructures can experience very large light shifts if the
driving frequencies are close to a resonance of the microstructures and an
atomic transition. Using the simple example of a quasi one-dimensional
waveguide structure we can analytically calculate the atomic AC Stark shift and
the modifications of the light field induced by the presence of the atom. A
large enhancement of the effective interaction strength is found due to a non
uniform mode density. Experimentally this should be visible by monitoring the
scattered light field as well as by the modification of the atomic trajectories
bouncing from the evanescent light.


title: Heating and decoherence suppression using decoupling techniques

abstract:
  We study the application of decoupling techniques to the case of a damped
vibrational mode of a chain of trapped ions, which can be used as a quantum bus
in linear ion trap quantum computers. We show that vibrational heating could be
efficiently suppressed using appropriate ``parity kicks''. We also show that
vibrational decoherence can be suppressed by this decoupling procedure, even
though this is generally more difficult because the rate at which the parity
kicks have to applied increases with the effective bath temperature.


title: Towards a quantum Hall effect for atoms using electric fields

abstract:
  An atomic analogue of Landau quantization based on the Aharonov-Casher (AC)
interaction is developed. The effect provides a first step towards an atomic
quantum Hall system using electric fields, which may be realized in a
Bose-Einstein condensate.


title: Effective Field Theories for the Casimir Effect at Finite Temperature

abstract:
  We discuss corrections to the Casimir effect at finite temperature and
effective field theory. Recently, it has been shown that effective field
theories can reproduce radiative corrections to the Casimir energy calculated
in full QED. We apply effective field theory methods at finite temperature and
reproduce the Casimir free energy. We show that the system undergoes
dimensional reduction at high temperature and that it can be described by an
effective three-dimensional field theory.


title: Classical simulation of noninteracting-fermion quantum circuits

abstract:
  We show that a class of quantum computations that was recently shown to be
efficiently simulatable on a classical computer by Valiant corresponds to a
physical model of noninteracting fermions in one dimension. We give an
alternative proof of his result using the language of fermions and extend the
result to noninteracting fermions with arbitrary pairwise interactions, where
gates can be conditioned on outcomes of complete von Neumann measurements in
the computational basis on other fermionic modes in the circuit. This last
result is in remarkable contrast with the case of noninteracting bosons where
universal quantum computation can be achieved by allowing gates to be
conditioned on classical bits (quant-ph/0006088).


title: Stochastic control of quantum coherence

abstract:
  The application of a random modulation of a system parameter usually
increases decoherence effects. Here we show how, employing an appropriate
stochastic modulation, it is instead possible to preserve the quantum coherence
of a system.


title: Qubit logic modeling by electronic circuits and electromagnetic signals

abstract:
  In the paper an approach is presented allowing to model quantum logic
circuits by electronic gates for discrete spatially modulated electromagnetic
signals. The designed circuitry is for modeling low scale quantum nets of
general design and quantum devices based only on superposition principle of
their work.


title:
Privacy Amplification in Quantum Key Distribution: Pointwise Bound
  versus Average Bound

abstract:
  In order to be practically useful, quantum cryptography must not only provide
a guarantee of secrecy, but it must provide this guarantee with a useful,
sufficiently large throughput value. The standard result of generalized privacy
amplification yields an upper bound only on the average value of the mutual
information available to an eavesdropper. Unfortunately this result by itself
is inadequate for cryptographic applications. A naive application of the
standard result leads one to incorrectly conclude that an acceptable upper
bound on the mutual information has been achieved. It is the pointwise value of
the bound on the mutual information, associated with the use of some specific
hash function, that corresponds to actual implementations. We provide a fully
rigorous mathematical derivation that shows how to obtain a cryptographically
acceptable upper bound on the actual, pointwise value of the mutual
information. Unlike the bound on the average mutual information, the value of
the upper bound on the pointwise mutual information and the number of bits by
which the secret key is compressed are specified by two different parameters,
and the actual realization of the bound in the pointwise case is necessarily
associated with a specific failure probability. The constraints amongst these
parameters, and the effect of their values on the system throughput, have not
been previously analyzed. We show that the necessary shortening of the key
dictated by the cryptographically correct, pointwise bound, can still produce
viable throughput rates that will be useful in practice.


title: Some bounds for quantum copying

abstract:
  We propose new optimality criterion for the estimation of state-dependent
cloning. We call this measure the relative error because the one compares the
errors in the copies with contiguous size taking into account the similarity of
states to be copied. A copying transformation and dimension of state space are
not specified. Only the unitarity of quantum mechanical transformations is
used. The presented approach is based on the notion of the angle between two
states. Firstly, several useful statements simply expressed in terms of angles
are proved. Among them there are the spherical triangle inequality and the
inequality establishing the upper bound on the modulus of difference between
probability distributions generated by two any states for an arbitrary
measurement. The tightest lower bound on the relative error is then obtained.
Hillery and Buzek originally examined an approximate state-dependent copying
and obtained the lower bound on the absolute error. We consider relationship
between the size of error and the corresponding probability distributions and
obtain the tightest lower bound on the absolute error. Thus, the proposed
approach supplements and reinforces the results obtained by Hillery and Buzek.
Finally, the basic findings of investigation for the relative error are
discussed.


title: Spatial correlations in hexagons generated via a Kerr nonlinearity

abstract:
  We consider the hexagonal pattern forming in the cross-section of an optical
beam produced by a Kerr cavity, and we study the quantum correlations
characterizing this structure. By using arguments related to the symmetry
broken by the pattern formation, we identify a complete scenario of six-mode
entanglement. Five independent phase quadratures combinations, connecting the
hexagonal modes, are shown to exhibit sub-shot-noise fluctuations. By means of
a non-linear quantum calculation technique, quantum correlations among the mode
photon numbers are demonstrated and calculated.


title:
Pseudo-Hermiticity of Hamiltonians under imaginary shift of the
  co-ordinate : real spectrum of complex potentials

abstract:
  We propose that the real spectrum and the orthogonality of the states for
several known complex potentials of both types, PT-symmetric and
non-PT-symmetric can be understood in terms of currently proposed
$\eta$-pseudo-Hermiticity (Mostafazadeh, quant-ph/0107001) of a Hamiltonian,
provided the Hermitian linear automorphism, $\eta$, is introduced as
$e^{-\theta p}$ which affects an imaginary shift of the co-ordinate :
$e^{-\theta p} x e^{\theta p} = x+i\theta$.


title: Quantum English Auctions

abstract:
  We continue the analysis of quantum-like description of markets and
economics. The approach has roots in the recently developed quantum game theory
and quantum computing. The present paper is devoted to quantum English auction
which are a special class of quantum market games. The approach allows to
calculate profit intensities for various possible strategies.


title: Perturbation theory for quantum-mechanical observables

abstract:
  The quantum-mechanical state vector is not directly observable even though it
is the fundamental variable that appears in Schrodinger's equation. In
conventional time-dependent perturbation theory, the state vector must be
calculated before the experimentally-observable expectation values of relevant
operators can be computed. We discuss an alternative form of time-dependent
perturbation theory in which the observable expectation values are calculated
directly and expressed in the form of nested commutators. This result is
consistent with the fact that the commutation relations determine the
properties of a quantum system, while the commutators often have a form that
simplifies the calculation and avoids canceling terms. The usefulness of this
method is illustrated using several problems of interest in quantum optics and
quantum information processing.


title:
Improving the Renormalization Group approach to the quantum-mechanical
  double well potential

abstract:
  The gap between ground and first excited state of the quantum-mechanical
double well is calculated using the Renormalization Group equations to the
second order in the derivative expansion, obtained within a class of proper
time regulators. Agreement with the exact results is obtained both in the
strong and weak coupling regime.


title:
Universal quantum computation using only projective measurement, quantum
  memory, and preparation of the 0 state

abstract:
  What resources are universal for quantum computation? In the standard model,
a quantum computer consists of a sequence of unitary gates acting coherently on
the qubits making up the computer. This paper shows that a very different model
involving only projective measurements, quantum memory, and the ability to
prepare the |0> state is also universal for quantum computation. In particular,
no coherent unitary dynamics are involved in the computation.


title: A comparison of the entanglement measures negativity and concurrence

abstract:
  In this paper we investigate two different entanglement measures in the case
of mixed states of two qubits. We prove that the negativity of a state can
never exceed its concurrence and is always larger then
$\sqrt{(1-C)^2+C^2}-(1-C)$ where $C$ is the concurrence of the state.
Furthermore we derive an explicit expression for the states for which the upper
or lower bound is satisfied. Finally we show that similar results hold if the
relative entropy of entanglement and the entanglement of formation are
compared.


title: Trajectories in the Context of the Quantum Newton's Law

abstract:
  In this paper, we apply the one dimensional quantum law of motion, that we
recently formulated in the context of the trajectory representation of quantum
mechanics, to the constant potential, the linear potential and the harmonic
oscillator. In the classically allowed regions, we show that to each classical
trajectory there is a family of quantum trajectories which all pass through
some points constituting nodes and belonging to the classical trajectory. We
also discuss the generalization to any potential and give a new definition for
de Broglie's wavelength in such a way as to link it with the length separating
adjacent nodes. In particular, we show how quantum trajectories have as a limit
when $\hbar \to 0$ the classical ones. In the classically forbidden regions,
the nodal structure of the trajectories is lost and the particle velocity
rapidly diverges.


title:
Local Primitive Causality and the Common Cause Principle in Quantum
  Field Theory

abstract:
  If \{A(V)\} is a net of local von Neumann algebras satisfying standard axioms
of algebraic relativistic quantum field theory and V_1 and V_2 are spacelike
separated spacetime regions, then the system (A(V_1),A(V_2),\phi) is said to
satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of
projections A \in A(V_1), B \in A(V_2) correlated in the normal state \phi
there exists a projection C belonging to a von Neumann algebra associated with
a spacetime region V contained in the union of the backward light cones of V_1
and V_2 and disjoint from both V_1 and V_2, a projection having the properties
of a Reichenbachian common cause of the correlation between A and B. It is
shown that if the net has the local primitive causality property then every
local system (A(V_1),A(V_2),\phi) with a locally normal and locally faithful
state \phi and open bounded V_1 and V_2 satisfies the Weak Reichenbach's Common
Cause Principle.


title: On the Squeezed Number States and their Phase Space Representations

abstract:
  We compute the photon number distribution, the Q distribution function and
the wave functions in the momentum and position representation for a single
mode squeezed number state using generating functions which allow to obtain any
matrix element in the squeezed number state representation from the matrix
elements in the squeezed coherent state representation. For highly squeezed
number states we discuss the previously unnoted oscillations which appear in
the Q function. We also note that these oscillations can be related to the
photon-number distribution oscillations and to the momentum representation of
the wave function.


title:
Quantum Measurement of a Single Spin using Magnetic Resonance Force
  Microscopy

abstract:
  Single-spin detection is one of the important challenges facing the
development of several new technologies, e.g. single-spin transistors and
solid-state quantum computation. Magnetic resonance force microscopy with a
cyclic adiabatic inversion, which utilizes a cantilever oscillations driven by
a single spin, is a promising technique to solve this problem. We have studied
the quantum dynamics of a single spin interacting with a quasiclassical
cantilever. It was found that in a similar fashion to the Stern-Gerlach
interferometer the quantum dynamics generates a quantum superposition of two
quasiclassical trajectories of the cantilever which are related to the two spin
projections on the direction of the effective magnetic field in the rotating
reference frame. Our results show that quantum jumps will not prevent a
single-spin measurement if the coupling between the cantilever vibrations and
the spin is small in comparison with the amplitude of the radio-frequency
external field.


title: Quantum coin flipping with arbitrary small bias is impossible

abstract:
  Lo and Chau showed that an ideal quantum coin flipping protocol is
impossible. The proof was simply derived from the impossibility proof of
quantum bit commitment. However, the proof still leaves the possibility of a
quantum coin flipping protocol with arbitrary small bias.
  In this paper, we show that a quantum coin flipping protocol with arbitrary
small bias is impossible and show the lower bound of the bias of quantum coin
flipping protocol.


title: Atomic scattering from Bose-Einstein condensates

abstract:
  Elastic scattering probes directly the interaction potential. For weakly
interacting condensates this potential is given by the condensate density. We
investigate how the differential and total cross sections reflect the density.
In particular, we have determined which signatures the Thomas Fermi
approximation leaves in contrast to an exact solution for the condensate wave
function within the Gross-Pitaevskii theory.


title: Simple trace criterion for classification of multilayers

abstract:
  The action of any lossless multilayer is described by a transfer matrix that
can be factorized in terms of three basic matrices. We introduce a simple trace
criterion that classifies multilayers in three classes with properties closely
related with one (and only one) of these three basic matrices.


title: Distillability, Bell inequalities and multiparticle bound entanglement

abstract:
  We study the relation between violation of Bell inequalities and
distillability properties of quantum states. Recently, D\"ur has shown that
there are some multiparticle bound entangled states, non-separable and
non-distillable, that violate a Bell inequality. We prove that for all the
states violating this inequality there exist at least one splitting of the
parties into two groups such that some pure-state entanglement can be
distilled, obtaining a connection between Bell inequalities and bipartite
distillable entanglement.


title: Macroscopic quantum fluctuations in noise-sustained optical patterns

abstract:
  We investigate quantum effects in pattern-formation for a degenerate optical
parametric oscillator with walk-off. This device has a convective regime in
which macroscopic patterns are both initiated and sustained by quantum noise.
Familiar methods based linearization about a pseudo-classical field fail in
this regime and new approaches are required. We employ a method in which the
pump field is treated as a $c$-number variable but is driven by the $c$-number
representation of the quantum sub-harmonic signal field. This allows us to
include the effects of the fluctuations in the signal on the pump, which in
turn act back on the signal. We find that the non-classical effects, in the
form of squeezing, survive just above the threshold of the convective regime.
Further above threshold the macroscopic quantum noise suppresses these effects.


title:
Schwinger, Pegg and Barnett and a relationship between angular and
  Cartesian quantum descriptions

abstract:
  From a development of an original idea due to Schwinger, it is shown that it
is possible to recover, from the quantum description of a degree of freedom
characterized by a finite number of states (\QTR{it}{i.e}., without classical
counterpart) the usual canonical variables of position/momentum \QTR{it}{and}
angle/angular momentum, relating, maybe surprisingly, the first as a limit of
the later.


title:
Chaos in the Quantum Double Well Oscillator: The Ehrenfest View
  Revisited

abstract:
  We treat the double well quantum oscillator from the standpoint of the
Ehrenfest equation but in a manner different from Pattanayak and Schieve. We
show that for short times there can be chaotic motion due to quantum
fluctuations, but over sufficiently long times the behaviour is normal.


title: Fermionic Linear Optics and Matchgates

abstract:
  Fermionic linear optics is efficiently classically simulatable. Here it is
shown that the set of states achievable with fermionic linear optics and
particle measurements is the closure of a low dimensional Lie group. The
weakness of fermionic linear optics and measurements can therefore be explained
and contrasted with the strength of bosonic linear optics with particle
measurements. An analysis of fermionic linear optics is used to show that the
two-qubit matchgates and the simulatable matchcircuits introduced by Valiant
generate a monoid of extended fermionic linear optics operators. A useful
interpretation of efficient classical simulations such as this one is as a
simulation of a model of non-deterministic quantum computation. Problem areas
for future investigations are suggested.


title:
Schmidt number of pure states in bipartite quantum systems as an
  algebraic-geometric invariant

abstract:
  Our previous work about algebraic-geometric invariants of the mixed states
are extended and a stronger separability criterion is given. We also show that
the Schmidt number of pure states in bipartite quantum systems, a classical
concept, is actually an algebraic-geometric invariant.


title:
Coherent and compatible information: a basis to information analysis of
  quantum systems

abstract:
  Relevance of key quantum information measures for analysis of quantum systems
is discussed. It is argued that possible ways of measuring quantum information
are based on compatibility/incompatibility of the quantum states of a quantum
system, resulting in the coherent information and introduced here the
compatible information measures, respectively. A sketch of an information
optimization of a quantum experimental setup is proposed.


title: Channel Estimation with Noisy Entanglement

abstract:
  We analyze the Pauli-channel estimation with mixed nonseparable states. It
turns out that within a specific range entanglement can serve as a nonclassical
resource. However, this range is rather small, that is entanglement is not very
robust for this application. We further show that Werner states yield the best
result of all Bell diagonal states with the same amount of entanglement.


title: Estimation of quantum channels with finite resources

abstract:
  We investigate the problem of determining the parameters that describe a
quantum channel. It is assumed that the users of the channel have at best only
partial knowledge of it and make use of a finite amount of resources to
estimate it. We discuss simple protocols for the estimation of the parameters
of several classes of channels that are studied in the current literature. We
define two different quantitative measures of the quality of the estimation
schemes, one based on the standard deviation, the other one on the fidelity.
The possibility of protocols that employ entangled particles is also
considered. It turns out that the use of entangled particles as a new kind of
nonclassical resource enhances the estimation quality of some classes of
quantum channel. Further, the investigated methods allow us to extend them to
higher dimensional quantum systems.


title:
Comments on some recently proposed experiments that should distinguish
  Bohmian mechanics from quantum mechanics

abstract:
  Recently Ghose (quant-ph/0001024,quant-ph/0003037,quant-ph/0103126) and
Golshani and Akhavan (quant-ph/0009040,quant-ph/0103100,quant-ph/0103101)
claimed to have found experiments that should be able to distinguish between
Standard Quantum Mechanics and Bohmian Mechanics. It is our aim to show that
the claims made by Ghose, Golshani and Akhavan are unfounded.


title: Mindless Sensationalism: A Quantum Framework for Consciousness

abstract:
  The ideas of Sensible Quantum Mechanics are expressed in lay terms for
philosophers of consciousness and others. A framework is proposed and explained
for the `psycho-physical-parallelism' between conscious experiences and the
mathematical structures of quantum physics (e.g., a set of quantum operators
obeying some algebra, and a quantum state giving the expectation value of each
operator). In particular, it is proposed that each set of possible conscious
experiences has a measure given by the expectation value of a corresponding
operator (a positive-operator-valued measure). Then one has a generalization of
the Weak Anthropic Principle named the Conditional Aesthemic Principle: given
that we are conscious beings, our conscious experiences are likely to be
typical experiences in the set of all conscious experiences with its measure.


title: Evolution of an Atom Impeded by Measurement: The Quantum Zeno Effect

abstract:
  A quantum system being observed evolves more slowly. This `'quantum Zeno
effect'' is reviewed with respect to a previous attempt of demonstration, and
to subsequent criticism of the significance of the findings. A recent
experiment on an {\it individual} cold trapped ion has been capable of
revealing the micro-state of this quantum system, such that the effect of
measurement is indeed discriminated from dephasing of the quantum state by
either the meter or the environment.


title: Path Integration for the Plane Pendulum with Finite Amplitude

abstract:
  Exact path integration for the one dimensional potential $V=b^2\cos 2q$ which
describes the finite amplitude pendulum is presented.


title: Coherent states for the hydrogen atom: discrete and continuous spectra

abstract:
  We construct the systems of generalised coherent states for the discrete and
continuous spectra of the hydrogen atom. These systems are expressed in
elementary functions and are invariant under the $SO(3, 2)$ (discrete spectrum)
and $SO(4, 1)$ (continuous spectrum) subgroups of the dynamical symmetry group
$SO(4, 2)$ of the hydrogen atom. Both systems of coherent states are particular
cases of the kernel of integral operator which interwines irreducible
representations of the $SO(4, 2)$ group.


title:
The Lorentz singular value decomposition and its applications to pure
  states of 3 qubits

abstract:
  All mixed states of two qubits can be brought into normal form by the action
of SLOCC operations of the kind $\rho'=(A\otimes B)\rho(A\otimes B)^\dagger$.
These normal forms can be obtained by considering a Lorentz singular value
decomposition on a real parameterization of the density matrix. We show that
the Lorentz singular values are variationally defined and give rise to
entanglement monotones, with as a special case the concurrence. Next a
necessary and sufficient criterion is conjectured for a mixed state to be
convertible into another specific one with a non-zero probability. Finally the
formalism of the Lorentz singular value decomposition is applied to tripartite
pure states of qubits. New proofs are given for the existence of the GHZ- and
W-class of states, and a rigorous proof for the optimal distillation of a
GHZ-state is derived.


title: Entangling macroscopic oscillators exploiting radiation pressure

abstract:
  It is shown that radiation pressure can be profitably used to entangle {\it
macroscopic} oscillators like movable mirrors, using present technology. We
prove a new sufficient criterion for entanglement and show that the achievable
entanglement is robust against thermal noise. Its signature can be revealed
using common optomechanical readout apparatus.


title: Imbedding nonlocality in a relativistic chronology

abstract:
  An alternative description imbedding nonlocality in a relativistic chronology
is proposed. It is argued that vindication of Quantum Mechanics in forthcoming
experiments with moving beam-splitters would mean that there is no real time
ordering behind the nonlocal correlations.


title: Phase Coherence and Control of Stored Photonic Information

abstract:
  We report the demonstration of phase coherence and control for the recently
developed "light storage" technique. Specifically, we use a pulsed magnetic
field to vary the phase of atomic spin excitations which result from the
deceleration and storing of a light pulse in warm Rb vapor. We then convert the
spin excitations back into light and detect the resultant phase shift in an
optical interferometric measurement. The coherent storage of photon states in
matter is essential for the practical realization of many basic concepts in
quantum information processing.


title: Novel Bell's inequalities for entangled K0 anti-K0 pairs

abstract:
  We derive new Bell's inequalities for entangled K0 anti-K0 pairs. This
requires 1) mutually exclusive setups allowing either K0 vs anti-K0 or KS vs KL
detection and 2) the use of kaon regenerators. The inequalities turn out to be
significantly violated by Quantum Mechanics, resulting in interesting tests of
Local Realism at phi-factories and p anti-p machines.


title: Robustness of adiabatic quantum computation

abstract:
  We study the fault tolerance of quantum computation by adiabatic evolution, a
quantum algorithm for solving various combinatorial search problems. We
describe an inherent robustness of adiabatic computation against two kinds of
errors, unitary control errors and decoherence, and we study this robustness
using numerical simulations of the algorithm.


title: Simple Scheme for Efficient Linear Optics Quantum Gates

abstract:
  We describe the construction of a conditional quantum control-not (CNOT) gate
from linear optical elements following the program of Knill, Laflamme and
Milburn [Nature {\bf 409}, 46 (2001)]. We show that the basic operation of this
gate can be tested using current technology. We then simplify the scheme
significantly.


title:
Existence of the Wigner function with correct marginal distributions
  along tilted lines on a lattice

abstract:
  In order to determine the Wigner function uniquely, we introduce a new
condition which ensures that the Wigner function has correct marginal
distributions along tilted lines. For a system in $N$ dimensional Hilbert
space, whose "phase space" is a lattice with $N^2$ sites, we get different
results depending on whether $N$ is odd or even. Under the new condition, the
Wigner function is determined if $N$ is an odd number, but it does not exist if
$N$ is even.


title: Conditional two mode squeezed vacuum teleportation

abstract:
  We show, by making conditional measurements on the Einstein-Podolsky-Rosen
(EPR) squeezed vacuum, that one can improve the efficacy of teleportation for
both the position difference, momentum sum and number difference, phase sum
continuous variable teleportation protocols. We investigate the relative
abilities of the standard and conditional EPR states, and show that by
conditioning we can improve the fidelity of teleportation of coherent states
from below to above the $\bar{F} = 2/3$ boundary.


title:
Quantum algorithm for measuring the energy of n qubits with unknown
  pair-interactions

abstract:
  The well-known algorithm for quantum phase estimation requires that the
considered unitary is available as a conditional transformation depending on
the quantum state of an ancilla register. We present an algorithm converting an
unknown n-qubit pair-interaction Hamiltonian into a conditional one such that
standard phase estimation can be applied to measure the energy. Our essential
assumption is that the considered system can be brought into interaction with a
quantum computer. For large n the algorithm could still be applicable for
estimating the density of energy states and might therefore be useful for
finding energy gaps in solid states.


title:
Quantum algorithm for finding periodicities in the spectrum of a
  black-box Hamiltonian or unitary transformation

abstract:
  Estimating the eigenvalues of a unitary transformation U by standard phase
estimation requires the implementation of controlled-U-gates which are not
available if U is only given as a black box.
  We show that a simple trick allows to measure eigenvalues of U\otimes
U^\dagger even in this case. Running the algorithm several times allows
therefore to estimate the autocorrelation function of the density of
eigenstates of U. This can be applied to find periodicities in the energy
spectrum of a quantum system with unknown Hamiltonian if it can be coupled to a
quantum computer.


title: One-dimensional quantum chaos: Explicitly solvable cases

abstract:
  We present quantum graphs with remarkably regular spectral characteristics.
We call them {\it regular quantum graphs}. Although regular quantum graphs are
strongly chaotic in the classical limit, their quantum spectra are explicitly
solvable in terms of periodic orbits. We present analytical solutions for the
spectrum of regular quantum graphs in the form of explicit and exact periodic
orbit expansions for each individual energy level.


title:
A Canonical Approach to the Quantization of the Damped Harmonic
  Oscillator

abstract:
  We provide a new canonical approach for studying the quantum mechanical
damped harmonic oscillator based on the doubling of degrees of freedom
approach. Explicit expressions for Lagrangians of the elementary modes of the
problem, characterising both forward and backward time propagations are given.
  A Hamiltonian analysis, showing the equivalence with the Lagrangian approach,
is also done. Based on this Hamiltonian analysis, the quantization of the model
is discussed.


title: A simple gate for linear optics quantum computing

abstract:
  We describe a simple scheme for implementing the non-linear sign gate of
Knill, Laflamme and Milburn (Nature, {\bf 409}, 46-52, Jan. 4 (2001)) which
forms the basis of an experiment underway at the University of Vienna.


title: Is "entanglement" always entangled?

abstract:
  Entanglement, including ``quantum entanglement,'' is a consequence of
correlation between objects. When the objects are subunits of pairs which in
turn are members of an ensemble described by a wave function, a correlation
among the subunits induces the mysterious properties of ``cat-states.''
However, correlation between subsystems can be present from purely non-quantum
sources, thereby entailing no unfathomable behavior. Such entanglement arises
whenever the so-called ``qubit space'' is not afflicted with Heisenberg
Uncertainty. It turns out that all optical experimental realizations of EPR's
\emph{Gedanken} experiment in fact do not suffer Heisenberg Uncertainty.
Examples will be analyzed and non-quantum models for some of these described.
The consequences for experiments that were to test EPR's contention in the form
of Bell's Theorem are drawn: \emph{valid tests of EPR's hypothesis have yet to
be done.}


title: On singularities of the mixed state phase

abstract:
  A recent proposal of Sjoqvist et.al. to extend Pancharatnam's criterion for
phase difference between two different pure states to the case of mixed states
in quantum mechanics is analyzed and the existence of phase singularities in
the parameter space of an interference experiment with particles in mixed
states pointed out. In the vicinity of such singular points the phase changes
sharply and precisely at these points it becomes undefined. A closed circuit in
the parameter space around such points results in a measurable phase shift
equal to 2n\pi, where n is an integer. Such effects have earlier been observed
in interference experiments with pure polarization states of light, a system
isomorphic to the spin-1/2 system in quantum mechanics. Implications of phase
singularities for the interpretation of experiments with partially polarized
and unpolarized neutrons are discussed. New kinds of topological phases
involving variables representing decoherence (depolarization) of pure states
are predicted and experiments to verify them suggested.


title:
The uniqueness question in the multidimensional moment problem with
  applications to phase space observables

abstract:
  The theory of holomorphic functions of several complex variables is applied
in proving a multidimensional variant of a theorem involving an exponential
boundedness criterion for the classical moment problem. A theorem of Petersen
concerning the relation between the multidimensional and one-dimensional moment
problems is extended for half-lines and compact subsets of the real line. These
results are used to solve the moment problem for the quantum phase space
observables generated by the number states.


title:
Entanglement purification with noisy apparatus can be used to factor out
  an eavesdropper

abstract:
  We give a proof that entanglement purification, even with noisy apparatus, is
sufficient to disentangle an eavesdropper (Eve) from the communication channel.
Our proof applies to all possible attacks (individual and coherent). Due to the
quantum nature of the entanglement purification protocol, it is also possible
to use the obtained quantum channel for secure transmission of quantum
information.


title: Laser phase modulation approaches towards ensemble quantum computing

abstract:
  Selective control of decoherence is demonstrated for a multilevel system by
generalizing the instantaneous phase of any chirped pulse as individual terms
of a Taylor series expansion. In the case of a simple two-level system, all odd
terms in the series lead to population inversion while the even terms lead to
self-induced transparency. These results also hold for multiphoton transitions
that do not have any lower-order photon resonance or any intermediate virtual
state dynamics within the laser pulse-width. Such results form the basis of a
robustly implementable CNOT gate.


title: Universal quantum gates

abstract:
  In this paper we study universality for quantum gates acting on qudits.Qudits
are states in a Hilbert space of dimension d where d is at least two. We
determine which 2-qudit gates V have the properties (i) the collection of all
1-qudit gates together with V produces all n-qudit gates up to arbitrary
precision, or (ii) the collection of all 1-qudit gates together with V produces
all n-qudit gates exactly. We show that (i) and (ii) are equivalent conditions
on V, and they hold if and only if V is not a primitive gate. Here we say V is
primitive if it transforms any decomposable tensor into a decomposable tensor.
We discuss some applications and also relations with work of other authors.


title: Polarization Entanglement Purification using Spatial Entanglement

abstract:
  Parametric down-conversion can produce photons that are entangled both in
polarization and in space. Here we show how the spatial entanglement can be
used to purify the polarization entanglement using only linear optical
elements. Spatial entanglement as an additional resource leads to a substantial
improvement in entanglement output compared to a previous scheme.
Interestingly, in the present context the thermal character of down-conversion
sources can be turned into an advantage. Our scheme is realizable with current
technology.


title: CP^n, or, entanglement illustrated

abstract:
  We show that many topological and geometrical properties of complex
projective space can be understood just by looking at a suitably constructed
picture. The idea is to view CP^n as a set of flat tori parametrized by the
positive octant of a round sphere. We pay particular attention to submanifolds
of constant entanglement in CP^3 and give a few new results concerning them.


title: Optical quantum computer based on RDS crystal

abstract:
  We have proposed the construction of optical quantum computer (OQC) on
regular domain structure (RDS) crystal. By using RDS crystal, we can perform
all the logical operations on one RDS crystal. Moreover, RDS crystals are
parctically independent to the heating effects i.e., can perform logic
operations constantly without cooling the RDS crystal. Also, we have proposed
the quantum parallelsim i.e., parallel coherent laser beams are injected at the
input of the RDS crystals. By using the RDS crystal we can perform the reduce
the requirements of the linear and nonlinear optical components.


title:
Scalable programmable quantum gates and a new aspect of the additivity
  problem for the classical capacity of quantum channels

abstract:
  We consider two apparently separated problems: in the first part of the paper
we study the concept of a scalable (approximate) programmable quantum gate
(SPQG). These are special (approximate) programmable quantum gates, with nice
properties that could have implications on the theory of universal computation.
Unfortunately, as we prove, such objects do not exist in the domain of usual
quantum theory. In the second part the problem of noisy dense coding (and
generalizations) is addressed. We observe that the additivity problem for the
classical capacity obtained is of apparently greater generality than for the
usual quantum channel (completely positive maps): i.e., the latter occurs as a
special case of the former, but, as we shall argue with the help of the
non-existence result of the first part, the former cannot be reduced to an
instance of the latter. We conclude by suggesting that the additivity problem
for the classical capacity of quantum channels, as posed until now, may
conceptually not be in its appropriate generality.


title: Computational model underlying the one-way quantum computer

abstract:
  In this paper we present the computational model underlying the one-way
quantum computer which we introduced recently [Phys. Rev. Lett. 86, 5188
(2001)]. The one-way quantum computer has the property that any quantum logic
network can be simulated on it. Conversely, not all ways of quantum information
processing that are possible with the one-way quantum computer can be
understood properly in network model terms. We show that the logical depth is,
for certain algorithms, lower than has so far been known for networks. For
example, every quantum circuit in the Clifford group can be performed on the
one-way quantum computer in a single step.


title:
Experimental Implementation of Hogg's Algorithm on a Three-Quantum-bit
  NMR Quantum Computer

abstract:
  Using nuclear magnetic resonance (NMR) techniques with three-qubit sample, we
have experimentally implemented the highly structured algorithm for the 1-SAT
problem proposed by Hogg. A simplified temporal averaging procedure was
employed to the three-qubit spin pseudo-pure state. The algorithm was completed
with only a single evaluation of structure of the problem and the solutions
were found with probability 100%, which outperform both unstructured quantum
and the best classical search algorithm.


title: Quantum anti-centrifugal force

abstract:
  In a two-dimensional world a free quantum particle of vanishing angular
momentum experiences an attractive force. This force originates from a
modification of the classical centrifugal force due to the wave nature of the
particle. For positive energies the quantum anti-centrifugal force manifests
itself in a bunching of the nodes of the energy wave functions towards the
origin. For negative energies this force is sufficient to create a bound state
in a two-dimensional delta function potential. In a counter-intuitive way the
attractive force pushes the particle away from the location of the delta
function potential. As a consequence, the particle is localized in a
band-shaped domain around the origin


title: When Worlds Collide: Quantum Probability From Observer Selection?

abstract:
  In Everett's many worlds interpretation, quantum measurements are considered
to be decoherence events. If so, then inexact decoherence may allow large
worlds to mangle the memory of observers in small worlds, creating a cutoff in
observable world size. Smaller world are mangled and so not observed. If this
cutoff is much closer to the median measure size than to the median world size,
the distribution of outcomes seen in unmangled worlds follows the Born rule.
Thus deviations from exact decoherence can allow the Born rule to be derived
via world counting, with a finite number of worlds and no new fundamental
physics.


title: Quantum mechanics and the continuum problem (with referee reports)

abstract:
  It is shown that Feynman's formulation of quantum mechanics can be reproduced
as a description of the set of intermediate cardinality. Properties of the set
follow directly from the independence of the continuum hypothesis. Six referee
reports of Physical Review Letters, Europhysics Letters, and Journal of Physics
A are enclosed.


title: The Origin of the Planck's Constant

abstract:
  In this paper, we discuss an equation which does not contain the Planck's
constant, but it will turn out the Planck's constant when we apply the equation
to the problems of particle diffraction.


title: Quantum Information in Space and Time

abstract:
  Many important results in modern quantum information theory have been
obtained for an idealized situation when the spacetime dependence of quantum
phenomena is neglected. However the transmission and processing of (quantum)
information is a physical process in spacetime. Therefore such basic notions in
quantum information theory as the notions of composite systems, entangled
states and the channel should be formulated in space and time. We emphasize the
importance of the investigation of quantum information in space and time.
Entangled states in space and time are considered. A modification of Bell`s
equation which includes the spacetime variables is suggested. A general
relation between quantum theory and theory of classical stochastic processes is
proposed. It expresses the condition of local realism in the form of a {\it
noncommutative spectral theorem}. Applications of this relation to the security
of quantum key distribution in quantum cryptography are considered.

categories: quant-ph cond-mat.mes-hall cs.IT gr-qc hep-ph hep-th math-ph math.IT math.MP math.PR


title: Deduction, Ordering, and Operations in Quantum Logic

abstract:
  We show that in quantum logic of closed subspaces of Hilbert space one cannot
substitute quantum operations for classical (standard Hilbert space) ones and
treat them as primitive operations. We consider two possible ways of such a
substitution and arrive at operation algebras that are not lattices what proves
the claim. We devise algorithms and programs which write down any two-variable
expression in an orthomodular lattice by means of classical and quantum
operations in an identical form. Our results show that lattice structure and
classical operations uniquely determine quantum logic underlying Hilbert space.
As a consequence of our result, recent proposals for a deduction theorem with
quantum operations in an orthomodular lattice as well as a substitution of
quantum operations for the usual standard Hilbert space ones in quantum logic
prove to be misleading. Quantum computer quantum logic is also discussed.

categories: quant-ph math-ph math.LO math.MP math.QA


title: Evolutionarily Stable Strategies in Quantum Hawk-Dove Game

abstract:
  We quantized the Hawk-Dove game by using the most general form of a pure
initial state to investigate the existence of pure and mixed Evolutionarily
Stable Strategies (ESS). An example is considered to draw a comparison between
classical and quantum version of the game. Our choice of most general initial
quantum state enables us to make the game symmetric or asymmetric. We show that
for a particular set of game parameters where there exist only mixed ESS in the
classical version of the game, however, quantization allows even a pure
strategy to be an ESS for symmetric game in addition to ixed ESS. On the other
hand only pure strategy ESS can exist for asymmetric quantum version of the
Hawk-Dove game.


title:
Optimal simulation of nonlocal Hamiltonians using local operations and
  classical communication

abstract:
  Consider a set of $N$ systems and an arbitrary interaction Hamiltonian $H$
that couples them. We investigate the use of local operations and classical
communication (LOCC), together with the Hamiltonian $H$, to simulate a unitary
evolution of the $N$ systems according to some other Hamiltonian $H'$. First,
we show that the most general simulation using $H$ and LOCC can be also
achieved, with the same time efficiency, by just interspersing the evolution of
$H$ with local unitary manipulations of each system and a corresponding local
ancilla (in a so-called LU+anc protocol). Thus, the ability to make local
measurements and to communicate classical information does not help in
non--local Hamiltonian simulation. Second, we show that both for the case of
two $d$-level systems ($d>2$), or for that of a setting with more than two
systems ($N>2$), LU+anc protocols are more powerful than LU protocols.
Therefore local ancillas are a useful resource for non--local Hamiltonian
simulation. Third, we use results of majorization theory to explicitly solve
the problem of optimal simulation of two-qubit Hamiltonians using LU
(equivalently, LU+anc, LO or LOCC).


title: Catalysis in non--local quantum operations

abstract:
  We show how entanglement can be used, without being consumed, to accomplish
unitary operations that could not be performed with out it. When applied to
infinitesimal transformations our method makes equivalent, in the sense of
Hamiltonian simulation, a whole class of otherwise inequivalent two-qubit
interactions. The new catalysis effect also implies the asymptotic equivalence
of all such interactions.


title: Geometric phases of mesoscopic spin in Bose-Einstein condensates

abstract:
  We propose a possible scheme for generating spin-J geometric phases using a
coupled two-mode Bose-Einstein condensate (BEC). First we show how to observe
the standard Berry phase using Raman coupling between two hyperfine states of
the BEC. We find that the presence of intrinsic interatomic collisions creates
degeneracy in energy that allows implementation of the non-Abelian geometric
phases as well. The evolutions produced can be used to produce interference
between different atomic species with high numbers of atoms or to fine control
the difference in atoms between the two species. Finally, we show that errors
in the standard Berry phase due to elastic collisions may be corrected by
controlling inelastic collisions between atoms.


title: Quantum Theory of Observers

abstract:
  This is an attempt to create a consistent and non-trivial extension of
quantum theory, describing in detail the quantum measurement process. A
tentative but concrete model is presented, based on the concept of multiple
observer/participators, represented by separate state vectors. The evolution is
deterministic, and in the chaotic regime implies approximate adherence to the
Born rule for probabilities. The model is applied in a number of contexts:
simple detectors, multi-state selectors, and intermittent systems. The results
are consistent with phenomenology. We also consider more speculative
applications, including specific spin and position `observables.' Finally the
outlook for the model is discussed, and its relation to other work.