title:
From limits of quantum nonlinear operations to multicopy entanglement
  witnesses and state spectrum estimation

abstract:
  Limits of nonlinear in quantum mechanics are studied. Impossibility of
physical implementation of the transformation $\varrho^{\otimes n} \to
\varrho^{n}$ in quantum mechanics is proved. For sake of further analysis the
simplest notion of structural completely positive approximation (SCPA) and
structural physical approximations (SPA) of unphysical map are introduced. Both
always exist for linear hermitian maps and can be optimised under natural
assumptions. However it is shown that some intuitively natural SPA of the
nonlinear operation $\varrho^{\otimes 2} \to \varrho^{2}$ that was already
proven to be unphysical is impossible. It is conjectured that there exist no
SPA of the operation $\varrho^{\otimes n} \to \varrho^{n}$ at all. It is
pointed out that, on the other hand, it is physically possible to measure the
trace of the second power of the state $Tr(\varrho^{2})$ if only two copies of
the system are available. This gives the interpretation of one of Tsallis
entropy as mean value of some ``multicopy'' observable. The (partial)
generalisation of this idea shows that each of higher order Tsallis entropies
can be measured with help of only two multicopy observables. Following this
observations the notion of multicopy entanglement witnesses is defined and
first example is provided. Finally, with help of multicopy observables simple
method of spectrum state estimation is pointed out and discussed.


title:
Casimir Problem in Spherical Dielectrics: A Quantum Statistical
  Mechanical Approach

abstract:
  The Casimir mutual free energy F for a system of two dielectric concentric
nonmagnetic spherical bodies is calculated, at arbitrary temperatures. Whereas
F has recently been evaluated for the special case of metals (refractive index
n=\infty), here analogous results are presented for dielectrics, and shown
graphically when n=2.0. Our calculational method relies upon quantum
statistical mechanics. The Debye expansions for the Riccati-Bessel functions
when carried out to a high order are found to be very useful in practice
(thereby overflow/underflow problems are easily avoided), and also to give
accurate results even for the lowest values of l. Another virtue of the Debye
expansions is that the limiting case of metals becomes quite amenable to an
analytical treatment in spherical geometry. We first discuss the zero-frequency
TE mode problem from a mathematical viewpoint and then, as physical input,
invoke the actual dispersion relations. The result of our analysis, based upon
adoption of the Drude dispersion relation as the most correct one at low
frequencies, is that the zero-frequency TE mode does not contribute for a
metal. Accordingly, F turns out in this case to be only one half of the
conventional value.


title: Discrete Cosine Transforms on Quantum Computers

abstract:
  A classical computer does not allow to calculate a discrete cosine transform
on N points in less than linear time. This trivial lower bound is no longer
valid for a computer that takes advantage of quantum mechanical superposition,
entanglement, and interference principles. In fact, we show that it is possible
to realize the discrete cosine transforms and the discrete sine transforms of
size NxN and types I,II,III, and IV with as little as O(log^2 N) operations on
a quantum computer, whereas the known fast algorithms on a classical computer
need O(N log N) operations.


title:
On the Irresistible Efficiency of Signal Processing Methods in Quantum
  Computing

abstract:
  We show that many well-known signal transforms allow highly efficient
realizations on a quantum computer. We explain some elementary quantum circuits
and review the construction of the Quantum Fourier Transform. We derive quantum
circuits for the Discrete Cosine and Sine Transforms, and for the Discrete
Hartley transform. We show that at most O(log^2 N) elementary quantum gates are
necessary to implement any of those transforms for input sequences of length N.


title: Topological Phases near a Triple Degeneracy

abstract:
  We study the pattern of three state topological phases that appear in systems
with real Hamiltonians and wave functions. We give a simple geometric
construction for representing these phases. We then apply our results to
understand previous work on three state phases. We point out that the ``mirror
symmetry'' of wave functions noticed in microwave experiments can be simply
understood in our framework.


title: Quantum computing and communication with decoherence-free atomic states

abstract:
  To resist decoherence from destroying the phase factor of qubit state, it is
important to use decoherence-free states for processing, transmitting and
storing quantum information in quantum computing and quantum communication. We
propose a practical scheme using four atoms with decoherence-free states in a
single-mode cavity to realize the entanglement and fundamental quantum logic
gates. The transmission of quantum information can be made directly from one
atom to another, in which the cavity is only virtually excited. The possible
application and the experimental requirement of our proposal are discussed


title:
Series solution to the laser-ion interaction in a Raman-type
  configuration

abstract:
  The Raman interaction of a trapped ultracold ion with two travelling wave
lasers is studied analytically with series solutions, in the absence of the
rotating wave approximation (RWA) and the restriction of both the Lamb-Dicke
limit and the weak excitation regime. The comparison is made between our
solutions and those under the RWA to demonstrate the validity region of the
RWA. As a practical example, the preparation of Schr\"odinger-cat states with
our solutions is proposed beyond the weak excitation regime.


title: Quantum computing with four-particle decoherence-free states in ion trap

abstract:
  Quantum computing gates are proposed to apply on trapped ions in
decoherence-free states. As phase changes due to time evolution of components
with different eigenenergies of quantum superposition are completely frozen,
quantum computing based on this model would be perfect. Possible application of
our scheme in future ion-trap quantum computer is discussed.


title: Squeezed states and quantum chaos

abstract:
  We examine the dynamics of a wave packet that initially corresponds to a
coherent state in the model of quantum kicked rotator. This main model of
quantum chaos, which allows for a transition from regular to to chaotic
behavior in the classical limit, may be realized in experiments with cold
atoms. We study the generation of squeezed states in the quasiclassical limit
and in a time interval when quantum-classical correspondence is yet
well-defined. We find that the degree of squeezing depends on the degree of
local instability in the system and increases with the Chirikov parameter of
stochasticity. We discuss the dependence of the degree of squeezing on the
initial width of the packet, the problems of stability and observability of
squeezed states at the transition to quantum chaos, as well as the dynamics of
wave packet destruction.


title:
Transmission and Reflection in a Double Potential Well: Doing it the
  Bohmian Way

abstract:
  The Bohm interpretation of quantum mechanics is applied to a transmission and
reflection process in a double potential well. We consider a time dependent
periodic wave function and study the particle trajectories. The average time,
eventally transmitted particles stay inside the barrier is the average
transmission time, which can be defined using the causal interpretation. The
question remains whether these transmission times can be experimentally
measured.


title: Secure assisted quantum computation

abstract:
  Suppose Alice wants to perform some computation that could be done quickly on
a quantum computer, but she cannot do universal quantum computation. Bob can do
universal quantum computation and claims he is willing to help, but Alice wants
to be sure that Bob cannot learn her input, the result of her calculation, or
perhaps even the function she is trying to compute. We describe a simple,
efficient protocol by which Bob can help Alice perform the computation, but
there is no way for him to learn anything about it. We also discuss techniques
for Alice to detect whether Bob is honestly helping her or if he is introducing
errors.


title: Time, Quantum Mechanics, and Probability

abstract:
  A "geometric" intepretation of probability is proposed, modelled on the
treatment of tense in 4-dimensional spacetime. It is applied to Everett's
approach to quantum mechanics, as formulated in terms of consistent histories.
Standard objections to Everett's approach, based on the difficulties of
interpreting probability in its terms, are considered in detail, but found to
be wanting.


title: Notation for general quantum teleportation

abstract:
  A new notation for the quantum teleportation of finite dimensional quantum
state through a generally entangled quantum channel is introduced. For a given
quantum channel an explict mathematical criterion that governs the faithful
teleportation is presented.


title:
The entanglement concentration and purification for entangled
  polarization photon state

abstract:
  We present a concentration and purification scheme for nonmaximally entangled
pure and mixed porization entangled state. We firstly show that two distant
parties Alice and Bob first start with two shared but less entangled photon
pure states to produce a four photon GHZ state, and then perform a 45
polarization measurement onto one of the two photons at each location such that
the remaining two photon are projected onto a maximally entangled state. We
further show the scheme also can be used to purify a class of mixed
polarization-entangled state.


title:
Generalised boundary conditions for the Aharonov-Bohm effect combined
  with a homogeneous magnetic field

abstract:
  The most general admissible boundary conditions are derived for an idealised
Aharonov-Bohm flux intersecting the plane at the origin on the background of a
homogeneous magnetic field. A standard technique based on self-adjoint
extensions yields a four-parameter family of boundary conditions; other two
parameters of the model are the Aharonov-Bohm flux and the homogeneous magnetic
field. The generalised boundary conditions may be regarded as a combination of
the Aharonov-Bohm effect with a point interaction. Spectral properties of the
derived Hamiltonians are studied in detail.


title:
Low rank separable states are a set of measure zero within the set of
  low rank states

abstract:
  It is shown that the set of rank r separable states is measure zero within
the set of low rank states provided r is less than an upper bound which depends
upon the number of particles and the dimensions of the spaces they are modelled
on. The upper bound is given. In the bipartite case in which both particles are
modelled on m-dimensional hilbert space it is (m-1)^2. In the case of p qubits
it is (2^p)-p. This paper is a corretion of one I recently posted and
subsequently withdrew. That paper claimed the set of rank r separable states is
measure zero if r is non-maximal rank. That may be true, but the proof in the
withdrawn paper was false.


title:
High contrast Mach-Zehnder lithium atom interferometer in the Bragg
  regime

abstract:
  We have constructed an atom interferometer of the Mach-Zehnder type,
operating with a supersonic beam of lithium. Atom diffraction uses Bragg
diffraction on laser standing waves. With first order diffraction, our
apparatus has given a large signal and a very good fringe contrast (74%), which
we believe to be the highest ever observed with atom interferometers. This
apparatus will be applied to high sensitivity measurements


title: A simple operational interpretation of the fidelity

abstract:
  This note presents a corollary to Uhlmann's theorem which provides a simple
operational interpretation for the fidelity of mixed states.


title: Entangled-photon Fourier optics

abstract:
  Entangled photons, generated by spontaneous parametric down-conversion from a
second-order nonlinear crystal, present a rich potential for imaging and
image-processing applications. Since this source is an example of a three-wave
mixing process, there is more flexibility in the choices of illumination and
detection wavelengths and in the placement of object(s) to be imaged. Moreover,
this source is entangled, a fact that allows for imaging configurations and
capabilities that cannot be achieved using classical sources of light. In this
paper we examine a number of imaging and image-processing configurations that
can be realized using this source. The formalism that we utilize facilitates
the determination of the dependence of imaging resolution on the physical
parameters of the optical arrangement.


title: Engineering an interaction and entanglement between distant atoms

abstract:
  We propose a scheme to generate an effective interaction of arbitrary
strength between the internal degrees of freedom of two atoms placed in distant
cavities connected by an optical fiber. The strength depends on the field
intensity in the cavities. As an application of this interaction, we calculate
the amount of entanglement it generates between the internal states of the
distant atoms. The scheme effectively converts entanglement distribution
networks to networks of interacting spins.


title: Single mode realizations of the Higgs algebra

abstract:
  In this paper we obtained for the Higgs algebra three kinds of single-mode
realizations such as the unitary Holstein-Primakoff-like realization, the
non-unitary Dyson-like realization and the unitary realization based upon
Villain-like realization. The corresponding similarity transformations between
the Holstein-Primakoff-like realizations and the Dyson-like realizations are
revealed.


title: Classical Aspects of Quantum Walls in One Dimension

abstract:
  We investigate the system of a particle moving on a half line x >= 0 under
the general walls at x = 0 that are permitted quantum mechanically. These
quantum walls, characterized by a parameter L, are shown to be realized as a
limit of regularized potentials. We then study the classical aspects of the
quantum walls, by seeking a classical counterpart which admits the same time
delay in scattering with the quantum wall, and also by examining the
WKB-exactness of the transition kernel based on the regularized potentials. It
is shown that no classical counterpart exists for walls with L < 0, and that
the WKB-exactness can hold only for L = 0 and L = infinity.


title: Entanglement of internal and external angular momenta of a single atom

abstract:
  We consider the exchange of spin and orbital angular momenta between a
circularly polarized Laguerre-Gaussian beam of light and a single atom trapped
in a two-dimensional harmonic potential. The radiation field is treated
classically but the atomic center-of-mass motion is quantized. The spin and
orbital angular momenta of the field are individually conserved upon
absorption, and this results in the entanglement of the internal and external
degrees of freedom of the atom. We suggest applications of this entanglement in
quantum information processing.


title: Electrodynamics of Bose-Einstein condensates in angular motion

abstract:
  A theory determining the electric and magnetic properties of vortex states in
Bose-Einstein condensates (BECs) is presented. The principal ingredient is the
Lagrangian of the system which we derive correct to the first order in the
atomic centre of mass velocity. For the first time using centre of mass
coordinates, a gauge transformation is performed and relevant relativistic
corrections are included. The Lagrangian is symmetric in the electric and
magnetic aspects of the problem and includes two key interaction terms, namely
the Aharanov-Casher and the Roentgen interaction terms. The constitutive
relations, which link the electromagnetic fields to the matter fields via their
electric polarisation and magnetisation, follow from the Lagrangian as well as
the corresponding Hamiltonian. These relations, together with a generalised
Gross-Pitaevskii equation, determine the magnetic (electric) monopole charge
distributions accompanying an order n vortex state when the constituent atoms
are characterised by an electric dipole (magnetic dipole). Field distributions
associated with electric dipole active (magnetic dipole active) BECs in a
vortex state are evaluated for an infinite- and a finite-length cylindrical
BEC. The predictd monopole charge distributions, both electric and magnetic,
automatically satisfy the requirement of global charge neutrality and the
derivations highlight the exact symmetry between the electric and magnetic
properties. Order of magnitude estimates of the effects are given for an atomic
gas BEC, superfluid helium and a spin-polarised hydrogen BEC.


title: Localization and Causality for a free particle

abstract:
  Theorems (most notably by Hegerfeldt) prove that an initially localized
particle whose time evolution is determined by a positive Hamiltonian will
violate causality. We argue that this apparent paradox is resolved for a free
particle described by either the Dirac equation or the Klein-Gordon equation
because such a particle cannot be localized in the sense required by the
theorems.


title:
Self-adjoint Time Operator is the Rule for Discrete Semibounded
  Hamiltonians

abstract:
  We prove explicitly that to every discrete, semibounded Hamiltonian with
constant degeneracy and with finite sum of the squares of the reciprocal of its
eigenvalues and whose eigenvectors span the entire Hilbert space there exists a
characteristic self-adjoint time operator which is canonically conjugate to the
Hamiltonian in a dense subspace of the Hilbert space. Moreover, we show that
each characteristic time operator generates an uncountable class of self-
adjoint operators canonically conjugate with the same Hamiltonian in the same
dense subspace.


title: Hilbert's Incompleteness, Chaitin's $\Omega$ number and Quantum Physics

abstract:
  To explore the limitation of a class of quantum algorithms originally
proposed for the Hilbert's tenth problem, we consider two further classes of
mathematically non-decidable problems, those of a modified version of the
Hilbert's tenth problem and of the computation of the Chaitin's $\Omega$
number, which is a representation of the G\"odel's Incompletness theorem. Some
interesting connection to Quantum Field Theory is pointed out.


title: A reformulation of Hilbert's tenth problem through Quantum Mechanics

abstract:
  Inspired by Quantum Mechanics, we reformulate Hilbert's tenth problem in the
domain of integer arithmetics into either a problem involving a set of
infinitely coupled differential equations or a problem involving a Shr\"odinger
propagator with some appropriate kernel. Either way, Mathematics and Physics
could be combined for Hilbert's tenth problem and for the notion of effective
computability.


title: Direct detection of quantum entanglement

abstract:
  Quantum entanglement, after playing a significant role in the development of
the foundations of quantum mechanics, has been recently rediscovered as a new
physical resource with potential commercial applications such as, for example,
quantum cryptography, better frequency standards or quantum-enhanced
positioning and clock synchronization. On the mathematical side the studies of
entanglement have revealed very interesting connections with the theory of
positive maps. The capacity to generate entangled states is one of the basic
requirements for building quantum computers. Hence, efficient experimental
methods for detection, verification and estimation of quantum entanglement are
of great practical importance. Here, we propose an experimentally viable,
\emph{direct} detection of quantum entanglement which is efficient and does not
require any \emph{a priori} knowledge about the quantum state. In a particular
case of two entangled qubits it provides an estimation of the amount of
entanglement. We view this method as a new form of quantum computation, namely,
as a decision problem with quantum data structure.


title:
Quantum Distillation Of Position Entanglement With The Polarization
  Degrees Of Freedom

abstract:
  Sources of entangled photon pairs using two parametric down-converters are
capable of generating interchangeable entanglement in two different degrees of
freedom. The connection between these two degrees of freedom allows the control
of the entanglement properties of one, by acting on the other degree of
freedom. We demonstrate experimentally, the quantum distillation of the
position entanglement using polarization analyzers.


title:
A security proof of quantum cryptography based entirely on entanglement
  purification

abstract:
  We give a proof that entanglement purification, even with noisy apparatus, is
sufficient to disentangle an eavesdropper (Eve) from the communication channel.
In the security regime, the purification process factorises the overall initial
state into a tensor-product state of Alice and Bob, on one side, and Eve on the
other side, thus establishing a completely private, albeit noisy, quantum
communication channel between Alice and Bob. The security regime is found to
coincide for all practical purposes with the purification regime of a two-way
recurrence protocol. This makes two-way entanglement purification protocols,
which constitute an important element in the quantum repeater, an efficient
tool for secure long-distance quantum cryptography.


title:
Mirror quiescence and high-sensitivity position measurements with
  feedback

abstract:
  We present a detailed study of how phase-sensitive feedback schemes can be
used to improve the performance of optomechanical devices. Considering the case
of a cavity mode coupled to an oscillating mirror by the radiation pressure, we
show how feedback can be used to reduce the position noise spectrum of the
mirror, cool it to its quantum ground state, or achieve position squeezing.
Then, we show that even though feedback is not able to improve the sensitivity
of stationary position spectral measurements, it is possible to design a
nonstationary strategy able to increase this sensitivity.

categories: quant-ph cond-mat.mes-hall gr-qc physics.ins-det


title: Why Quantum Theory?

abstract:
  The usual formulation of quantum theory is rather abstract. In recent work I
have shown that we can, nevertheless, obtain quantum theory from five
reasonable axioms. Four of these axioms are obviously consistent with both
classical probability theory and quantum theory. The remaining axiom requires
that there exists a continuous reversible transformation between any two pure
states. The requirement of continuity rules out classical probability theory.
In this paper I will summarize the main points of this new approach. I will
leave out the details of the proof that these axioms are equivalent to the
usual formulation of quantum theory (for these see quant-ph/0101012).


title: Quantum computing classical physics

abstract:
  In the past decade quantum algorithms have been found which outperform the
best classical solutions known for certain classical problems as well as the
best classical methods known for simulation of certain quantum systems. This
suggests that they may also speed up the simulation of some classical systems.
I describe one class of discrete quantum algorithms which do so--quantum
lattice gas automata--and show how to implement them efficiently on standard
quantum computers.


title: Quantum systems as classical systems

abstract:
  A characteristical property of a classical physical theory is that the
observables are real functions taking an exact outcome on every (pure) state;
in a quantum theory, at the contrary, a given observable on a given state can
take several values with only a predictable probability. However, even in the
classical case, when an observer is intrinsically unable to distinguish between
some distinct states he can convince himself that the measure of its
''observables'' can have several values in a random way with a statistical
character. What kind of statistical theory is obtainable in this way? It is
possible, for example, to obtain exactly the statistical previsions of quantum
mechanics? Or, in other words, can a physical system showing a classical
behaviour appear to be a quantum system to a confusing observer? We show that
from a mathematical viewpoint it is not difficult to produce a theory with
hidden variables having this property. We don't even try to justify in physical
terms the artificial construction we propose; what we do is to give a general
and rigorous argument showing how the interplay between the classical and
quantum mechanics we offer is interpretable as the difference between an
imaginary very expert observer and another nonexpert observer. This proves also
that besides the well known theorems concerning the impossibility of hidden
variables (cfr. Von Neumann [Neu] and Jauch-Piron [J-P]) there is also room for
a result in favor of the possibility.


title:
Quantum Structures: An Attempt to Explain the Origin of their Appearance
  in Nature

abstract:
  We explain the quantum structure as due to the presence of two effects, (a) a
real change of state of the entity under influence of the measurement and, (b)
a lack of knowledge about a deeper deterministic reality of the measurement
process. We present a quantum machine, where we can illustrate in a simple way
how the quantum structure arises as a consequence of the two mentioned effects.
We introduce a parameter epsilon that measures the size of the lack of
knowledge on the measurement process, and by varying this parameter, we
describe a continuous evolution from a quantum structure (maximal lack of
knowledge) to a classical structure (zero lack of knowledge). We show that for
intermediate values of epsilon we find a new type of structure, that is neither
quantum nor classical. We apply the model that we have introduced to situations
of lack of knowledge about the measurement process appearing in other regions
of reality. More specifically we investigate the quantum-like structures that
appear in the situation of psychological decision processes, where the subject
is influenced during the testing, and forms some of his opinions during the
testing process. Our conclusion is that in the light of this explanation, the
quantum probabilities are epistemic and not ontological, which means that
quantum mechanics is compatible with a determinism of the whole.


title: Probability and the Many-Worlds Interpretation of Quantum Theory

abstract:
  Two works related to the concept of probability in the framework of the
many-worlds interpretation are presented. The first deals with recent
controversy in classical probability theory. Elga and D. Lewis argues that
Sleeping Beauty should have different credences for the result of a fair coin
toss in a particular situation. It is argued that when the coin is replaced by
a quantum coin, the credence is unambiguous and since one should not expect a
difference between classical and quantum coins, this provides a particular
resolution of the controversy. Second work is an analysis of a recent criticism
by Byrne and Hall of Everett-type approach presented by Chalmers. It is shown
that the criticism has no universal validity and that the Byrne and Hall
rejection of any Everett-type interpretation of quantum mechanics is unfounded.


title: A Practical Trojan Horse for Bell-inequality-based Quantum Cryptography

abstract:
  Quantum Cryptography, or more accurately, Quantum Key Distribution (QKD) is
based on using an unconditionally secure ``quantum channel'' to share a secret
key among two users. A manufacturer of QKD devices could, intentionally or not,
use a (semi-)classical channel instead of the quantum channel, which would
remove the supposedly unconditional security. One example is the BB84 protocol,
where the quantum channel can be implemented in polarization of single photons.
Here, use of several photons instead of one to encode each bit of the key
provides a similar but insecure system. For protocols based on violation of a
Bell inequality (e.g., the Ekert protocol) the situation is somewhat different.
While the possibility is mentioned by some authors, it is generally thought
that an implementation of a (semi-)classical channel will differ significantly
from that of a quantum channel. Here, a counterexample will be given using an
identical physical setup as is used in photon-polarization Ekert QKD. Since the
physical implementation is identical, a manufacturer may include this
modification as a Trojan Horse in manufactured systems, to be activated at will
by an eavesdropper. Thus, the old truth of cryptography still holds: you have
to trust the manufacturer of your cryptographic device. Even when you do
violate the Bell inequality.


title:
A mechanistic macroscopic physical entity with a three-dimensional
  Hilbert space description

abstract:
  It is sometimes stated that Gleason's theorem prevents the construction of
hidden-variable models for quantum entities described in a more than
two-dimensional Hilbert space. In this paper however we explicitly construct a
classical (macroscopical) system that can be represented in a three-dimensional
real Hilbert space, the probability structure appearing as the result of a lack
of knowledge about the measurement context. We briefly discuss Gleason's
theorem from this point of view.


title: Optical Holonomic Quantum Computation

abstract:
  Holonomic quantum computation (HQC) is materialized here with quantum optics
components. Holonomies are the generalization of the Berry phases to unitary
matrices with dimensionality the same as the degree of degeneracy of the
system. In a nonlinear Kerr medium the degenerate states of laser beams are
interpreted as qubits. Control manipulations with displacers, squeezers and
two-mode interfering devices performed in a cyclic, adiabatic fashion produce
holonomies. Here, they are employed as logical gates for our HQC proposal. The
effects of errors from imperfect control of classical parameters, the looping
variation of which builds up holonomic gates, are investigated.


title:
The Sasaki Hook is not a [Static] Implicative Connective but Induces a
  Backward [in Time] Dynamic One that Assigns Causes

abstract:
  In this paper we argue that the Sasaki adjunction, which formally encodes the
logicality that different authors tried to attach to the Sasaki hook as a
`quantum implicative connective', has a fundamental dynamic nature and encodes
the so-called `causal duality' (Coecke, Moore and Stubbe 2001;
quant-ph/0009100) for the particular case of a quantum measurement with a
projector as corresponding self-adjoint operator. In particular: The action of
the Sasaki hook $(a\stackrel{S}{\to}-)$ for fixed antecedent $a$ assigns to
some property ``the weakest cause before the measurement of actuality of that
property after the measurement'', i.e. ${(a\stackrel{S}{\to}b)}$ is the weakest
property that guarantees actuality of $b$ after performing the measurement
represented by the projector that has the `subspace $a$' as eigenstates for
eigenvalue 1, say, the measurement that `tests' $a$ . From this we conclude
that the logicality attributable to quantum systems contains a fundamentally
dynamic ingredient: Causal duality actually provides a new dynamic
interpretation of orthomodularity. We also reconsider the status of the Sasaki
hook within `dynamic (operational) quantum logic' (DOQL). We can derive two
labeled dynamic hooks (forwardly and backwardly) that encode how quantum
measurements act on properties. In an even more radical perspective one could
say that the transition from either classical or constructive/intuitionistic
logic to quantum logic entails besides the introduction of an additional unary
connective `operational resolution' (Coecke 2001a; math.LO/0011208) the shift
from a binary connective implication to a ternary connective where two of the
arguments refer to qualities of the system and the third, the new one, to an
obtained outcome (in a measurement).


title:
Universal quantum computation with two- and three-qubit projective
  measurements

abstract:
  We present a finite set of projective measurements that, together with
quantum memory and preparation of the |0> state, suffice for universal quantum
computation. This extends work of Nielsen [quant-ph/0108020], who proposed a
scheme in which an arbitrary unitary operation on n qubits can be simulated
using only projective measurements on at most 2n qubits. All measurements in
our set involve two qubits, except two measurements which involve three qubits.
Thus we improve by one the upper bound, implied by Nielsen's results, on the
maximum number of qubits needed to participate in any single measurement to
achieve universal quantum computation. Each of our measurements is two-valued,
and each can be expressed mathematically as a Boolean combination of
single-qubit measurements.


title: Chow's theorem and universal holonomic quantum computation

abstract:
  A theorem from control theory relating the Lie algebra generated by vector
fields on a manifold to the controllability of the dynamical system is shown to
apply to Holonomic Quantum Computation. Conditions for deriving the holonomy
algebra are presented by taking covariant derivatives of the curvature
associated to a non-Abelian gauge connection. When applied to the Optical
Holonomic Computer, these conditions determine that the holonomy group of the
two-qubit interaction model contains $SU(2) \times SU(2)$. In particular, a
universal two-qubit logic gate is attainable for this model.


title: Quantum Teleportation and Entanglement Swapping for Spin Systems

abstract:
  We analyse quantum teleportation (QT) and entanglement swapping (ES) for spin
systems. If the permitted operations are restricted to the Ising interaction,
plus local rotations and spin measurements, high-fidelity teleportation is
achievable for quantum states that are close to the maximally weighted spin
state. ES is achieved, and is maximized for a combination of entangled states
and Bell measurements that is different from the QT case. If more general local
unitary transformations are considered, then it is possible to achieve perfect
teleportation and ES.


title: Stabilizer codes can be realized as graph codes

abstract:
  We establish the connection between a recent new construction technique for
quantum error correcting codes, based on graphs, and the so-called stabilizer
codes: Each stabilizer code can be realized as a graph code and vice versa.


title: Reply to K A Kirkpatrick

abstract:
  This is a reply to an article with the same title in which Kirkpatrick
claimed that the considerations I put forward some thirty years ago on quantum
mixtures are incorrect. It is shown here that Kirkpatrick's reasoning is
erroneous.


title: Measuring quantum entanglement without prior state reconstruction

abstract:
  It is shown that, despite strong nonlinearity, entanglement of formation of
two-qubit state can be measured without prior state reconstruction. Collective
measurements on small number of copies are provided that allow to determine
quantum concurrence {\it via} estimation of only {\it four} parameters. It is
also pointed out that another entanglement measure based on so called
negativity can also be measured in similar way. The result is related to
general problem: what kind of information can be extracted efficiently from
unknown quantum state ?


title: Quantum Theory finally reconciled with Special Relativity

abstract:
  In 1935 Einstein, Podolsky and Rosen (EPR) pointed out that Quantum Mechanics
apparently implied some mysterious, instantaneous action at a distance. This
paradox is supposed to be related to the probabilistic nature of the theory,
but since deterministic alternatives involving "Hidden Variables" hardly agree
with the experiments, the scientific community is now accepting this ``quantum
nonlocality" as if it were a reality. However, I have argued recently that
Quantum Electrodynamics is free from the EPR paradox, due to an indetermination
on the number of the unobserved "soft photons" that can be present in any step
of any experiment. Here, I will provide a more general proof, based on an
approach to the "problem of measurement" that implies the full reconciliation
of Quantum Field Theory with Special Relativity. I will then conclude with some
considerations on the interpretation of the Quantum Theory itself.


title:
Quantum operations that cannot be implemented using a small mixed
  environment

abstract:
  To implement any quantum operation (a.k.a. ``superoperator'' or ``CP map'')
on a d-dimensional quantum system, it is enough to apply a suitable overall
unitary transformation to the system and a d^2-dimensional environment which is
initialized in a fixed pure state. It has been suggested that a d-dimensional
environment might be enough if we could initialize the environment in a mixed
state of our choosing. In this note we show with elementary means that certain
explicit quantum operations cannot be realized in this way. Our counterexamples
map some pure states to pure states, giving strong and easily manageable
conditions on the overall unitary transformation. Everything works in the more
general setting of quantum operations from d-dimensional to d'-dimensional
spaces, so we place our counterexamples within this more general framework.


title: Some bounds for quantum copying with multiple copies

abstract:
  We study the relative error of the state-dependent N=>L cloning. A copying
transformation and dimension of state space are not specified. Only the
unitarity of quantum mechanical transformations is used. The proposed approach
is based on the notion of the angle between two states. Firstly, the notion of
the angle between two states is discussed. The lower bound on the relative
error of copying with multiple copies is examined. In addition, the lower bound
on the absolute error is then studied. We compare the obtained bounds with the
case of maximizing the global fidelity.


title: Geometric Manipulation of Trapped Ions for Quantum Computation

abstract:
  We propose an experimentally feasible scheme to achieve quantum computation
based solely on geometric manipulations of a quantum system. The desired
geometric operations are obtained by driving the quantum system to undergo
appropriate adiabatic cyclic evolutions. Our implementation of the
all-geometric quantum computation is based on laser manipulation of a set of
trapped ions. An all-geometric approach, apart from its fundamental interest,
promises a possible way for robust quantum computation.


title: Equivalent efficiency of a simulated photon-number detector

abstract:
  Homodyne detection is considered as a way to improve the efficiency of
communication near the single-photon level. The current lack of commercially
available {\it infrared} photon-number detectors significantly reduces the
mutual information accessible in such a communication channel. We consider
simulating direct detection via homodyne detection. We find that our particular
simulated direct detection strategy could provide limited improvement in the
classical information transfer. However, we argue that homodyne detectors (and
a polynomial number of linear optical elements) cannot simulate photocounters
arbitrarily well, since otherwise the exponential gap between quantum and
classical computers would vanish.


title: Quantum computation with trapped ions in an optical cavity

abstract:
  Two-qubit logical gates are proposed on the basis of two atoms trapped in a
cavity setup. Losses in the interaction by spontaneous transitions are
efficiently suppressed by employing adiabatic transitions and the Zeno effect.
Dynamical and geometrical conditional phase gates are suggested. This method
provides fidelity and a success rate of its gates very close to unity. Hence,
it is suitable for performing quantum computation.


title:
SO(3,2) structure and distributions of two-component Bose-Einstein
  condensate with lower excitations

abstract:
  The wave function describing two-component Bose-Einstein condensate with
weakly excitations has been found, by using the SO(3,2) algebraic mean-field
approximation. We show that the two-component modified BEC (see eq.(\ref{ga}))
possesses uniquely super-Poissonian distribution in a fixed magnetic field
along z-direction. The distribution will be uncertain, if B=0.


title: Backwards-induction outcome in a quantum game

abstract:
  In economics duopoly is a market dominated by two firms large enough to
influence the market price. Stackelberg presented a dynamic form of duopoly
that is also called `leader-follower' model. We give a quantum perspective on
Stackelberg duopoly that gives a backwards-induction outcome same as the Nash
equilibrium in static form of duopoly also known as Cournot's duopoly. We find
two qubit quantum pure states required for this purpose.


title:
Quantum key distribution for d-level systems with generalized Bell
  states

abstract:
  Using the generalized Bell states and controlled not gates, we introduce an
enatanglement-based quantum key distribution (QKD) of d-level states (qudits).
In case of eavesdropping, Eve's information gain is zero and a quantum error
rate of (d-1)/d is introduced in Bob's received qudits, so that for large d,
comparison of only a tiny fraction of received qudits with the sent ones can
detect the presence of Eve.


title:
Quantum phase gate for photonic qubits using only beam splitters and
  post-selection

abstract:
  We show that a beam splitter of reflectivity one-third can be used to realize
a quantum phase gate operation if only the outputs conserving the number of
photons on each side are post-selected.


title: Entanglement transfer from dissociated molecules to photons

abstract:
  We introduce and study the concept of a reversible transfer of the quantum
state of two internally-translationally entangled fragments, formed by
molecular dissociation, to a photon pair. The transfer is based on intracavity
stimulated Raman adiabatic passage and it requires a combination of processes
whose principles are well established.


title: Two Slits Interference Is Compatible with Particles' Trajectories

abstract:
  We propose a simple numerical experiment of two slits interference of
particles. It disproves the popular belief that such an interference is
incompatible with a knowledge which slit each particle came through or, more
generally, ``quantum particles could not have trajectories''. Our model is an
illustration to the contextual interpretation of quantum probabilities.


title:
Efficient and robust entanglement generation in a many-particle system
  with resonant dipole-dipole interactions

abstract:
  We propose and discuss a scheme for robust and efficient generation of
many-particle entanglement in an ensemble of Rydberg atoms with resonant
dipole-dipole interactions. It is shown that in the limit of complete dipole
blocking, the system is isomorphic to a multimode Jaynes-Cummings model. While
dark-state population transfer is not capable of creating entanglement, other
adiabatic processes are identified that lead to complex, maximally entangled
states, such as the N-particle analog of the GHZ state in a few steps. The
process is robust, works for even and odd particle numbers and the
characteristic time for entanglement generation scales with N^a, with a being
less than unity.


title: The Parallel Principle

abstract:
  Von Neumann's psycho-physical parallelism requires the existence of an
interaction between subjective experiences and material systems. A hypothesis
is proposed that amends physics in a way that connects subjective states with
physical states, and a general model of the interaction is provided. A specific
example shows how the theory applies to pain consciousness. The implications
concerning quantum mechanical state creation and reduction are discussed, and
some mechanisms are suggested to seed the process. An experiment that tests the
hypothesis is described elsewhere. Key Words: von Neumann, psycho-physical,
consciousness, state reduction, state collapse, macroscopic superpositions,
conscious observer.


title: A proposal for founding mistrustful quantum cryptography on coin tossing

abstract:
  A significant branch of classical cryptography deals with the problems which
arise when mistrustful parties need to generate, process or exchange
information. As Kilian showed a while ago, mistrustful classical cryptography
can be founded on a single protocol, oblivious transfer, from which general
secure multi-party computations can be built.
  The scope of mistrustful quantum cryptography is limited by no-go theorems,
which rule out, inter alia, unconditionally secure quantum protocols for
oblivious transfer or general secure two-party computations. These theorems
apply even to protocols which take relativistic signalling constraints into
account. The best that can be hoped for, in general, are quantum protocols
computationally secure against quantum attack. I describe here a method for
building a classically certified bit commitment, and hence every other
mistrustful cryptographic task, from a secure coin tossing protocol. No
security proof is attempted, but I sketch reasons why these protocols might
resist quantum computational attack.


title: Approximate Quantum Cloning with Nuclear Magnetic Resonance

abstract:
  Here we describe a Nuclear Magnetic Resonance (NMR) experiment that uses a
three qubit NMR device to implement the one to two approximate quantum cloning
network of Buzek et al.


title: Quantum Bit String Commitment

abstract:
  A bit string commitment protocol securely commits $N$ classical bits in such
a way that the recipient can extract only $M<N$ bits of information about the
string. Classical reasoning might suggest that bit string commitment implies
bit commitment and hence, given the Mayers-Lo-Chau theorem, that
non-relativistic quantum bit string commitment is impossible. Not so: there
exist non-relativistic quantum bit string commitment protocols, with security
parameters $\epsilon$ and $M$, that allow $A$ to commit $N = N(M, \epsilon)$
bits to $B$ so that $A$'s probability of successfully cheating when revealing
any bit and $B$'s probability of extracting more than $N'=N-M$ bits of
information about the $N$ bit string before revelation are both less than
$\epsilon$. With a slightly weakened but still restrictive definition of
security against $A$, $N$ can be taken to be $O(\exp (C N'))$ for a positive
constant $C$. I briefly discuss possible applications.


title: From Quantum Cheating to Quantum Security

abstract:
  For thousands of years, code-makers and code-breakers have been competing for
supremacy. Their arsenals may soon include a powerful new weapon: quantum
mechanics. We give an overview of quantum cryptology as of November 2000.


title: Dynamic and Geometric Phase Formulasin the Hestenes-Dirac Theory

abstract:
  We examine the dynamic and geometric phases of the electron in quantum
mechanics using Hestenes' spacetime algebra formalism. First the standard
dynamic phase formula is translated into the spacetime algebra. We then define
new formulas for the dynamic and geometric phases that can be used in Hestenes'
formalism.


title: Quantum Lower Bound for the Collision Problem

abstract:
  The collision problem is to decide whether a function X:{1,..,n}->{1,..,n} is
one-to-one or two-to-one, given that one of these is the case. We show a lower
bound of Theta(n^{1/5}) on the number of queries needed by a quantum computer
to solve this problem with bounded error probability. The best known upper
bound is O(n^{1/3}), but obtaining any lower bound better than Theta(1) was an
open problem since 1997. Our proof uses the polynomial method augmented by some
new ideas. We also give a lower bound of Theta(n^{1/7}) for the problem of
deciding whether two sets are equal or disjoint on a constant fraction of
elements. Finally we give implications of these results for quantum complexity
theory.


title: Semiclassical approach to tunneling through a double barrier structure

abstract:
  We consider a symmetric double barrier heterostructure enclosing a well and
propose a solution for the transmission problem using a generalized WKB
approach which accounts for the amplitude suppression and phase shift due to
the barriers. This approach allows us to address both off-resonance and
resonance cases and, in the latter case, verify the coherent destruction of
tunneling.


title: Two-component Fermi gas in a one-dimensional harmonic trap

abstract:
  A many body theory for a two-component system of spin polarized interacting
fermions in a one-dimensional harmonic trap is developed. The model considers
two different states of the same fermionic species and treats the dominant
interactions between the two using the bosonization method for forward
scattering. Asymptotically exact results for the one-particle matrix elements
at zero temperature are given. Using them, occupation probabilities of
oscillator states are discussed. Particle and momentum densities are calculated
and displayed. It is demonstrated how interactions modify all these quantities.
An asymptotic connection with Luttinger liquids is suggested. The relation of
the coupling constant of the theory to the dipole-dipole interaction is also
discussed.


title: To the nonlinear quantum mechanics

abstract:
  The Schroedinger equation with the nonlinear term is derived by the natural
generalization of the hydrodynamical model of quantum mechanics. The nonlinear
term appears to be logically necessary because it enables explanation of the
classical limit of the wave function, the collaps of the wave function and
solves the Schroedinger cat paradox.


title: Secure communication with a publicly known key

abstract:
  We present a scheme for direct and confidential communication between Alice
and Bob, where there is no need for establishing a shared secret key first, and
where the key used by Alice even will become known publicly. The communication
is based on the exchange of single photons and each and every photon transmits
one bit of Alice's message without revealing any information to a potential
eavesdropper.


title:
Structural physical approximations of unphysical maps and generalized
  quantum measurements

abstract:
  We investigate properties of the structural physical approximation (SPA) of
the partial transposition map recently introduced by Horodecki and Ekert
[quant-ph/0111064]. We focus on the case of two-qubit states and show that in
this case the map has the structure of a generalized quantum measurement
followed by preparation of a suitable output state. We also introduce SPA for
map that transforms two copies of density matrix of a single qubit onto a
square of that matrix. We prove that also this map is essentially a generalized
quantum measurement.


title: Modified Grover's algorithm for an expectation value quantum computer

abstract:
  The translation of Grover's search algorithm from its standard version,
designed for implementation on a single quantum system amenable to projective
measurements, into one suitable for an ensemble of quantum computers, whose
outputs are expectation values of observables, is described in detail. A
filtering scheme, which effectively determines expectation values on a limited
portion of the quantum state, is presented and used to locate a single item for
searches involving more than one marked item. A truncated version of Grover's
algorithm, requiring fewer steps than the translated standard version but
locating marked items just as successfully, is proposed. For quantum
computational devices which only return expectation values, the truncated
version is superior to its standard counterpart. This indicates that it is
possible to modify quantum algorithms so as to reduce the required temporal
resources by using the ensemble's spatial resources.


title: Effects of noisy entangled state transmission on quantum teleportation

abstract:
  Quantum teleportation requires the transmission of entangled pairs to Alice
and Bob. Transmission errors modify the entangled state before the
teleportation can be performed. We determine the changes in the output state
caused by such transmission errors. It is shown that the errors caused by
entanglement transmission are equivalent to the errors caused in a direct
transmission of a quantum state from Alice to Bob.


title:
Generating and probing a two-photon Fock state with a single atom in a
  cavity

abstract:
  A two-photon Fock state is prepared in a cavity sustaining a "source mode "
and a "target mode", with a single circular Rydberg atom. In a third-order
Raman process, the atom emits a photon in the target while scattering one
photon from the source into the target. The final two-photon state is probed by
measuring by Ramsey interferometry the cavity light shifts induced by the
target field on the same atom. Extensions to other multi-photon processes and
to a new type of micromaser are briefly discussed.


title:
Interpolating Coherent States for Heisenberg-Weyl and Single-Photon
  SU(1,1) Algebras

abstract:
  New quantal states which interpolate between the coherent states of the
Heisenberg_Weyl and SU(1,1) algebras are introduced. The interpolating states
are obtained as the coherent states of a closed and symmetric algebra which
interpolates between the two algebras. The overcompleteness of the
interpolating coherent states is established. Differential operator
representations in suitable spaces of entire functions are given for the
generators of the algebra. A nonsymmetric set of operators to realize the
Heisenberg-Weyl algebra is provided and the relevant coherent states are
studied.


title:
Management of the Angular Momentum of Light: Preparation of Photons in
  Multidimensional Vector States of Angular

abstract:
  We put forward schemes to prepare photons in multi-dimensional vector states
of orbital angular momentum. We show realizable light distributions that yield
prescribed states with finite or infinite normal modes. In particular, we show
that suitable light vortex-pancakes allow the add-drop of specific vector
projections. We suggest that such photons might allow the generation of it
engineered quNits in multi-dimensional quantum information systems.


title: Irreducibility of n-ary quantum information

abstract:
  Quantum information is radically different from classical information in that
the quantum formalism (Hilbert space) makes necessary the introduction of
irreducible ``nits,'' n being an arbitrary natural number (bigger than one),
not just bits.


title: Relativistic Quantum Newton's Law For A Spinless Particle

abstract:
  For a one-dimensional stationary system, we derive a third order equation of
motion representing a first integral of the relativistic quantum Newton's law.
We then integrate this equation in the constant potential case and calculate
the time spent by a particle tunneling through a potential barrier.


title: Invariant information and quantum state estimation

abstract:
  The invariant information introduced by Brukner and Zeilinger, Phys. Rev.
Lett. 83, 3354 (1999), is reconsidered from the point of view of quantum state
estimation. We show that it is directly related to the mean error of the
standard reconstruction from the measurement of a complete set of mutually
complementary observables. We give its generalization in terms of the Fisher
information. Provided that the optimum reconstruction is adopted, the
corresponding quantity loses its invariant character.


title: A Geometric Picture of Entanglement and Bell Inequalities

abstract:
  We work in the real Hilbert space H_s of hermitian Hilbert-Schmid operators
and show that the entanglement witness which shows the maximal violation of a
generalized Bell inequality (GBI) is a tangent functional to the convex set S
subset H_s of separable states. This violation equals the euclidean distance in
H_s of the entangled state to S and thus entanglement, GBI and tangent
functional are only different aspects of the same geometric picture. This is
explicitly illustrated in the example of two spins, where also a comparison
with familiar Bell inequalities is presented.


title:
Larmor precession and tunneling time of a relativistic neutral spinning
  particle through an arbitrary potential barrier

abstract:
  The Larmor precession of a relativistic neutral spin-1/2 particle in a
uniform constant magnetic field confined to the region of a one-dimensional
arbitrary potential barrier is investigated. The spin precession serves as a
clock to measure the time spent by a quantum particle traversing a potential
barrier. With the help of general spin coherent state it is explicitly shown
that the precession time is equal to the dwell time.


title: Incompleteness, Complexity, Randomness and Beyond

abstract:
  Goedel's Incompleteness Theorems have the same scientific status as
Einstein's principle of relativity, Heisenberg's uncertainty principle, and
Watson and Crick's double helix model of DNA. Our aim is to discuss some new
faces of the incompleteness phenomenon unveiled by an information-theoretic
approach to randomness and recent developments in quantum computing.


title: EPR Type Nonlocality in Classical Electrodynamics!

abstract:
  It is shown that classical electrodynamics in its alternative
Kemmer-Duffin-Petiau-Harish-Chandra formulation surprisingly reveals a Hilbert
space structure leading to the possibility of entangled states of classical
radiation, and this in turn implies the violation of Einstein-Bell locality in
spite of Lorentz invariance.


title: Quantum-Statistical Computation

abstract:
  Systems of spin 1, such as triplet pairs of spin-1/2 fermions (like
orthohydrogen nuclei) make useful three-terminal elements for quantum
computation, and when interconnected by qubit equality relations are universal
for quantum computation. This is an instance of quantum-statistical
computation: some of the logical relations of the problem are satisfied
identically in virtue of quantum statistics, which takes no time. We show
heuristically that quantum-statistical ground-mode computation is substantially
faster than pure ground-mode computation when the ground mode is reached by
annealing.


title: Relativistic Quantum Newton's Law and photon trajectories

abstract:
  Using the relativistic quantum Hamilton-Jacobi equation within the framework
of the equivalence postulate, and grounding one self on both relativistic and
quantum Lagrangians, we construct a Lagrangian of relativistic quantum system
in one dimension and derive a third order equation of motion representing a
first integral of the relativistic quantum Newton's law. Then, we investigate
the free particle case and establish the photon's trajectories.


title: Two-qubit Projective Measurements are Universal for Quantum Computation

abstract:
  Nielsen [quant-ph/0108020] showed that universal quantum computation is
possible given quantum memory and the ability to perform projective
measurements on up to 4-qubits. We describe an improved method that requires
only 2-qubit measurements, which are both sufficient and necessary. We present
a method to partially collapse the $C_k$-hierarchy in the indirect construction
of unitary gates [Gottesman and Chuang, Nature, {\bf 402} 309 (1999)], and
apply the method to find discrete universal sets of 2-qubit measurements.


title: Observable Dirac-type singularities in Berry's phase and the monopole

abstract:
  The physical reality and observability of 2n\pi Berry phases, as opposed to
the usually considered modulo 2\pi topological phases is demonstrated with the
help of computer simulation of a model adiabatic evolution whose parameters are
varied along a closed loop in the parameter space. Using the analogy of Berry's
phase with the Dirac monopole, it is concluded that an interferometer loop
taken around a magnetic monopole of strength n/2 yields an observable 2n\pi
phase shift, where n is an integer. An experiment to observe the effect is
proposed.


title: Instantaneous measurement of non-local variables

abstract:
  It is shown, under the assumption of possibility to perform an arbitrary
local operation, that all nonlocal variables related to two or more separate
sites can be measured instantaneously, except for a finite time required for
bringing to one location the classical records from these sites which yield the
result of the measurement. It is a verification measurement: it yields reliably
the eigenvalues of the nonlocal variables, but it does not prepare the
eigenstates of the system.


title:
Quantum irreversibility, perturbation independent decay, and the
  parametric theory of the local density of states

abstract:
  The idea of perturbation independent decay (PID) has appeared in the context
of survival-probability studies, and lately has emerged in the context of
quantum irreversibility studies. In both cases the PID reflects the Lyapunov
instability of the underlying semiclassical dynamics, and it can be
distinguished from the Wigner-type decay that holds in the perturbative regime.
The theory of the survival probability is manifestly related to the parametric
theory of the local density of states (LDOS). In this Paper we demonstrate that
in spite of the common "ideology", the physics of quantum irreversibility is
{\em not} trivially related to the parametric theory of the LDOS. Rather, it is
essential to take into account subtle cross correlations which are not captured
by the LDOS alone.


title:
Intensity-intensity correlations as a probe of interferences - under
  conditions of none in the intensity

abstract:
  The different behaviour of first order interferences and second order
correlations are investigated for the case of two coherently excited atoms. For
intensity measurements this problem is equivalent to Young's double slit
experiment and was investigated in an experiment by Eichmann et al. [Phys. Rev.
Lett. 70, 2359 (1993)] and later analyzed in detail by Itano et al. [Phys. Rev.
A 57, 4176 (1998)]. Our results show that in cases where the intensity
interferences disappear the intensity-intensity correlations can display an
interference pattern with a visibility of up to 100%. The contrast depends on
the polarization selected for the detection and is independent of the strength
of the driving field. The nonclassical nature of the calculated
intensity-intensity correlations is also discussed.


title: Gain tuning and fidelity in continuous variable quantum teleportation

abstract:
  The fidelity of continuous variable teleportation can be optimized by
changing the gain in the modulation of the output field. We discuss the gain
dependence of fidelity for coherent, vacuum and one photon inputs and propose
optimal gain tuning strategies for corresponding input selections.


title: Deformed versus undeformed cat states encoding qubit

abstract:
  We study the possibility of exploiting superpositions of coherent states to
encode qubit. A comparison between the use of deformed and undeformed bosonic
algebra is made in connection with the amplitude damping errors.


title: Temporal imperfections building up correcting codes

abstract:
  We address the timing problem in realizing correcting codes for quantum
information processing. To deal with temporal uncertainties we employ a
consistent quantum mechanical approach. The conditions for optimizing the
effect of error correction in such a case are determined.


title: Dialogue on Classical and Quantum between mathematician and experimenter

abstract:
  This dialogue took place at V\"axj\"o, 19 November 2001. The main aim of our
meeting in V\"axj\"o was to clarify our viewpoints on foundations of quantum
mechanics. The most attractive in our discussion was the extreme difference in
our quantum experiences. On one side, pure mathematician (specializing in
foundations of probability theory), Andrei Khrennikov; on the other side, pure
experimenter (specializing in neutron and electron interferometry), Johann
Summhammer. On one hand, an attempt to test mathematical models for larger and
larger domains of physical reality. On the other hand, an attempt to create
this reality from experimental information - roughly speaking from clicks of
detectors.


title:
Numerical simulation of interference experiments in a local hidden
  variables model

abstract:
  We present a theoretical model which allows to keep track of all photons in
an interferometer. The model is implemented in a numerical scheme, and we
simulate photon interference measurements on one, two, four, and eight slits.
Measurements are simulated for the high intensity regime, where we show that
our simulations describe all experimental results so far. With a slightly
modified concept we can also model interference experiments in the low
intensity regime, these experiments have recently been performed with single
molecules. Finally, we predict the result of polarization measurements, which
allow to check the model experimentally.


title: Wannier-Stark resonances in optical and semiconductor superlattices

abstract:
  In this work, we discuss the resonance states of a quantum particle in a
periodic potential plus a static force. Originally this problem was formulated
for a crystal electron subject to a static electric field and it is nowadays
known as the Wannier-Stark problem. We describe a novel approach to the
Wannier-Stark problem developed in recent years. This approach allows to
compute the complex energy spectrum of a Wannier-Stark system as the poles of a
rigorously constructed scattering matrix and solves the Wannier-Stark problem
without any approximation. The suggested method is very efficient from the
numerical point of view and has proven to be a powerful analytic tool for
Wannier-Stark resonances appearing in different physical systems such as
optical lattices or semiconductor superlattices.


title:
Uniform Finite Generation of Compact Lie Groups and universal quantum
  gates

abstract:
  Consider a compact connected Lie group $G$ and the corresponding Lie algebra
$\cal L$. Let $\{X_1,...,X_m\}$ be a set of generators for the Lie algebra
$\cal L$. We prove that $G$ is uniformly finitely generated by
$\{X_1,...,X_m\}$. This means that every element $K \in G$ can be expressed as
$K=e^{Xt_1}e^{Xt_2} \cdot \cdot \cdot e^{Xt_l}$, where the indeterminates $X$
are in the set $\{X_1,...,X_m \}$, $t_i \in \RR$, $i=1,...,l$, and the number
$l$ is uniformly bounded. This extends a previous result by F. Lowenthal in
that we do not require the connected one dimensional Lie subgroups
corresponding to the $X_i$, $i=1,...,m$, to be compact.
  We discuss the consequence of this result to the question of universality of
quantum gates in quantum computing.


title: Rabi oscillations and macroscopic quantum superposition states

abstract:
  A two-level atom interacting with a single radiation mode is considered,
without the rotating-wave approximation, in the strong coupling regime. It is
shown that, in agreement with the recent results on Rabi oscillations in a
Josephson junction (Y. Nakamura, Yu. A. Pashkin and J. S. Tsai, Phys. Rev.
Lett. {\bf 87}, 246601 (2001)), the Rabi frequency is indeed proportional to
first kind integer order Bessel functions in the limit of a large number of
photons and the dressed states are macroscopic quantum superposition states. To
approach this problem analytically use is made of the dual Dyson series and the
rotating-wave approximation.


title:
Different versions of perturbation expansion based on the
  single-trajectory quadrature method

abstract:
  The newly developed single trajectory quadrature method is applied to a
two-dimensional example. The results based on different versions of new
perturbation expansion and the new Green's function deduced from this method
are compared to each other, also compared to the result from the traditional
perturbation theory. As the first application to higher-dimensional
non-separable potential the obtained result further confirms the applicability
and potential of this new method.


title:
On local indistinguishability of orthogonal pure states by using a bound
  on distillable entanglement

abstract:
  We show that the four states a|00>+b|11>, b^*|00>-a^*|11>, c|01>+d|10> and
d^*|01>-c^*|10> cannot be discriminated with certainty if only local operations
and classical communication (LOCC) are allowed and if only a single copy is
provided, except in the case when they are simply |00>, |11>, |01> and |10> (in
which case they are trivially distinguishable with LOCC). We go on to show that
there exists a continuous range of values of a, b, c and d such that even three
states among the above four are not locally distinguishable, if only a single
copy is provided. The proof follows from the fact that logarithmic negativity
is an upper bound of distillable entanglement.


title:
Information transfer in quantum measurements: irreversibility and
  amplification

abstract:
  The aim of these lectures is to investigate the transfer of information
occurring in course of quantum interactions. In particular, I shall explore
circumstances in which such an information transfer with the quantum
environment of the considered quantum system leads to the destruction of the
phase coherence between the states of the privileged basis in the system
Hilbert space. This basis shall be called the pointer basis. I shall argue that
states of this pointer basis correspond to the ``classical'' states of the
observables of the quantum system in question.


title: Phase-transition-like Behavior of Quantum Games

abstract:
  The discontinuous dependence of the properties of a quantum game on its
entanglement has been shown up to be very much like phase transitions viewed in
the entanglement-payoff diagram [J. Du et al., Phys. Rev. Lett, 88, 137902
(2002)]. In this paper we investigate such phase-transition-like behavior of
quantum games, by suggesting a method which would help to illuminate the origin
of such kind of behavior. For the particular case of the generalized Prisoners'
Dilemma, we find that, for different settings of the numerical values in the
payoff table, even though the classical game behaves the same, the quantum game
exhibits different and interesting phase-transition-like behavior.


title:
Exact positivity of the Wigner and P-functions of a Markovian open
  system

abstract:
  We discuss the case of a Markovian master equation for an open system, as it
is frequently found from environmental decoherence. We prove two theorems for
the evolution of the quantum state. The first one states that for a generic
initial state the corresponding Wigner function becomes strictly positive after
a finite time has elapsed. The second one states that also the P-function
becomes exactly positive after a decoherence time of the same order. Therefore
the density matrix becomes exactly decomposable into a mixture of Gaussian
pointer states.


title: Quantum optical coherence tomography with dispersion cancellation

abstract:
  We propose a new technique, called quantum optical coherence tomography
(QOCT), for carrying out tomographic measurements with dispersion-cancelled
resolution. The technique can also be used to extract the frequency-dependent
refractive index of the medium. QOCT makes use of a two-photon interferometer
in which a swept delay permits a coincidence interferogram to be traced. The
technique bears a resemblance to classical optical coherence tomography (OCT).
However, it makes use of a nonclassical entangled twin-photon light source that
permits measurements to be made at depths greater than those accessible via
OCT, which suffers from the deleterious effects of sample dispersion. Aside
from the dispersion cancellation, QOCT offers higher sensitivity than OCT as
well as an enhancement of resolution by a factor of 2 for the same source
bandwidth. QOCT and OCT are compared using an idealized sample.


title: Reconsideration of quantum measurements

abstract:
  The usual conjectures of quantum measurements approaches, inspired from the
traditional interpretation of Heisenberg's ("uncertainty") relations, are
proved as being incorrect. A group of reconsidered conjectures and a
corresponding new approach are set forth. The quantum measurements, regarded
experimentally as statistical samplings, are described theoretically by means
of linear integral transforms of quantum probability density and current, from
intrinsic into recorded readings. Accordingly, the quantum observables appear
as random variables, valuable, in both readings, through probabilistic
numerical parameters (characteristics). The measurements uncertainties (errors)
are described by means of the intrinsic-recorded changes for the alluded
parameters or for the informational entropies. The present approach, together
with other author's investigations, give a natural and unified reconsideration
of primary problems of Heisenberg's relations and quantum measurements. The
respective reconsideration can offer some nontrivial elements for an expected
re-examination of some disputed subsequent questions regarding the foundations
and interpretation of quantum mechanics.


title:
Quantum Stationary Hamilton Jacobi Equation in 3-D for symmetrical
  potentials. Introduction of the Spin

abstract:
  We establish the quantum stationary Hamilton-Jacobi equation in 3-D and its
solutions for three symmetrical potentials, Cartesian symmetry potential,
spherical symmetry potential and cylindrical symmetry potential. For the two
last potentials, a new interpretation of the Spin is proposed within the
framework of trajectory representation.


title: Quantum non-locality in two three-level systems

abstract:
  Recently a new Bell inequality has been introduced (CGLMP,KKCZO) that is
strongly resistant to noise for maximally entangled states of two
$d$-dimensional quantum systems. We prove that a larger violation, or
equivalently a stronger resistance to noise, is found for a non-maximally
entangled state. It is shown that the resistance to noise is not a good measure
of non-locality and we introduce some other possible measures. The
non-maximally entangled state turns out to be more robust also for these
alternative measures. From these results it follows that two Von Neumann
measurements per party may be not optimal for detecting non-locality. For
$d=3,4$, we point out some connections between this inequality and
distillability. Indeed, we demonstrate that any state violating it, with the
optimal Von Neumann settings, is distillable.


title: Extension of quantum information theory to curved spacetimes

abstract:
  The representation of measurements by positive operator valued measures and
the description of the most general state transformations by means of
completely positive maps are two basic concepts of quantum information theory.
These concepts can be trivially extended to field theories in curved spacetime
if all the representations of canonical commutation or anticommutation
relations are unitarily equivalent. We show that both concepts can be applied
even when there is no such unitary equivalence.


title: Anisotropy of Electrons Accelerated by a High-Intensity Laser Pulse

abstract:
  We describe a realistic model for a focused high-intensity laser pulse in
three dimensions. Relativistic dynamics of an electron submitted to such pulse
is described by equations of motion with ponderomotive potential depending on a
single free parameter in the problem, which we refer to as the "asymmetry
parameter". It is shown that the asymmetry parameter can be chosen to provide
quantitative agreement of the developed theory with experimental results of
Malka et al. [Phys. Rev. Lett. 78, 3314 (1997)] who detected angular asymmetry
in the spatial pattern of electrons accelerated in vacuum by a high-intensity
laser pulse.


title: The Majorization Arrow in Quantum Algorithm Design

abstract:
  We apply majorization theory to study the quantum algorithms known so far and
find that there is a majorization principle underlying the way they operate.
Grover's algorithm is a neat instance of this principle where majorization
works step by step until the optimal target state is found. Extensions of this
situation are also found in algorithms based in quantum adiabatic evolution and
the family of quantum phase-estimation algorithms, including Shor's algorithm.
We state that in quantum algorithms the time arrow is a majorization arrow.


title: Quantum Information Processing in Strongly Detuned Optical Cavities

abstract:
  We demonstrate that quantum information processing can be implemented with
ions trapped in a far detuned optical cavity. For sufficiently large detuning
the system becomes insensitive to cavity decay. Following recent experimental
progress, this scheme can be implemented with currently available technology.


title: Stabilization of impurity states in crossed magnetic and electric fields

abstract:
  It is shown that the renormalizability of the zero-range interaction in the
two-dimensional space is always followed by the existence of a bound state,
which is not true for odd-dimensional spaces. A renormalization procedure is
defined and the exact retarded Green's function for electrons moving in two
dimensions and interacting with both crossed magnetic and electric fields and
an attractive zero-range interaction is constructed. Imaginary parts of poles
of this Green's function determine lifetimes of quasi-bound (resonance) states.
It is shown that for some particular parameters the stabilization against decay
occurs even for strong electric fields.


title: Quantum state conversion by cross-Kerr interaction

abstract:
  A generalized Mach-Zehnder-type interferometer equipped with cross-Kerr
elements is proposed to convert N-photon truncated single-mode quantum states
into (N+1)-mode single-photon states, which are suitable for further state
manipulation by means of beam splitter arrays and ON/OFF-detections, and vice
versa. Applications to the realization of unitary and non-unitary
transformations, quantum state reconstruction, and quantum telemanipulation are
studied.


title: Flower-like squeezing in the motion of a laser-driven trapped ion

abstract:
  We investigate the Nth order amplitude squeezing in the fan-state |\xi
;2k,f>_F which is a linear superposition of the 2k-quantum nonlinear coherent
states. Unlike in usual states where an ellipse is the symbol of squeezing, a
4k-winged flower results in the fan state. We first derive the analytical
expression of squeezing for arbitrary k, N, f and then study in detail the case
of a laser-driven trapped ion characterized by a specific form of the nonlinear
function f. We show that the lowest order in which squeezing may appear and the
number of directions along which the amplitude may be squeezed depend only on k
whereas the precise directions of squeezing are determined also by the other
physical parameters involved. Finally, we present a scheme to produce such
fan-states.


title: Coherent States from Combinatorial Sequences

abstract:
  We construct coherent states using sequences of combinatorial numbers such as
various binomial and trinomial numbers, and Bell and Catalan numbers. We show
that these states satisfy the condition of the resolution of unity in a natural
way. In each case the positive weight functions are given as solutions of
associated Stieltjes or Hausdorff moment problems, where the moments are the
combinatorial numbers.


title:
Local Realistic Model for the Dynamics of Bulk-Ensemble NMR Information
  Processing

abstract:
  We construct a local realistic hidden-variable model that describes the
states and dynamics of bulk-ensemble NMR information processing up to about 12
nuclear spins. The existence of such a model rules out violation of any Bell
inequality, temporal or otherwise, in present high-temperature, liquid-state
NMR experiments. The model does not provide an efficient description in that
the number of hidden variables grows exponentially with the number of nuclear
spins.


title: General impossible operations in quantum information

abstract:
  We prove a general limitation in quantum information that unifies the
impossibility principles such as no-cloning and no-anticloning. Further, we
show that for an unknown qubit one cannot design a universal Hadamard gate for
creating equal superposition of the original and its complement state.
Surprisingly, we find that Hadamard transformations exist for an unknown qubit
chosen either from the polar or equatorial great circles. Also, we show that
for an unknown qubit one cannot design a universal unitary gate for creating
unequal superpositions of the original and its complement state. We discuss why
it is impossible to design a controlled-NOT gate for two unknown qubits and
discuss the implications of these limitations.


title:
Reconstructing the formalism of quantum mechanics in the ``contextual
  objectivity" point of view

abstract:
  In a previous preprint (quant-ph/0012122) we introduced a ``contextual
objectivity" formulation of quantum mechanics (QM). A central feature of this
approach is to define the quantum state in physical rather than in mathematical
terms, in such a way that it may be given an "objective reality". Here we use
some ideas about the system dimensionality, taken from quant-ph/0101012, to
propose a possible axiomatic approach to QM. In this approach the structure of
QM appears as a direct consequence of the non-commutative character of the
(classical geometrical) group of "knobs transformations", that relate between
themselves the different positions of the measurement apparatus.


title: The simplest non-trivial model of chaotic causal dynamics

abstract:
  The simplest non-trivial model of chaotic Bohmian dynamics is identified. We
argue that its most important features can be observed in more complex models,
above all, the presumable mechanism of the appearance of chaos in the
Bohmian-type dynamical systems.


title: Field quantization for chaotic resonators with overlapping modes

abstract:
  Feshbach's projector technique is employed to quantize the electromagnetic
field in optical resonators with an arbitray number of escape channels. We find
spectrally overlapping resonator modes coupled due to the damping and noise
inflicted by the external radiation field. For wave chaotic resonators the mode
dynamics is determined by a non--Hermitean random matrix. Upon including an
amplifying medium, our dynamics of open-resonator modes may serve as a starting
point for a quantum theory of random lasing.


title: The Quantum State of a Propagating Laser Field

abstract:
  Optical implementations of quantum communication protocols typically involve
laser fields. However, the standard description of the quantum state of a laser
field is surprisingly insufficient to understand the quantum nature of such
implementations. In this paper, we give a quantum information-theoretic
description of a propagating continuous-wave laser field and reinterpret
various quantum-optical experiments in light of this. A timely example is found
in a recent controversy about the quantum teleportation of continuous
variables. We show that contrary to the claims of T. Rudolph and B. C. Sanders
[Phys. Rev. Lett. 87, 077903 (2001)], a conventional laser can be used for
quantum teleportation with continuous variables and for generating
continuous-variable quantum entanglement. Furthermore, we show that optical
coherent states do play a privileged role in the description of propagating
laser fields even though they cannot be ascribed such a role for the
intracavity field.


title: Conditional Spin Resonance with Trapped Ions

abstract:
  Internal states of different ions in an electrodynamic trap are coupled when
a static magnetic field is applied -- analogous to spin-spin coupling in
molecules used for NMR. This spin-spin interaction can be used, for example, to
implement quantum logic operations in ion traps using NMR methods. The
collection of trapped ions can be viewed as a $N$-qubit molecule with
adjustable coupling constants.


title: Numerical Experiment on Interference for Macroscopic Particles

abstract:
  We consider a classical analogue of the well known quantum two-slit
experiment. Charged particles are scattered on flat screen with two slits and
hit the second screen. We show that the probability distribution on the second
screen when both slits are open is not given by the sum of distributions for
each slit separately, but has an extra interference term that is given with the
quantum rule of the addition of probabilistic alternatives. We show that the
proposed classical model has a context dependence and could be adequately
described with contextual formalism.


title: Generation of fan-states of radiation field in a cavity

abstract:
  A scheme of generating recently introduced fan-states | \alpha, 2k>_F (\alpha
is complex, k=1,2,3,...) is proposed basing on a \Lambda-type atom-cavity field
interaction. We show that with suitable atomic preparations and measurements a
passage of a sequence of N atoms through a cavity may transform an initial
field coherent state | \alpha> to a fan-state | \alpha, 2k>_F with k=2^{N-2}.


title:
Polariton Analysis of a Four-Level Atom Strongly Coupled to a Cavity
  Mode

abstract:
  We present a complete analytical solution for a single four-level atom
strongly coupled to a cavity field mode and driven by external coherent laser
fields. The four-level atomic system consists of a three-level subsystem in an
EIT configuration, plus an additional atomic level; this system has been
predicted to exhibit a photon blockade effect. The solution is presented in
terms of polaritons. An effective Hamiltonian obtained by this procedure is
analyzed from the viewpoint of an effective two-level system, and the dynamic
Stark splitting of dressed states is discussed. The fluorescence spectrum of
light exiting the cavity mode is analyzed and relevant transitions identified.


title:
Correlation between plasma and temperature corrections to the Casimir
  force

abstract:
  When comparing experimental results with theoretical predictions of the
Casimir force, the accuracy of the theory is as important as the precision of
experiments. Here we evaluate the Casimir force when finite conductivity of the
reflectors and finite temperature are simultaneously taken into account. We
show that these two corrections are correlated, i.e. that they can not, in
principle, be evaluated separately and simply multiplied. We estimate the
correlation factor which measures the deviation from this common approximation.
We focus our attention on the case of smooth and plane plates with a metallic
optical response modeled by a plasma model.


title:
Darboux transformations and hidden quadratic supersymmetry of the
  one-dimensional stationary Dirac equation

abstract:
  A matricial Darboux operator intertwining two one-dimensional stationary
Dirac Hamiltonians is constructed. This operator is such that the potential of
the second Dirac Hamiltonian as well as the corresponding eigenfunctions are
determined through the knowledge of only two eigenfunctions of the first Dirac
Hamiltonian. Moreover this operator together with its adjoint and the two
Hamiltonians generate a quadratic deformation of the superalgebra subtending
the usual supersymmetric quantum mechanics. Our developments are illustrated on
the free particle case and the generalized Coulomb interaction. In the latter
case, a relativistic counterpart of shape-invariance is observed.


title: Systems and Subsystems in Quantum Communication

abstract:
  In this paper we develop the conditional density matrix formalism for
adequate description of division and unificationof quantum systems.
Applications of this approach to the descriptions of parapositronium, quantum
teleportation and others examples are discussed.


title:
Violation of Bell inequality for thermal states of interaction qubits
  via a multi-qubit Heisenberg model

abstract:
  We study the violations of Bell inequality for thermal states of qubits in a
multi-qubit Heisenberg model as a function of temperature and external magnetic
fields. Unlike the behaviors of the entanglement the violation can not be
obtained by increasing the temperature or the magnetic field. The threshold
temperatures of the violation are found be less than that of the entanglement.
We also consider a realistic cavity-QED model which is a special case of the
mutli-qubit Heisenberg model.


title: Implementation of Universal Control on a Decoherence-Free Qubit

abstract:
  We demonstrate storage and manipulation of one qubit encoded into a
decoherence-free subspace (DFS) of two nuclear spins using liquid state nuclear
magnetic resonance (NMR) techniques. The DFS is spanned by states that are
unaffected by arbitrary collective phase noise. Encoding and decoding
procedures reversibly map an arbitrary qubit state from a single data spin to
the DFS and back. The implementation demonstrates the robustness of the DFS
memory against engineered dephasing with arbitrary strength as well as a
substantial increase in the amount of quantum information retained, relative to
an un-encoded qubit, under both engineered and natural noise processes. In
addition, a universal set of logical manipulations over the encoded qubit is
also realized. Although intrinsic limitations prevent maintaining full noise
tolerance during quantum gates, we show how the use of dynamical control
methods at the encoded level can ensure that computation is protected with
finite distance. We demonstrate noise-tolerant control over a DFS qubit in the
presence of engineered phase noise significantly stronger than observed from
natural noise sources.


title: On Quantum Control via Encoded Dynamical Decoupling

abstract:
  I revisit the ideas underlying dynamical decoupling methods within the
framework of quantum information processing, and examine their potential for
direct implementations in terms of encoded rather than physical degrees of
freedom. The usefulness of encoded decoupling schemes as a tool for engineering
both closed- and open-system encoded evolutions is investigated based on simple
examples.


title: The quantum dynamics of two coupled qubits

abstract:
  We investigate the difference between classical and quantum dynamics of
coupled magnetic dipoles. We prove that in general the dynamics of the
classical interaction Hamiltonian differs from the corresponding quantum model,
regardless of the initial state. The difference appears as non
positive-definite diffusion terms in the quantum evolution equation of an
appropriate positive phase-space probability density. Thus, it is not possible
to express the dynamics in terms of a convolution of a positive transition
probability function and the initial condition as can be done in the classical
case. We conclude that the dynamics is a quantum element of NMR quantum
information processing. There are two limits where our quantum evolution
coincide with the classical one: the short time limit before spin-spin
interaction sets in and the long time limit when phase diffusion is
incorporated.


title:
The creation of large photon-number path entanglement conditioned on
  photodetection

abstract:
  Large photon-number path entanglement is an important resource for enhanced
precision measurements and quantum imaging. We present a general constructive
protocol to create any large photon number path-entangled state based on the
conditional detection of single photons. The influence of imperfect detectors
is considered and an asymptotic scaling law is derived.


title:
Path integral for a pair of time-dependent coupled and driven
  oscillators

abstract:
  The propagator for a certain class of two time-dependent coupled and driven
harmonic oscillators with time-varying angular frequencies and masses is
evaluated by path integration. This is simply done through suitably chosen
generalized canonical transformations and without presupposing the knownledge
of any auxiliary equation. The time-dependent oscillators system with an
exponentially growing masses and coupling coefficient in time may be considered
as particular case.


title: Entanglement Concentration Using Quantum Statistics

abstract:
  We propose an entanglement concentration scheme which uses only the effects
of quantum statistics of indistinguishable particles. This establishes the fact
that useful quantum information processing can be accomplished by quantum
statistics alone. Due to the basis independence of statistical effects, our
protocol requires less knowledge of the initial state than most entanglement
concentration schemes. Moreover, no explicit controlled operation is required
at any stage.


title: Seven Steps Towards the Classical World

abstract:
  Classical physics is about real objects, like apples falling from trees,
whose motion is governed by Newtonian laws. In standard Quantum Mechanics only
the wave function or the results of measurements exist, and to answer the
question of how the classical world can be part of the quantum world is a
rather formidable task. However, this is not the case for Bohmian mechanics,
which, like classical mechanics, is a theory about real objects. In Bohmian
terms, the problem of the classical limit becomes very simple: when do the
Bohmian trajectories look Newtonian?


title:
Comments on `Stable Quantum Computation of Unstable Classical Chaos,'
  `Efficient Quantum Computing Insensitive to Phase Errors,' and `Quantum
  Computer Inverting Time Arrow for Macroscopic Systems'

abstract:
  Recently, the paper B. Georgeot and D.L. Shepelyansky, Phys. Rev. Lett._86_,
5393 (2001) has been criticized [C. Zalka, quant-ph/0110019; L. Di'osi,
quant-ph/0110026]. The Letter claims an exponential speedup and reduction in
error sensitivity, when phase-space density evolution under the Arnold cat map
is performed on a quantum computer. On the one hand, some points have not yet
been made by previous respondents. On the other, the authors' reaction
[quant-ph/0110142] raises new issues. The present note addresses both.


title: Distinguishing separable and entangled states

abstract:
  We show how to design families of operational criteria that distinguish
entangled from separable quantum states. The simplest of these tests
corresponds to the well-known Peres-Horodecki positive partial transpose (PPT)
criterion, and the more complicated tests are strictly stronger. The new
criteria are tractable due to powerful computational and theoretical methods
for the class of convex optimization problems known as semidefinite programs.
We successfully applied the results to many low-dimensional states from the
literature where the PPT test fails. As a byproduct of the criteria, we provide
an explicit construction of the corresponding entanglement witnesses.


title: What is Bohmian Mechanics

abstract:
  Bohmian mechanics is a quantum theory with a clear ontology. To make clear
what we mean by this, we shall proceed by recalling first what are the problems
of quantum mechanics. We shall then briefly sketch the basics of Bohmian
mechanics and indicate how Bohmian mechanics solves these problems and
clarifies the status and the role of of the quantum formalism.


title: On the Classical Limit of Quantum Mechanics

abstract:
  Contrary to the widespread belief, the problem of the emergence of classical
mechanics from quantum mechanics is still open. In spite of many results on the
$\h \to 0$ asymptotics, it is not yet clear how to explain within standard
quantum mechanics the classical motion of macroscopic bodies. In this paper we
shall analyze special cases of classical behavior in the framework of a precise
formulation of quantum mechanics, Bohmian mechanics, which contains in its own
structure the possibility of describing real objects in an observer-independent
way.


title: Phase Space Geometry in Classical and Quantum Mechanics

abstract:
  Phase space is the state space of classical mechanics, and this manifold is
normally endowed only with a symplectic form. The geometry of quantum mechanics
is necessarily more complicated. Arguments will be given to show that
augmenting the symplectic manifold of classical phase space with a Riemannian
metric is sufficient for describing quantum mechanics. In particular, using
such spaces, a fully satisfactory geometric version of quantization will be
developed and described.


title:
Geometric quantization of mechanical systems with time-dependent
  parameters

abstract:
  Quantum systems with adiabatic classical parameters are widely studied, e.g.,
in the modern holonomic quantum computation. We here provide complete geometric
quantization of a Hamiltonian system with time-dependent parameters, without
the adiabatic assumption. A Hamiltonian of such a system is affine in the
temporal derivative of parameter functions. This leads to the geometric Berry
factor phenomena.


title:
Entanglement versus Bell violations and their behaviour under local
  filtering operations

abstract:
  We discuss the relations between the violation of the CHSH Bell inequality
for systems of two qubits on the one side and entanglement of formation, local
filtering operations, and the entropy and purity on the other. We calculate the
extremal Bell violations for a given amount of entanglement of formation and
characterize the respective states, which turn out to have extremal properties
also with respect to the entropy, purity and several entanglement monotones.
The optimal local filtering operations leading to the maximal Bell violation
for a given state are provided and the special role of the resulting Bell
diagonal states in the context of Bell inequalities is discussed.


title: Encoded Universality from a Single Physical Interaction

abstract:
  We present a theoretical analysis of the paradigm of encoded universality,
using a Lie algebraic analysis to derive specific conditions under which
physical interactions can provide universality. We discuss the significance of
the tensor product structure in the quantum circuit model and use this to
define the conjoining of encoded qudits. The construction of encoded gates
between conjoined qudits is discussed in detail. We illustrate the general
procedures with several examples from exchange-only quantum computation. In
particular, we extend our earlier results showing universality with the
isotropic exchange interaction to the derivation of encoded universality with
the anisotropic exchange interaction, i.e., to the XY model. In this case the
minimal encoding for universality is into qutrits rather than into qubits as
was the case for isotropic (Heisenberg) exchange. We also address issues of
fault-tolerance, leakage and correction of encoded qudits.