title: Quantum Algorithms and the Genetic Code

abstract:
  Replication of DNA and synthesis of proteins are studied from the view-point
of quantum database search. Identification of a base-pairing with a quantum
query gives a natural (and first ever) explanation of why living organisms have
4 nucleotide bases and 20 amino acids. It is amazing that these numbers arise
as solutions to an optimisation problem. Components of the DNA structure which
implement Grover's algorithm are identified, and a physical scenario is
presented for the execution of the quantum algorithm. It is proposed that
enzymes play a crucial role in maintaining quantum coherence of the process.
Experimental tests that can verify this scenario are pointed out.

categories: quant-ph cond-mat hep-th physics.bio-ph q-bio.GN


title: Spectroscopic studies in open quantum systems

abstract:
  The spectroscopic properties of an open quantum system are determined by the
eigenvalues and eigenfunctions of an effective Hamiltonian H consisting of the
Hamiltonian H_0 of the corresponding closed system and a non-Hermitian
correction term W arising from the interaction via the continuum of decay
channels. The eigenvalues E_R of H are complex. They are the poles of the
S-matrix and provide both the energies and widths of the states. We illustrate
the interplay between Re(H) and Im(H) by means of the different interference
phenomena between two neighboured resonance states. Level repulsion along the
real axis appears if the interaction is caused mainly by Re(H) while a
bifurcation of the widths appears if the interaction occurs mainly due to
Im(H). We then calculate the poles of the S-matrix and the corresponding
wavefunctions for a rectangular microwave resonator with a scatter as a
function of the area of the resonator as well as of the degree of opening to a
guide. The calculations are performed by using the method of exterior complex
scaling. Re(W) and Im(W) cause changes in the structure of the wavefunctions
which are permanent, as a rule. At full opening to the lead, short-lived
collective states are formed together with long-lived trapped states. The
wavefunctions of the short-lived states at full opening to the lead are very
different from those at small opening. The resonance picture obtained from the
microwave resonator shows all the characteristic features known from the study
of many-body systems in spite of the absence of two-body forces. The poles of
the S-matrix determine the conductance of the resonator. Effects arising from
the interplay between resonance trapping and level repulsion along the real
axis are not involved in the statistical theory.


title: Methodology for quantum logic gate constructions

abstract:
  We present a general method to construct fault-tolerant quantum logic gates
with a simple primitive, which is an analog of quantum teleportation. The
technique extends previous results based on traditional quantum teleportation
(Gottesman and Chuang, Nature {\bf 402}, 390, 1999) and leads to
straightforward and systematic construction of many fault-tolerant encoded
operations, including the $\pi/8$ and Toffoli gates. The technique can also be
applied to the construction of remote quantum operations that cannot be
directly performed.


title: Heating of trapped ions from the quantum ground state

abstract:
  We have investigated motional heating of laser-cooled 9Be+ ions held in
radio-frequency (Paul) traps. We have measured heating rates in a variety of
traps with different geometries, electrode materials, and characteristic sizes.
The results show that heating is due to electric-field noise from the trap
electrodes which exerts a stochastic fluctuating force on the ion. The scaling
of the heating rate with trap size is much stronger than that expected from a
spatially uniform noise source on the electrodes (such as Johnson noise from
external circuits), indicating that a microscopic uncorrelated noise source on
the electrodes (such as fluctuating patch-potential fields) is a more likely
candidate for the source of heating.


title: Symplectic areas, quantization, and dynamics in electromagnetic fields

abstract:
  A gauge invariant quantization in a closed integral form is developed over a
linear phase space endowed with an inhomogeneous Faraday electromagnetic
tensor. An analog of the Groenewold product formula (corresponding to Weyl
ordering) is obtained via a membrane magnetic area, and extended to the product
of N symbols. The problem of ordering in quantization is related to different
configurations of membranes: a choice of configuration determines a phase
factor that fixes the ordering and controls a symplectic groupoid structure on
the secondary phase space. A gauge invariant solution of the quantum evolution
problem for a charged particle in an electromagnetic field is represented in an
exact continual form and in the semiclassical approximation via the area of
dynamical membranes.


title: On the Non-Orthonormality of Lippmann-Schwinger-Low States

abstract:
  It is pointed out that for a general short-ranged potential the
Lippmann-Schwinger-Low scattering state $|\psi^L_k>$ does not strictly satisfy
the Schrodinger eigen equation, and the pair $|\psi^L_n>$, $|\psi^L_k>$ is
mutually nonorthogonal if $E_n=E_k$. For this purpose, we carefully use an
infinitesimal adiabatic parameter $\epsilon$, a nonlinear relation among
transition amplitudes, and a separable interaction as illustration.


title: Phase properties of a new nonlinear coherent state

abstract:
  We study phase properties of a displacement operator type nonlinear coherent
state. In particular we evaluate the Pegg-Barnett phase distribution and
compare it with phase distributions associated with the Husimi Q function and
the Wigner function. We also study number- phase squeezing of this state.


title: Security of classical noise-based cryptography

abstract:
  We examine security of a protocol on cryptographic key distribution via
classical noise proposed by Yuen and Kim (Phys. Lett. A 241 135 (1998)).
Theoretical and experimental analysis in terms of the secure key distribution
rate shows that secure key distribution is possible even if the eavesdropper
could receive more photons than the legitimate receiver, as long as the
signal-to-noise-ratio (SNR) of the receiver is better than -9dB of the
eavesdropper's SNR. Secure key distribution was demonstrated at the maximum
rate of 0.04 bit per sender's bit and transmission rate of 2 Mb/s in the
experiment employing conventional fiber optics. The present protocol has
advantages of the efficient key distribution and the simple implementation over
other quantum key distribution protocols. However, careful design and
management are necessary to keep the security of the crypto-system.


title:
Nonlocal properties of two-qubit gates and mixed states and optimization
  of quantum computations

abstract:
  Entanglement of two parts of a quantum system is a non-local property
unaffected by local manipulations of these parts. It is described by quantities
invariant under local unitary transformations. Here we present, for a system of
two qubits, a set of invariants which provides a complete description of
non-local properties. The set contains 18 real polynomials of the entries of
the density matrix. We prove that one of two mixed states can be transformed
into the other by single-bit operations if and only if these states have equal
values of all 18 invariants. Corresponding local operations can be found
efficiently. Without any of these 18 invariants the set is incomplete.
  Similarly, non-local, entangling properties of two-qubit unitary gates are
invariant under single-bit operations. We present a complete set of 3 real
polynomial invariants of unitary gates. Our results are useful for optimization
of quantum computations since they provide an effective tool to verify if and
how a given two-qubit operation can be performed using exactly one elementary
two-qubit gate, implemented by a basic physical manipulation (and arbitrarily
many single-bit gates).


title: The Persistence of Memory: Surreal Trajectories in Bohm's Theory

abstract:
  In this paper I describe the history of the surreal trajectories problem and
argue that in fact it is not a problem for Bohm's theory. More specifically, I
argue that one can take the particle trajectories predicted by Bohm's theory to
be the actual trajectories that particles follow and that there is no reason to
suppose that good particle detectors are somehow fooled in the context of the
surreal trajectories experiments. Rather than showing that Bohm's theory
predicts the wrong particle trajectories or that it somehow prevents one from
making reliable measurements, such experiments ultimately reveal the special
role played by position and the fundamental incompatibility between Bohm's
theory and relativity.


title:
Continuous pumping and control of mesoscopic superposition state in a
  lossy QED cavity

abstract:
  Here we consider the continuous pumping of a dissipative QED cavity and
derive the time-dependent density operator of the cavity field prepared
initially as a superposition of mesoscopic coherent states. The control of the
coherence of this superposition is analyzed considering the injection of a beam
of two-level Rydberg atoms through the cavity. Our treatment is compared to
other approaches.


title:
The thermodynamic cost of reliability and low temperatures: Tightening
  Landauer's principle and the Second Law

abstract:
  Landauer's principle states that the erasure of one bit of information
requires the free energy kT ln 2. We argue that the reliability of the bit
erasure process is bounded by the accuracy inherent in the statistical state of
the energy source (`the resources') driving the process. We develop a general
framework describing the `thermodynamic worth' of the resources with respect to
reliable bit erasure or good cooling. This worth turns out to be given by the
distinguishability of the resource's state from its equilibrium state in the
sense of a statistical inference problem. Accordingly, Kullback-Leibler
relative information is a decisive quantity for the `worth' of the resource's
state. Due to the asymmetry of relative information, the reliability of the
erasure process is bounded rather by the relative information of the
equilibrium state wit respect to the actual state than by the relative
information of the actual state with respect to the equilibrium state (which is
the free energy up to constants).


title: Lyapunov exponent in quantum mechanics. A phase-space approach

abstract:
  Using the symplectic tomography map, both for the probability distributions
in classical phase space and for the Wigner functions of its quantum
counterpart, we discuss a notion of Lyapunov exponent for quantum dynamics.
Because the marginal distributions, obtained by the tomography map, are always
well defined probabilities, the correspondence between classical and quantum
notions is very clear. Then we also obtain the corresponding expressions in
Hilbert space. Some examples are worked out. Classical and quantum exponents
are seen to coincide for local and non-local time-dependent quadratic
potentials. For non-quadratic potentials classical and quantum exponents are
different and some insight is obtained on the taming effect of quantum
mechanics on classical chaos. A detailed analysis is made for the standard map.
Providing an unambiguous extension of the notion of Lyapunov exponent to
quantum mechnics, the method that is developed is also computationally
efficient in obtaining analytical results for the Lyapunov exponent, both
classical and quantum.


title:
Coherent states sometimes look like squeezed states, and visa versa: The
  Paul trap

abstract:
  Using the Paul Trap as a model, we point out that the same wave functions can
be variously coherent or squeezed states, depending upon the system they are
applied to.


title: Beyond single-photon localization at the edge of a Photonic Band Gap

abstract:
  We study spontaneous emission in an atomic ladder system, with both
transitions coupled near-resonantly to the edge of a photonic band gap
continuum. The problem is solved through a recently developed technique and
leads to the formation of a ``two-photon+atom'' bound state with fractional
population trapping in both upper states. In the long-time limit, the atom can
be found excited in a superposition of the upper states and a ``direct''
two-photon process coexists with the stepwise one. The sensitivity of the
effect to the particular form of the density of states is also explored.


title: Robustness of Wave Functions of Interacting Many Bosons in a Leaky Box

abstract:
  We study the robustness, against the leakage of bosons, of wave functions of
interacting many bosons confined in a finite box, by deriving and analyzing a
general equation of motion for the reduced density operator. We identify a
robust wave function that remains a pure state, whereas other wave functions,
such as the Bogoliubov's ground state and the ground state with a fixed number
of bosons, evolve into mixed states. Although these states all have the
off-diagonal long-range order, and almost the same energy densities, we argue
that only the robust state is realized as a macroscopic quantum state.


title: Cloning and quantum computation

abstract:
  We discuss how quantum information distribution can improve the performance
of some quantum computation tasks. This distribution can be naturally
implemented with different types of quantum cloning procedures. We give two
examples of tasks for which cloning provides some enhancement in performance,
and briefly discuss possible extensions of the idea.


title:
Towards the elusive Efimov state of the ^4He_3 molecule through a new
  atom-optical state-selection technique

abstract:
  Excited states and excitation energies of weakly bound systems, e.g. atomic
few-body systems and clusters, are difficult to study experimentally. For this
purpose we propose a new and very general atom-optical method which is based on
inelastic diffraction from transmission gratings. The technique is applicable
to the recently found helium trimer molecule ^4He_3, allowing for the first
time an investigation of the possible existence of an excited trimer state and
determination of its excitation energy. This would be of fundamental importance
for the famous Efimov effect.


title: Classical Topology and Quantum States

abstract:
  Any two infinite-dimensional (separable) Hilbert spaces are unitarily
isomorphic. The sets of all their self-adjoint operators are also therefore
unitarily equivalent. Thus if all self-adjoint operators can be observed, and
if there is no further major axiom in quantum physics than those formulated for
example in Dirac's `Quantum Mechanics', then a quantum physicist would not be
able to tell a torus from a hole in the ground. We argue that there are indeed
such axioms involving observables with smooth time evolution: they contain
commutative subalgebras from which the spatial slice of spacetime with its
topology (and with further refinements of the axiom, its $C^K-$ and $C^\infty-$
structures) can be reconstructed using Gel'fand - Naimark theory and its
extensions. Classical topology is an attribute of only certain quantum
observables for these axioms, the spatial slice emergent from quantum physics
getting progressively less differentiable with increasingly higher excitations
of energy and eventually altogether ceasing to exist. After formulating these
axioms, we apply them to show the possibility of topology change and to discuss
quantized fuzzy topologies. Fundamental issues concerning the role of time in
quantum physics are also addressed.


title:
Some properties of eigenvalues and eigenfunctions of the cubic
  oscillator with imaginary coupling constant

abstract:
  Comparison between the exact value of the spectral zeta function,
$Z_{H}(1)=5^{-6/5}[3-2\cos(\pi/5)]\Gamma^2(1/5)/\Gamma(3/5)$, and the results
of numeric and WKB calculations supports the conjecture by Bessis that all the
eigenvalues of this PT-invariant hamiltonian are real. For one-dimensional
Schr\"odinger operators with complex potentials having a monotonic imaginary
part, the eigenfunctions (and the imaginary parts of their logarithmic
derivatives) have no real zeros.

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


title: On the Complexity of Quantum ACC

abstract:
  For any $q > 1$, let $\MOD_q$ be a quantum gate that determines if the number
of 1's in the input is divisible by $q$. We show that for any $q,t > 1$,
$\MOD_q$ is equivalent to $\MOD_t$ (up to constant depth). Based on the case
$q=2$, Moore \cite{moore99} has shown that quantum analogs of AC$^{(0)}$,
ACC$[q]$, and ACC, denoted QAC$^{(0)}_{wf}$, QACC$[2]$, QACC respectively,
define the same class of operators, leaving $q > 2$ as an open question. Our
result resolves this question, proving that QAC$^{(0)}_{wf} =$ QACC$[q] = $
QACC for all $q$. We also develop techniques for proving upper bounds for QACC
in terms of related language classes. We define classes of languages EQACC,
NQACC and BQACC$_{\rats}$. We define a notion $\log$-planar QACC operators and
show the appropriately restricted versions of EQACC and NQACC are contained in
P/poly. We also define a notion of $\log$-gate restricted QACC operators and
show the appropriately restricted versions of EQACC and NQACC are contained in
TC$^{(0)}$. To do this last proof, we show that TC$^{(0)}$ can perform iterated
addition and multiplication in certain field extensions. We also introduce the
notion of a polynomial-size tensor graph and show that families of such graphs
can encode the amplitudes resulting from apply an arbitrary QACC operator to an
initial state.


title: An Unentangled Gleason's Theorem

abstract:
  The purpose of this note is to give a generalization of Gleason's theorem
inspired by recent work in quantum information theory on "nonlocality without
entanglement." For multipartite quantum systems, each of dimension three or
greater, the only nonnegative frame functions over the set of unentangled
states are those given by the standard Born probability rule. However, if one
system is of dimension 2 this is not necessarily the case.


title: Phase measurements at the theoretical limit

abstract:
  It is well known that the result of any phase measurement on an optical mode
made using linear optics has an introduced uncertainty in addition to the
intrinsic quantum phase uncertainty of the state of the mode. The best
previously published technique [H. M. Wiseman and R.B. Killip, Phys. Rev. A 57,
2169 (1998)] is an adaptive technique that introduces a phase variance that
scales as n^{-1.5}, where n is the mean photon number of the state. This is far
above the minimum intrinsic quantum phase variance of the state, which scales
as n^{-2}. It has been shown that a lower limit to the phase variance that is
introduced scales as ln(n)/n^2. Here we introduce an adaptive technique that
attains this theoretical lower limit.


title: On The Significance of Bell's Locality Condition

abstract:
  Reviewing the general representation of a stochastic local hidden variables
theory in the context of an ideal Bohm's version of the EPR experiment, we show
explicitly that the violation of Bell's locality condition is due to the
assumption of ``outcome independence'' at the hidden variables level. Also, we
show that if we introduce determinism, the assumption of outcome independence
will be allowed.


title: Temperature dependence of the Casimir effect between metallic mirrors

abstract:
  We calculate the Casimir force and free energy for plane metallic mirrors at
non-zero temperature. Numerical evaluations are given with temperature and
conductivity effects treated simultaneously. The results are compared with the
approximation where both effects are treated independently and the corrections
simply multiplied. The deviation between the exact and approximated results
takes the form of a temperature dependent function for which an analytical
expression is given. The knowledge of this function allows simple and accurate
estimations at the % level.


title: On the weak-coupling limit and complete positivity

abstract:
  We consider two non-interacting systems embedded in a heat bath. If they
remain dynamically independent, physical inconsistencies are avoided only if
the single-system reduced dynamics is completely positive also beyond the
weak-coupling limit.


title: Information-Theoretic Analyses of Two-Level Quantum Systems

abstract:
  This paper has been superseded by quant-ph/0006009, "Quantum State Estimation
Using Non-separable Measurements".


title: Robust unravelings for resonance fluorescence

abstract:
  Monitoring the fluorescent radiation of an atom unravels the master equation
evolution by collapsing the atomic state into a pure state which evolves
stochastically. A robust unraveling is one that gives pure states that, on
average, are relatively unaffected by the master equation evolution (which
applies once the monitoring ceases). The ensemble of pure states arising from
the maximally robust unraveling has been suggested to be the most natural way
of representing the system [H.M. Wiseman and J.A. Vaccaro, Phys. Lett. A {\bf
250}, 241 (1998)]. We find that the maximally robust unraveling of a resonantly
driven atom requires an adaptive interferometric measurement proposed by
Wiseman and Toombes [Phys. Rev. A {\bf 60}, 2474 (1999)]. The resultant
ensemble consists of just two pure states which, in the high driving limit, are
close to the eigenstates of the driving Hamiltonian $\Omega\sigma_{x}/2$. This
ensemble is the closest thing to a classical limit for a strongly driven atom.
We also find that it is possible to reasonably approximate this ensemble using
just homodyne detection, an example of a continuous Markovian unraveling. This
has implications for other systems, for which it may be necessary in practice
to consider only continuous Markovian unravelings.


title:
Unitary relation between a harmonic oscillator of time-dependent
  frequency and a simple harmonic oscillator with and without an inverse-square
  potential

abstract:
  The unitary operator which transforms a harmonic oscillator system of
time-dependent frequency into that of a simple harmonic oscillator of different
time-scale is found, with and without an inverse-square potential. It is shown
that for both cases, this operator can be used in finding complete sets of wave
functions of a generalized harmonic oscillator system from the well-known sets
of the simple harmonic oscillator. Exact invariants of the time-dependent
systems can also be obtained from the constant Hamiltonians of unit mass and
frequency by making use of this unitary transformation. The geometric phases
for the wave functions of a generalized harmonic oscillator with an
inverse-square potential are given.


title: Quantum lower bounds by quantum arguments

abstract:
  We propose a new method for proving lower bounds on quantum query algorithms.
Instead of a classical adversary that runs the algorithm with one input and
then modifies the input, we use a quantum adversary that runs the algorithm
with a superposition of inputs. If the algorithm works correctly, its state
becomes entangled with the superposition over inputs. We bound the number of
queries needed to achieve a sufficient entanglement and this implies a lower
bound on the number of queries for the computation.
  Using this method, we prove two new $\Omega(\sqrt{N})$ lower bounds on
computing AND of ORs and inverting a permutation and also provide more uniform
proofs for several known lower bounds which have been previously proven via
variety of different techniques.


title:
Rules for Integrals over Products of Distributions from Coordinate
  Independence of Path Integrals

abstract:
  In perturbative calculations of quantum mechanical path integrals in
curvilinear coordinates, Feynman diagrams involve multiple temporal integrals
over products of distributions, which are mathematically undefined. We derive
simple rules for their evaluation from the requirement of coordinate
independence of path integrals.


title: Conditions for manipulation of a set of entangled pure states

abstract:
  We derive a sufficient condition for a set of pure states, each entangled in
two remote $N$-dimensional systems, to be transformable to
$k$-dimensional-subspace equivalent entangled states ($k\leq N$) by same local
operations and classical communication. If $k=N$, the condition is also
necessary. This condition reveals the function of the relative marginal density
operators of the entangled states in the entanglement manipulation without
sufficient information of the initial states.


title: Quantum oscillator as 1D anyon

abstract:
  It is shown that in one spatial dimension the quantum oscillator is dual to
the charged particle situated in the field described by the superposition of
Coulomb and Calogero-Sutherland potentials.

categories: quant-ph cond-mat.stat-mech hep-th math-ph math.MP


title:
Generalised coherent states and the diagonal representation for
  operators

abstract:
  We consider the problem of existence of the diagonal representation for
operators in the space of a family of generalized coherent states associated
with an unitary irreducible representation of a (compact) Lie group. We show
that necessary and sufficient conditions for the possibility of such a
representation can be obtained by combining Clebsch-Gordan theory and the
reciprocity theorems associated with induced unitary group representation.
  Applications to several examples involving $SU(2),$ $SU(3),$ and the
Heisenberg-Weyl group are presented, showing that there are simple examples of
generalized coherent states which do not meet these conditions. Our results are
relevant for phase-space description of quantum mechanics and quantum state
reconstruction problems.


title: Nonextensive approach to decoherence in quantum mechanics

abstract:
  We propose a nonextensive generalization (q parametrized) of the von Neumann
equation for the density operator. Our model naturally leads to the phenomenon
of decoherence, and unitary evolution is recovered in the limit of q -> 1. The
resulting evolution yields a nonexponential decay for quantum coherences, fact
that might be attributed to nonextensivity. We discuss, as an example, the loss
of coherence observed in trapped ions.


title: Dynamical Generation of Noiseless Quantum Subsystems

abstract:
  We present control schemes for open quantum systems that combine decoupling
and universal control methods with coding procedures. By exploiting a general
algebraic approach, we show how appropriate encodings of quantum states result
in obtaining universal control over dynamically-generated noise-protected
subsystems with limited control resources. In particular, we provide an
efficient scheme for performing universal encoded quantum computation in a wide
class of systems subjected to linear non-Markovian quantum noise and supporting
Heisenberg-type internal Hamiltonians.


title: Eigenvalues, Peres' separability condition and entanglement

abstract:
  The general expression with the physical significance and positive definite
condition of the eigenvalues of $4\times 4$ Hermitian and trace-one matrix are
obtained. This implies that the eigenvalue problem of the $4\times 4$ density
matrix is generally solved. The obvious expression of Peres' separability
condition for an arbitrary state of two qubits is then given out and it is very
easy to use. Furthermore, we discuss some applications to the calculation of
the entanglement, the upper bound of the entanglement, and a model of the
transfer of entanglement in a qubit chain through a noisy channel.


title: Test of quantum nonlocality for cavity fields

abstract:
  There have been studies on formation of quantum-nonlocal states in spatially
separate two cavities. We suggest a nonlocal test for the field prepared in the
two cavities. We couple classical driving fields with the cavities where a
nonlocal state is prepared. Two independent two-level atoms are then sent
through respective cavities to interact off-resonantly with the cavity fields.
The atomic states are measured after the interaction. Bell's inequality can be
tested by the joint probabilities of two-level atoms being in their excited or
ground states. We find that quantum nonlocality can also be tested using a
single atom sequentially interacting with the two cavities. Potential
experimental errors are also considered. We show that with the present
experimental condition of 5% error in the atomic velocity distribution, the
violation of Bell's inequality can be measured.


title: Operator monotones, the reduction criterion and the relative entropy

abstract:
  We introduce the theory of operator monotone functions and employ it to
derive a new inequality relating the quantum relative entropy and the quantum
conditional entropy. We present applications of this new inequality and in
particular we prove a new lower bound on the relative entropy of entanglement
and other properties of entanglement measures.


title:
Fast Quantum Search Algorithms in Protein Sequence Comparison - Quantum
  Biocomputing

abstract:
  Quantum search algorithms are considered in the context of protein sequence
comparison in biocomputing. Given a sample protein sequence of length m (i.e m
residues), the problem considered is to find an optimal match in a large
database containing N residues. Initially, Grover's quantum search algorithm is
applied to a simple illustrative case - namely where the database forms a
complete set of states over the 2^m basis states of a m qubit register, and
thus is known to contain the exact sequence of interest. This example
demonstrates explicitly the typical O(sqrt{N}) speedup on the classical O(N)
requirements. An algorithm is then presented for the (more realistic) case
where the database may contain repeat sequences, and may not necessarily
contain an exact match to the sample sequence. In terms of minimizing the
Hamming distance between the sample sequence and the database subsequences the
algorithm finds an optimal alignment, in O(sqrt{N}) steps, by employing an
extension of Grover's algorithm, due to Boyer, Brassard, Hoyer and Tapp for the
case when the number of matches is not a priori known.


title: The Physical Implementation of Quantum Computation

abstract:
  After a brief introduction to the principles and promise of quantum
information processing, the requirements for the physical implementation of
quantum computation are discussed. These five requirements, plus two relating
to the communication of quantum information, are extensively explored and
related to the many schemes in atomic physics, quantum optics, nuclear and
electron magnetic resonance spectroscopy, superconducting electronics, and
quantum-dot physics, for achieving quantum computing.


title: Quantum Tomography Via Group Theory

abstract:
  Amongst the multitude of state reconstruction techniques, the so-called
"quantum tomography" seems to be the most fruitful. In this letter, I will
start by developing the mathematical apparatus of quantum tomography and,
later, I will explain how it can be applied to various quantum systems.


title: Cavity Field Reconstruction at Finite Temperature

abstract:
  We present a scheme to reconstruct the quantum state of a field prepared
inside a lossy cavity at finite temperature. Quantum coherences are normally
destroyed by the interaction with an environment, but we show that it is
possible to recover complete information about the initial state (before
interaction with its environment), making possible to reconstruct any
$s$-parametrized quasiprobability distribution, in particular, the Wigner
function.


title: Unitary transformation approach for the trapped ion dynamics

abstract:
  We present a way of treating the problem of the interaction of a single
trapped ion with laser beams based on successive aplications of unitary
transformations onto the Hamiltonian. This allows the diagonalization of the
Hamiltonian, by means of recursive relations, without performing the Lamb-Dicke
approximation.


title:
A group of invariance transformations for nonrelativistic quantum
  mechanics

abstract:
  This paper defines, on the Galilean space-time, the group of asymptotically
Euclidean transformations (AET), which are equivalent to Euclidean
transformations at space-time infinity, and proposes a formulation of
nonrelativistic quantum mechanics which is invariant under such
transformations. This formulation is based on the asymptotic quantum measure,
which is shown to be invariant under AET's. This invariance exposes an
important connection between AET's and Feynman path integrals, and reveals the
nonmetric character of the asymptotic quantum measure. The latter feature
becomes even clearer when the theory is formulated in terms of the
coordinate-free formalism of asymptotically Euclidean manifold, which do not
have a metric structure. This mathematical formalism suggests the following
physical interpretation: (i) Particles evolution is represented by trajectories
on an asymptotically Euclidean manifold; (ii) The metric and the law of motion
are not defined a priori as fundamental entities, but they are properties of a
particular class of reference frames; (iii) The universe is considered as a
probability space in which the asymptotic quantum measure plays the role of a
probability measure. Points (ii) and (iii) are used to build the asymptotic
measurement theory, which is shown to be consistent with traditional quantum
measurement theory. The most remarkable feature of this measurement theory is
the possibility of having a nonchaotic distribution of the initial conditions
(NCDIC), an extremely counterintuitive but not paradoxical phenomenon which
allows to interpret typical quantum phenomena, such as particle diffraction and
tunnel effect, while still providing a description of their motion in terms of
classical trajectories.


title: Quantum searching with continuous variables

abstract:
  A fast quantum search algorithm for continuous variables is presented. The
result is the quantum continuous variable analog of Grover's algorithm
originally proposed for qubits. A continuous variable analog of the Hadamard
(i.e., Fourier transform) operation is used in conjunction with inversion about
the average of quantum states to allow the approximate identification of an
unknown quantum state in a way that gives a square-root speed-up over search
algorithms using classical continuous variables. Also, we show that this
quantum search algorithm is robust for a generalised Fourier transformation on
continuous variables.


title:
Spiked and PT-symmetrized decadic potentials supporting elementary
  N-plets of bound states

abstract:
  We show that the potential wells with a central spike
  V(x) = x^{10} + a x^8 + b x^6+ c x^4 + d x^2 + f/x^2 possess arbitrary finite
multiplets of elementary exact bound states. The strong asymptotic growth of
V(x) implies an ambiguity in the PT-symmetric quantization via complex boundary
conditions but the three eligible recipes coincide at our exceptional
solutions.


title: Decoherence and Planck's Radiation Law

abstract:
  The foundations of environment-induced decoherence theory are discussed and
the role of unphysical assumptions is pointed out. An alternative
interpretation of decoherence is proposed.


title: NMR Quantum Computation: a Critical Evaluation

abstract:
  Liquid state nuclear magnetic resonance (NMR) techniques have produced some
spectacular successes in the construction of small quantum computers, and NMR
is currently by far the leading technology for quantum computation. There are,
however, a number of significant problems with any attempt to scale up the
technology to produce computers of any useful size. While it is probable that
some of these will be successfully sidestepped during the next few years, it is
unlikely that they will all be solved; thus current liquid state NMR techniques
are unlikely to provide a viable technology for practical quantum computation.


title:
Pressure dependence of the Mg $3s4s^3S_1 \to 3s3p^3P_{0,1,2}$ transition
  in superfluid $^4$He

abstract:
  The pressure shifts of the $3s4s^3S_1 \to 3s3p^3P_{0,1,2}$ transition of
magnesium atoms immersed in superfluid helium have been measured at $(1.3\pm0.1
)$K between saturated vapour pressure and $24 $bar. The wavelength is blue
shifted linearly by $(0.07\pm0.01) \frac{nm}{bar}$. This value can be
satisfactorily described in the framework of the standard bubble model.


title:
A Tentative Expression of the Karolyhazy Uncertainty of the Space-Time
  Structure through Vacuum Spreads in Quantum Gravity

abstract:
  In the existing expositions of the Karolyhazy model, quantum mechanical
uncertainties are mimicked by classical spreads. It is shown how to express
those uncertainties through entities of the future unified theory of general
relativity and quantum theory.


title: Optimal quantum teleportation with an arbitrary pure state

abstract:
  We derive the maximum fidelity attainable for teleportation using a shared
pair of d-level systems in an arbitrary pure state. This derivation provides a
complete set of necessary and sufficient conditions for optimal teleportation
protocols. We also discuss the information on the teleported particle which is
revealed in course of the protocol using a non-maximally entangled state.


title:
Operational criterion and constructive checks for the separability of
  low rank density matrices

abstract:
  We consider low rank density operators $\varrho$ supported on a $M\times N$
Hilbert space for arbitrary $M$ and $N$ ($M\leq N$) and with a positive partial
transpose (PPT) $\varrho^{T_A}\ge 0$. For rank $r(\varrho) \leq N$ we prove
that having a PPT is necessary and sufficient for $\varrho$ to be separable; in
this case we also provide its minimal decomposition in terms of pure product
states. It follows from this result that there is no rank 3 bound entangled
states having a PPT. We also present a necessary and sufficient condition for
the separability of generic density matrices for which the sum of the ranks of
$\varrho$ and $\varrho^{T_A}$ satisfies $r(\varrho)+r(\varrho^{T_A}) \le
2MN-M-N+2$. This separability condition has the form of a constructive check,
providing thus also a pure product state decomposition for separable states,
and it works in those cases where a system of couple polynomial equations has a
finite number of solutions, as expected in most cases.


title: Integrity bases for local invariants of composite quantum systems

abstract:
  Unitary group branchings appropriate to the calculation of local invariants
of density matrices of composite quantum systems are formulated using the
method of $S$-function plethysms. From this, the generating function for the
number of invariants at each degree in the density matrix can be computed. For
the case of two two-level systems the generating function is $F(q) = 1 + q +
4q^{2} + 6 q^{3} + 16 q^{4} + 23 q^{5} + 52 q^{6} + 77 q^{7} + 150 q^{8} + 224
q^{9} + 396 q^{10} + 583 q^{11}+ O(q^{12})$. Factorisation of such series leads
in principle to the identification of an integrity basis of algebraically
independent invariants. This note replaces Appendix B of our paper\cite{us} J
Phys {\bf A33} (2000) 1895-1914 (\texttt{quant-ph/0001076}) which is incorrect.


title:
Prospects for photon blockade in four level systems in the N
  configuration with more than one atom

abstract:
  We show that for appropriate choices of parameters it is possible to achieve
photon blockade in idealised one, two and three atom systems. We also include
realistic parameter ranges for rubidium as the atomic species. Our results
circumvent the doubts cast by recent discussion in the literature (Grangier et
al Phys. Rev Lett. 81, 2833 (1998), Imamoglu et al Phys. Rev. Lett. 81, 2836
(1998)) on the possibility of photon blockade in multi-atom systems.


title: Fast quantum gates for cold trapped ions

abstract:
  We present an alternative scheme for the generation of a 2-qubit quantum gate
interaction between laser-cooled trapped ions. The scheme is based on the AC
Stark shift (lightshift) induced by laser light resonant with the ionic
transition frequency. At {\it specific} laser intensities, the shift of the
ionic levels allows the resonant excitation of transitions involving the
exchange of motional quanta. We compare the performance of this scheme with
respect to that of related ion-trap proposals and find that, for an
experimental realisation using travelling-wave radiation and working in the
Lamb-Dicke regime, an improvement of over an order of magnitude in the gate
switching rate is possible.


title: Double jumps and transition rates for two dipole-interacting atoms

abstract:
  Cooperative effects in the fluorescence of two dipole-interacting atoms, with
macroscopic quantum jumps (light and dark periods), are investigated. The
transition rates between different intensity periods are calculated in closed
form and are used to determine the rates of double jumps between periods of
double intensity and dark periods, the mean duration of the three intensity
periods and the mean rate of their occurrence. We predict, to our knowledge for
the first time, cooperative effects for double jumps, for atomic distances from
one and to ten wave lengths of the strong transition. The double jump rate, as
a function of the atomic distance, can show oscillations of up to 30% at
distances of about a wave length, and oscillations are still noticeable at a
distance of ten wave lengths. The cooperative effects of the quantities and
their characteristic behavior turn out to be strongly dependent on the laser
detuning.


title: Completely Positive Quantum Dissipation

abstract:
  A completely positive master equation describing quantum dissipation for a
Brownian particle is derived starting from microphysical collisions, exploiting
a recently introduced approach to subdynamics of a macrosystem. The obtained
equation can be cast into Lindblad form with a single generator for each
Cartesian direction. Temperature dependent friction and diffusion coefficients
for both position and momentum are expressed in terms of the collision
cross-section.


title: Quantum Phase Transitions in a Linear Ion Trap

abstract:
  We show that the quantum phase transition of the Tavis-Cummings model can be
realised in a linear ion trap of the kind proposed for quantum computation. The
Tavis-Cummings model describes the interaction between a bosonic degree of
freedom and a collective spin. In an ion trap, the collective spin system is a
symmetrised state of the internal electronic states of N ions, while the
bosonic system is the vibrational degree of freedom of the centre of mass mode
for the ions.


title:
Optimal local preparation of an arbitrary mixed state of two qubits.
  Closed expression for the single copy case

abstract:
  In this note we consider the problem of preparing a {\em single} copy of an
arbitrary two-qubit mixed state $\rho$ starting from an entangled pure state
$\psi$ and using only local operations assisted with classical communication.
We present an analytical expression for the minimal amount of pure state
entanglement required, and describe the corresponding local strategy. We also
examine optimal probabilistic generalizations of the previous process.


title:
Parallel Quantum Computation, the Library of Babel and Quantum
  Measurement as the Efficient Librarian

abstract:
  The complementary roles played by parallel quantum computation and quantum
measurement in originating the quantum speed-up are illustrated through an
analogy with a famous metaphor by J.L. Borges.


title: Simple Proof of Security of the BB84 Quantum Key Distribution Protocol

abstract:
  We prove the security of the 1984 protocol of Bennett and Brassard (BB84) for
quantum key distribution. We first give a key distribution protocol based on
entanglement purification, which can be proven secure using methods from Lo and
Chau's proof of security for a similar protocol. We then show that the security
of this protocol implies the security of BB84. The entanglement-purification
based protocol uses Calderbank-Shor-Steane (CSS) codes, and properties of these
codes are used to remove the use of quantum computation from the Lo-Chau
protocol.


title: Symmetric Classical Mechanics

abstract:
  We investigate the possibility that the semiclassical limit of quantum
mechanics might be correctly described by a classical dynamical theory, other
than standard classical mechanics. Using a set of classicality criteria
proposed in a related paper, we show that the time evolution of a set of
quantum initial data satisfying these criteria is fully consistent with the
predictions of a new theory of classical dynamics. The dynamical structure of
the new theory is given by the Moyal bracket. This is a Lie bracket that was
first derived as the dynamical structure of the Moyal-Weyl-Wigner formulation
of quantum mechanics. We present a new derivation of the Moyal bracket, this
time in the context of the semiclassical limit of quantum mechanics and thus
prove that both classical and quantum dynamics can be formulated in terms of
the same canonical structure.


title: Space Searches with a Quantum Robot

abstract:
  Quantum robots are described as mobile quantum computers and ancillary
systems that move in and interact with arbitrary environments. Their dynamics
is given as tasks which consist of sequences of alternating computation and
action phases. A task example is considered in which a quantum robot searches a
space region to find the location of a system. The possibility that the search
can be more efficient than a classical search is examined by considering use of
Grover's Algorithm to process the search results. For reversible searches this
is problematic for two reasons. One is the removal of entanglements generated
by the search process. The other is that even if the entanglement can be
avoided, the search process in 2-D space regions is no more efficient than a
classical search. However, quantum searches of space regions with 3 or more
dimensions are more efficient than classical searches. Reasons why quantum
robots are interesting independent of these results are briefly summarized.


title: Some remarks on separability of states

abstract:
  Several problems concerning separable states are clarified on the basis of
Choi's scheme and old Kadison and Tomiyama results. Moreover, we generalize
Terhal's construction of positive maps.


title: Separability properties of tripartite states with UxUxU-symmetry

abstract:
  We study separability properties in a 5-dimensional set of states of quantum
systems composed of three subsystems of equal but arbitrary finite Hilbert
space dimension. These are the states, which can be written as linear
combinations of permutation operators, or, equivalently, commute with unitaries
of the form UxUxU. We compute explicitly the following subsets: (1)
triseparable states, which are convex combinations of triple tensor products,
(2) biseparable states, which are separable for a twofold partition of the
system, and (3) states with positive partial transpose with respect to such a
partition.


title:
Motional sidebands and direct measurement of the cooling rate in the
  resonance fluorescence of a single trapped ion

abstract:
  Resonance fluorescence of a single trapped ion is spectrally analyzed using a
heterodyne technique. Motional sidebands due to the oscillation of the ion in
the harmonic trap potential are observed in the fluorescence spectrum. From the
width of the sidebands the cooling rate is obtained and found to be in
agreement with the theoretical prediction.


title:
On the possibility of quantum computation based on photon exchange
  interactions

abstract:
  We examine several proposed schemes by Franson et al. for quantum logic gates
based on non-local exchange interactions between two photons in a medium. In
these schemes the presence of a {\em single} photon in a given mode is supposed
to induce a large phase shift on another photon propagating in the same medium.
We conclude that the schemes proposed so far are not able to produce the
required conditional phase shift, even though the proposals contain many
stimulating and intriguing ideas.


title: Extended coherent states and modified perturbation theory

abstract:
  An extended coherent state for describing a system of two interacting quanum
objects is considered. A modified perturbation theory based on using the
extended coherent states is formulated.


title:
New experimental test of Bell inequalities by the use of a non-maximally
  entangled photon state

abstract:
  We report on the first realisation of a test of Bell inequalities using
non-maximally entangled states. It is based on the superposition of type I
parametric down conversion produced in two different non-linear crystals pumped
by the same laser, but with different polarisations. We discuss the advantages
and the possible developments of this configuration.


title:
Resonance Fluorescence Spectrum of a Trapped Ion Undergoing Quantum
  Jumps

abstract:
  We experimentally investigate the resonance fluorescence spectrum of single
171Yb and 172Yb ions which are laser cooled to the Lamb-Dicke regime in a
radiofrequency trap. While the fluorescence scattering of 172Yb is continuous,
the 171Yb fluorescence is interrupted by quantum jumps because a nonvanishing
rate of spontaneous transitions leads to electron shelving in the metastable
hyperfine sublevel 2D3/2(F=2). The average duration of the resulting dark
periods can be varied by changing the intensity of a repumping laser field.
Optical heterodyne detection is employed to analyze the fluorescence spectrum
near the Rayleigh elastic scattering peak. It is found that the stochastic
modulation of the fluorescence emission by quantum jumps gives rise to a
Lorentzian component in the fluorescence spectrum, and that the linewidth of
this component varies according to the average duration of the dark
fluorescence periods. The experimental observations are in quantitative
agreement with theoretical predictions.


title: An NMR-based nanostructure switch for quantum logic

abstract:
  We propose a nanostructure switch based on nuclear magnetic resonance (NMR)
which offers reliable quantum gate operation, an essential ingredient for
building a quantum computer. The nuclear resonance is controlled by the magic
number transitions of a few-electron quantum dot in an external magnetic field.


title: Atomic Quantum State Teleportation and Swapping

abstract:
  A set of protocols for atomic quantum state teleportation and swapping
utilizing Einstein-Podolsky-Rosen light is proposed. The protocols are suitable
for collective spin states of a macroscopic sample of atoms, i.e. for
continuous atomic variables. Feasibility of experimental realization for
teleportation of a gas sample of atoms is analyzed.


title:
Classical and quantum mechanics on information spaces with applications
  to cognitive, psychological, social and anomalous phenomena

abstract:
  We use the system of p-adic numbers for the description of information
processes. Basic objects of our models are so called transformers of
information, basic processes are information processes, the statistics are
information statistics (thus we present a model of information reality). The
classical and quantum mechanical formalisms on information p-adic spaces are
developed. It seems that classical and quantum mechanical models on p-adic
information spaces can be applied for the investigation of flows of information
in cognitive and social systems, since a p-adic metric gives quite natural
description of the ability to form associations.


title: Non-Kolmogorov probability models and modified Bell's inequality

abstract:
  We analyse the proof of Bell's inequality and demonstrate that this
inequality is related to one particular model of probability theory, namely
Kolmogorov measure-theoretical axiomatics, 1933. We found a (numerical)
statistical correction to Bell's inequality. Such an additional term in the
right hand side of Bell's inequality can be considered as a probability
invariant of a quantum state. This is a measure of nonreproducibility of hidden
variables in different runs of experiments. Experiments to verify Bell's
inequality can be considered as just experiments to estimate this constant. It
seems that Bell's inequality could not be used as a crucial reason to deny
local realism. We consider deterministic as well as stochastic hidden variables
models.


title: The Modal Interpretation of Algebraic Quantum Field Theory

abstract:
  In a recent article, Dieks has proposed a way to implement the modal
interpretation of (nonrelativistic) quantum theory in relativistic quantum
field theory. We show that his proposal fails to yield a well-defined
prescription for which observables in a local spacetime region possess definite
values. On the other hand, we demonstrate that there is a well-defined and
unique way of extending the modal interpretation to the local algebras of
relativistic quantum field theory. This extension, however, faces a potentially
serious difficulty in connection with ergodic states of a field.


title:
Finite temperature excitations of an inhomogneous trapped Bose gas with
  Feshbach resonances

abstract:
  We derive and discuss the temperature dependance of the condensate and
noncondensate density profile of a Bose-Einstein condensate gas with Feshbach
resonance in a parabolic trap. These quantities are calculated
self-consistently using the generalized Hartree-Fock-Bogoliubov (HFB) equations
within the Bogoliubov approximation. At zero temperature, the HFB equation can
be solved by means of a variation method that give the low excitation spectrum.
Moreover, within the two-body collision theory, we estimate the relationship
between the atom number and the external magnetic field $B$, it is in good
agreement with the data in recent experiments.


title: Parallel and Anti-Parallel Spins: More Differences

abstract: The authors have withdrawn this paper.


title: Casimir force at both non-zero temperature and finite conductivity

abstract:
  We find the joint effect of non-zero temperature and finite conductivity onto
the Casimir force between real metals. Configurations of two parallel plates
and a sphere (lens) above a plate are considered. Perturbation theory in two
parameters (the relative temperature and the relative penetration depth of zero
point oscillations into the metal) is developed. Perturbative results are
compared with computations. Recent evidence concerning possible existence of
large temperature corrections at small separations between the real metals is
not supported.


title: Quantum Computing with Neutral Atoms in an Optical Lattice

abstract:
  We present a proposal for quantum information processing with neutral atoms
trapped in optical lattices as qubits. Initialization and coherent control of
single qubits can be achieved with standard laser cooling and spectroscopic
techniques. We consider entangling two-qubit logic gates based on optically
induced dipole-dipole interactions, calculating a figure-of-merit for various
protocols. Massive parallelism intrinsic to the lattice geometry makes this an
intriguing system for scalable, fault-tolerant quantum computation.


title: Maximally entangled mixed states in two qubits

abstract:
  We propose novel mixed states in two qubits, ``maximally entangled mixed
states'', which have a property that the amount of entanglement of these states
cannot be increased further by applying any unitary operations. The property is
proven when the rank of the states is less than 4, and confirmed numerically in
the other general cases. The corresponding entanglement of formation specified
by its eigenvalues gives an upper bound of that for density matrices with same
eigenvalues.


title: Factoring the unitary evolution operator and quantifying entanglement

abstract:
  The unitary evolution can be represented by a finite product of exponential
operators. It leads to a perturbative expression of the density operator of a
close system. Based on the perturbative expression scheme, we present a
entanglement measure, this measure has the advantage that it is easy to compute
for a general dynamical process.


title: Lambda's, V's and optimal cloning with stimulated emission

abstract:
  We show that optimal universal cloning of the polarization state of photons
can be achieved via stimulated emission in three-level systems, both of the
Lambda and the V type. We establish the equivalence of our systems with coupled
harmonic oscillators, which permits us to analyze the structure of the cloning
transformations realized. These transformations are shown to be equivalent to
the optimal cloning transformations for qubits discovered by Buzek and Hillery,
and Gisin and Massar. The down-conversion cloner discovered previously by some
of the authors is obtained as a limiting case. We demonstrate an interesting
equivalence between systems of Lambda atoms and systems of pairwise entangled V
atoms. Finally we discuss the physical differences between our photon cloners
and the qubit cloners considered previously and prove that the bounds on the
fidelity of the clones derived for qubits also apply in our situation.


title:
Quantum mechanical probabilities and general probabilistic constraints
  for Einstein-Podolsky-Rosen-Bohm experiments

abstract:
  Relativistic causality, namely, the impossibility of signaling at
superluminal speeds, restricts the kinds of correlations which can occur
between different parts of a composite physical system. Here we establish the
basic restrictions which relativistic causality imposes on the joint
probabilities involved in an experiment of the Einstein-Podolsky-Rosen-Bohm
type. Quantum mechanics, on the other hand, places further restrictions beyond
those required by general considerations like causality and consistency. We
illustrate this fact by considering the sum of correlations involved in the
CHSH inequality. Within the general framework of the CHSH inequality, we also
consider the nonlocality theorem derived by Hardy, and discuss the constraints
that relativistic causality, on the one hand, and quantum mechanics, on the
other hand, impose on it. Finally, we derive a simple inequality which can be
used to test quantum mechanics against general probabilistic theories.


title:
Light Pulse Squeezed State Formation In Medium With The Relaxation Kerr
  Nonlinearity

abstract:
  The consistent theory of formation of pulsed squeezed states as a result of
self-action of ultrashort light pulse in the medium with relaxation Kerr
nonlinearity has been developed. A simple method to form the ultrashort light
pulse with sub-Poissonian photon statistics is analyzed too.


title:
Quantum theory of self-action of ultrashort light pulses in an inertial
  nonlinear medium

abstract:
  The systematic theory of the formation of the short light pulses in the
squeezed state during the propagation in a medium with inertial Kerr
nonlinearity is developed. The algebra of time-dependent Bose-operators is
elaborated and the normal-ordering theorem for them is formulated. It is
established that the spectral region where the quadrature fluctuations are
weaker than the shot-noise, depends on both the relaxation time of the
nonlinearity and the magnitude of the nonlinear phase shift. It is also shown
that the frequency at which suppression of the fluctuation is greatest can be
controlled by adjusting the phase of the initial coherent light pulse. The
spectral correlation function of photons is introduced and photon antibunching
is found.


title: Controlling decoherence of a two-level-atom in a lossy cavity

abstract:
  By use of external periodic driving sources, we demonstrate the possibility
of controlling the coherent as well as the decoherent dynamics of a two-level
atom placed in a lossy cavity.
  The control of the coherent dynamics is elucidated for the phenomenon of
coherent destruction of tunneling (CDT), i.e., the coherent dynamics of a
driven two-level atom in a quantum superposition state can be brought
practically to a complete standstill. We study this phenomenon for different
initial preparations of the two-level atom. We then proceed to investigate the
decoherence originating from the interaction of the two-level atom with a lossy
cavity mode. The loss mechanism is described in terms of a microscopic model
that couples the cavity mode to a bath of harmonic field modes. A suitably
tuned external cw-laser field applied to the two-level atom slows down
considerably the decoherence of the atom. We demonstrate the suppression of
decoherence for two opposite initial preparations of the atomic state: a
quantum superposition state as well as the ground state. These findings can be
used to the effect of a proficient battling of decoherence in qubit
manipulation processes.


title: Fermi gas in harmonic oscillator potentials

abstract:
  Assuming the validity of grand canonical statistics, we study the properties
of a spin-polarized Fermi gas in harmonic traps. Universal forms of Fermi
temperature $T_F$, internal energy $U$ and the specific heat per particle of
the trapped Fermi gas are calculated as a {\it function} of particle number,
and the results compared with those of infinite number particles.


title: Silicon-based Quantum Computation

abstract:
  An architecture for a quantum computer is presented in which spins associated
with donors in silicon function as qubits. Quantum operations on the spins are
performed using a combination of voltages applied to gates adjacent to the
spins and radio frequency applied magnetic fields resonant with spin
transitions. Initialization and measurement of electron spins is made by
electrostatic probing of a two electron system, whose orbital configuration
must depend on the spin states of the electrons because of the Pauli Principle.
Specific devices will be discussed which perform all the necessary operations
for quantum computing, with an emphasis placed on the qualitative principles
underlying their operation.
  The likely impediments to achieving large-scale quantum computation using
this architecture will be addressed: the computer must operate at extremely low
temperature, must be fabricated from devices built with near atomic precision,
and will require extremely accurate gating operations in order to perform
quantum logic. Refinements to the computer architecture will be presented which
could remedy each of these deficiencies. I will conclude by discussing a
specific realization of the computer using Si/SiGe heterostructures into which
donors are deposited using a low energy focused ion beam.


title: Structure of the Algebra of Effective Observables in Quantum Mechanics

abstract:
  A subclass of dynamical semigroups induced by the interaction of a quantum
system with an environment is introduced. Such semigroups lead to the selection
of a stable subalgebra of effective observables. The structure of this
subalgebra is completely determined.


title: Measurements of Nondegenerate Discrete Observables

abstract:
  Every measurement on a quantum system causes a state change from the system
state just before the measurement to the system state just after the
measurement conditional upon the outcome of measurement. This paper determines
all the possible conditional state changes caused by measurements of
nondegenerate discrete observables. For this purpose, the following conditions
are shown to be equivalent for measurements of nondegenerate discrete
observables: (i) The joint probability distribution of the outcomes of
successive measurements depends affinely on the initial state. (ii) The
apparatus has an indirect measurement model. (iii) The state change is
described by a positive superoperator valued measure. (iv) The state change is
described by a completely positive superoperator valued measure. (v) The output
state is independent of the input state and the family of output states can be
arbitrarily chosen by the choice of the apparatus. The implications to the
measurement problem are discussed briefly.


title: Resonant cancellation of off-resonant effects in a multilevel qubit

abstract:
  Off-resonant effects are a significant source of error in quantum
computation. This paper presents a group theoretic proof that off-resonant
transitions to the higher levels of a multilevel qubit can be completely
prevented in principle. This result can be generalized to prevent unwanted
transitions due to qubit-qubit interactions. A simple scheme exploiting dynamic
pulse control techniques is presented that can cancel transitions to higher
states to arbitrary accuracy.


title: One Complexity Theorist's View of Quantum Computing

abstract:
  The complexity of quantum computation remains poorly understood. While
physicists attempt to find ways to create quantum computers, we still do not
have much evidence one way or the other as to how useful these machines will
be. The tools of computational complexity theory should come to bear on these
important questions. Quantum computing often scares away many potential
researchers from computer science because of the apparent background need in
quantum mechanics and the alien looking notation used in papers on the topic.
This paper will give an overview of quantum computation from the point of view
of a complexity theorist. We will see that one can think of BQP as yet another
complexity class and study its power without focusing on the physical aspects
behind it.


title: Comment on `Quantum Games and Quantum Strategies'

abstract:
  In a recent paper, Eisert et al. presented a quantum mechanical
generalization of Prisoner's Dilemma. They asserted that the maximally
entangled game exhibits a unique Nash equilibrium which yields a pay-off
equivalent to cooperative behaviour. In this comment we show that their
observation is incorrect: there is no Nash equilibrium in the space of
deterministic quantum strategies.


title:
An Experiment to Distinguish Between de Broglie-Bohm and Standard
  Quantum Mechanics

abstract:
  An experiment is suggested that is capable of distinguishing between the de
Broglie-Bohm theory and standard quantum mechanics.


title: On the Additivity of the Entanglement of Formation

abstract:
  We withdraw this paper due to insufficient arguments in the derivation of
Theorem 1. See quant-ph/0005062 for the new paper


title: Perturbative expansion for master equation and it applications

abstract:
  We construct generally applicable small-loss rate expansions for the density
operator of an open system. Successive terms of those expansions yield
characteristic loss rates for dissipation processes. Three applications are
presented in order to give further insight into the context of those
expansions. The first application, of a two-level atom coupling to a bosonic
environment, shows the procedure and the advantage of the expansion, whereas
the second application that consists of a single mode field in a cavity with
linewidth $\kappa$ due to partial transmission through one mirror illustrates a
practical use of those expansions in quantum measurements, and the third one,
for an atom coupled to modes of a lossy cavity shows the another use of the
perturbative expansion.


title:
Unified approach to quantum capacities: towards quantum noisy coding
  theorem

abstract:
  Basing on unified approach to {\it all} kinds of quantum capacities we show
that the rate of quantum information transmission is bounded by the maximal
attainable rate of coherent information. Moreover, we show that, if for any
bipartite state the one-way distillable entanglement is no less than coherent
information, then one obtains Shannon-like formulas for all the capacities. The
inequality also implies that the decrease of distillable entanglement due to
mixing process does not exceed of corresponding loss information about a
system.


title: Consistent histories, the quantum Zeno effect, and time of arrival

abstract:
  We present a decomposition of the general quantum mechanical evolution
operator, that corresponds to the path decomposition expansion, and interpret
its constituents in terms of the quantum Zeno effect (QZE). This decomposition
is applied to a finite dimensional example and to the case of a free particle
in the real line, where the possibility of boundary conditions more general
than those hitherto considered in the literature is shown. We reinterpret the
assignment of consistent probabilities to different regions of spacetime in
terms of the QZE. The comparison of the approach of consistent histories to the
problem of time of arrival with the solution provided by the probability
distribution of Kijowski shows the strength of the latter point of view.


title: Formation of ultrashort pulses with sub-Poissonian photon statistics

abstract:
  A simple method for the production of ultrashort light pulses (USPs) with
suppressed photon fluctuations is considered. The method is based on self-phase
modulation (SPM) of an USP in a nonlinear medium (optical fibre) and subsequent
transmission of pulse through a dispersive optical element.


title: The Haroche-Ramsey experiment as a generalized measurement

abstract:
  A number of atomic beam experiments, related to the Ramsey experiment and a
recent experiment by Brune et al., are studied with respect to the question of
complementarity. Three different procedures for obtaining information on the
state of the incoming atom are compared. Positive operator-valued measures are
explicitly calculated. It is demonstrated that, in principle, it is possible to
choose the experimental arrangement so as to admit an interpretation as a joint
non-ideal measurement yielding interference and ``which-way'' information.
Comparison of the different measurements gives insight into the question of
which information is provided by a (generalized) quantum mechanical
measurement. For this purpose the subspaces of Hilbert-Schmidt space, spanned
by the operators of the POVM, are determined for different measurement
arrangements and different values of the parameters.


title: Interferometers and Decoherence Matrices

abstract:
  It is shown that the Lorentz group is the natural language for two-beam
interferometers if there are no decoherence effects. This aspect of the
interferometer can be translated into six-parameter representations of the
Lorentz group, as in the case of polarization optics where there are two
orthogonal components of one light beam. It is shown that there are groups of
transformations which leave the coherency or density matrix invariant, and this
symmetry property is formulated within the framework of Wigner's little groups.
An additional mathematical apparatus is needed for the transition from a pure
state to an impure state. Decoherence matrices are constructed for this
process, and their properties are studied in detail. Experimental tests of this
symmetry property are possible.


title: About the Dirac Equation with a $\delta$ potential

abstract:
  An elementary treatment of the Dirac Equation in the presence of a
three-dimensional spherically symmetric $\delta (r-r_0)$-potential is
presented. We show how to handle the matching conditions in the configuration
space, and discuss the occurrence of supercritical effects.


title: Strict Holism in a Quantum Superposition of Macroscopic States

abstract:
  We show that some N-particle quantum systems are holistic, such that the
system is deterministic, whereas its parts are random. The total correlation is
not sufficient to determine the probability distribution, showing a need for
extra measurements. We propose a formal definition of holism not based on
separability.


title:
Indistinguishability and nonlocality in Einstein-Podolsky-Rosen
  experiment

abstract:
  Quasi-set theory allows us a non trivial relation between
indistinguishability and nonlocality into the context of Einstein-
Podolsky-Rosen experiment. Quasi-set theory is a set theory which provides a
manner for dealing with collections of indistinguishable but not identical
elementary particles.


title: On a quantum version of Shannon's conditional entropy

abstract:
  In this article we propose a quantum version of Shannon's conditional
entropy. Given two density matrices $\rho$ and $\sigma$ on a finite dimensional
Hilbert space and with $S(\rho)=-\tr\rho\ln\rho$ being the usual von Neumann
entropy, this quantity $S(\rho|\sigma)$ is concave in $\rho$ and satisfies
$0\le S(\rho|\sigma)\le S(\rho)$, a quantum analogue of Shannon's famous
inequality. Thus we view $S(\rho|\sigma)$ as the entropy of $\rho$ conditioned
by $\sigma$.


title: Berry's Phase in the Presence of a Dissipative Medium

abstract:
  We consider the spin 1/2 model coupled to a slowly varying magnetic field in
the presence of a weak damping represented by a Lindblad-form operators. We
show that Berry's geometrical phase remains unaltered by the two dissipation
mechanism considered. Dissipation effects are twofold: a shrinking in the
modulus of the Bloch's vector, which characterizes coherence loss and a time
dependent (dissipation related) precession angle. We show that the line
broadening of the Fourier transformation of the components of magnetization is
only due to the presence of dissipation.


title:
Generalized Schmidt decomposition and classification of
  three-quantum-bit states

abstract:
  We prove for any pure three-quantum-bit state the existence of local bases
which allow to build a set of five orthogonal product states in terms of which
the state can be written in a unique form. This leads to a canonical form which
generalizes the two-quantum-bit Schmidt decomposition. It is uniquely
characterized by the five entanglement parameters. It leads to a complete
classification of the three-quantum-bit states. It shows that the right outcome
of an adequate local measurement always erases all entanglement between the
other two parties.


title: Decoherence and Measurement in Open Quantum Systems

abstract:
  We review results of a recently developed model of a microscopic quantum
system interacting with the macroscopic world components which are modeled by
collections of bosonic modes. The interaction is via a general operator
$\Lambda$ of the system, coupled to the creation and annihilation operators of
the environment modes. We assume that in the process of a nearly instantaneous
quantum measurement, the function of the environment involves two distinct
parts: the pointer and the bath. Interaction of the system with the bath leads
to decoherence such that the system and the pointer both evolve into a
statistical mixture state described by the density matrix such that the system
is in one of the eigenstates of $\Lambda$ with the correct quantum mechanical
probability, whereas the expectation values of pointer operators retain
amplified information on that eigenstate. We argue that this process represents
the initial step of a quantum measurement. Calculation of the elements of the
reduced density matrix of the system and pointer is carried out exactly, and
time dependence of decoherence is identified. We discuss general implications
of our model of energy-conserving coupling to a heat bath for processes of
adiabatic quantum decoherence. We also evaluate changes in the expectation
values of certain pointer operators and suggest that these can be interpreted
as macroscopic indicators of the measurement outcome.


title:
Single Atoms in an Optical Dipole Trap: Towards a Deterministic Source
  of Cold Atoms

abstract:
  We describe a simple experimental technique which allows us to store a small
and deterministic number of neutral atoms in an optical dipole trap. The
desired atom number is prepared in a magneto-optical trap overlapped with a
single focused Nd:YAG laser beam. Dipole trap loading efficiency of 100 % and
storage times of about one minute have been achieved. We have also prepared
atoms in a certain hyperfine state and demonstrated the feasibility of a
state-selective detection via resonance fluorescence at the level of a few
neutral atoms. A spin relaxation time of the polarized sample of $4.2\pm 0.7$ s
has been measured. Possible applications are briefly discussed.


title:
Fidelity and information in the quantum teleportation of continuous
  variables

abstract:
  Ideally, quantum teleportation should transfer a quantum state without
distortion and without providing any information about that state. However,
quantum teleportation of continuous electromagnetic field variables introduces
additional noise, limiting the fidelity of the quantum state transfer. In this
article, the operator describing the quantum state transfer is derived. The
transfer operator modifies the probability amplitudes of the quantum state in a
shifted photon number base by enhancing low photon numbers and suppressing high
photon numbers. This modification of the statistical weight corresponds to a
measurement of finite resolution performed on the original quantum state. The
limited fidelity of quantum teleportation is thus shown to be a direct
consequence of the information obtained in the measurement.


title: Information transfer and fidelity in quantum copiers

abstract:
  We find that very different quantum copying machines are optimal depending on
the indicator used to assess their performance. Several quantum copying machine
models acting on non-orthogonal input states are investigated, and assessed
according to two types of criteria: Transfer of (Shannon) information encoded
in the initial states to the copies, and fidelity between the copies and the
initial states. Transformations which optimise information transfer for
messages encoded in qubits are found. If the message is decoded one symbol
at-a-time, information is best copied by a Wootters-Zurek copier.


title: Entangled States of N Identical Particles

abstract:
  We explore the connection between quantum entanglement and the exchange
symmetry of the states of N identical particles. Each particle has n-levels.
The N particles span the nN dimensional Hilbert space. We shall call the
general state of the particle as a qunit. The direct product of the N qunit
space is given a decomposition in terms of states with definite permutation
symmetry that are found to have a measure of entanglement which is related to
the representation of the permutation group. The maximally entangled states are
generated from the linear combinations of fully correlated but unentangled
states. The states of lower entanglement are generated from the manifold of
partially correlated states. The degree of exchange symmetry is found to be
related to a group theoretical measure of entanglement.
  Email: Jagdish_Rai@hotmail.com, jrai@iitk.ac.in Email: srai56@hotmail.com


title:
Derivation of Standard Treatment of Spin Addition From Probability
  Amplitudes

abstract:
  In a recent paper, we introduced a new way of treating systems of compounded
angular momentum. We obtained the probability amplitudes for measurements on
the systems and used these to derive the matrix treatment of compounded spin.
However, the matrix forms are in 3- and 4- dimensional space and are therefore
entirely different from the standard forms. This raises the question of the
connection between these forms and the standard forms. In this paper, we answer
this question. We not only derive the standard matrix treatment of spin
addition - we discover a more generalized form of the theory. We apply the new
generalized theory to the singlet and triplet states arising from the addition
of the spins of two systems of spin 1/2 each. We obtain new generalized forms
of the vectors and operators for these cases, and show that they reduce to the
standard forms in the appropriate limit.


title: Bell's Theorem and Nonlinear Systems

abstract:
  For all Einstein-Podolsky-Rosen-type experiments on deterministic systems the
Bell inequality holds, unless non-local interactions exist between certain
parts of the setup. Here we show that in nonlinear systems the Bell inequality
can be violated by non-local effects that are arbitrarily weak. Then we show
that the quantum result of the existing Einstein-Podolsky-Rosen-type
experiments can be reproduced within deterministic models that include
arbitrarily weak non-local effects.


title: Local and Nonlocal Properties of Werner States

abstract:
  We consider a special kind of mixed states -- a {\it Werner derivative},
which is the state transformed by nonlocal unitary -- local or nonlocal --
operations from a Werner state. We show the followings. (i) The amount of
entanglement of Werner derivatives cannot exceed that of the original Werner
state. (ii) Although it is generally possible to increase the entanglement of a
single copy of a Werner derivative by LQCC, the maximal possible entanglement
cannot exceed the entanglement of the original Werner state. The extractable
entanglement of Werner derivatives is limited by the entanglement of the
original Werner state.


title: Optimal Encryption of Quantum Bits

abstract:
  We characterize the complete set of protocols that may be used to securely
encrypt n quantum bits using secret and random classical bits. In addition to
the application of such quantum encryption protocols to quantum data security,
our framework allows for generalizations of many classical cryptographic
protocols to quantum data. We show that the encrypted state gives no
information without the secret classical data, and that 2n random classical
bits are the minimum necessary for informationally secure quantum encryption.
Moreover, the quantum operations are shown to have a surprising structure in a
canonical inner product space. This quantum encryption protocol is a
generalization of the classical one time pad concept. A connection is made
between quantum encryption and quantum teleportation, and this allows for a new
proof of optimality of teleportation.


title: Partial Teleportation of Entanglement in the Noisy Environment

abstract:
  Partial teleportation of entanglement is to teleport one particle of an
entangled pair through a quantum channel. This is conceptually equivalent to
quantum swapping. We consider the partial teleportation of entanglement in the
noisy environment, employing the Werner-state representation of the noisy
channel for the simplicity of calculation. To have the insight of the many-body
teleportation, we introduce the measure of correlation information and study
the transfer of the correlation information and entanglement. We find that the
fidelity gets smaller as the initial-state is entangled more for a given
entanglement of the quantum channel. The entangled channel transfers at least
some of the entanglement to the final state.


title:
Measurements in quantum physics: towards a physical picture of relevant
  processes

abstract:
  We propose a new structure of ensembles in quantum theory, based on the
recently introduced intrinsic properties of electrons and photons. On this
statistical basis the spreading of a wave-packet, collapse of the wave
function, the quantum eraser, and interaction-free measurements are re-analyzed
and the usual conceptual problems removed.


title: Entanglement and Collective Quantum Operations

abstract:
  We show how shared entanglement, together with classical communication and
local quantum operations, can be used to perform an arbitrary collective
quantum operation upon N spatially-separated qubits. A simple
teleportation-based protocol for achieving this, which requires 2(N-1) ebits of
shared, bipartite entanglement and 4(N-1) classical bits, is proposed. In terms
of the total required entanglement, this protocol is shown to be optimal for
even N in both the asymptotic limit and for `one-shot' applications.


title: The Representation of Natural Numbers in Quantum Mechanics

abstract:
  This paper represents one approach to making explicit some of the assumptions
and conditions implied in the widespread representation of numbers by composite
quantum systems. Any nonempty set and associated operations is a set of natural
numbers or a model of arithmetic if the set and operations satisfy the axioms
of number theory or arithmetic. This work is limited to k-ary representations
of length L and to the axioms for arithmetic modulo k^{L}. A model of the
axioms is described based on states in and operators on an abstract L fold
tensor product Hilbert space H^{arith}. Unitary maps of this space onto a
physical parameter based product space H^{phy} are then described. Each of
these maps makes states in H^{phy}, and the induced operators, a model of the
axioms. Consequences of the existence of many of these maps are discussed along
with the dependence of Grover's and Shor's Algorithms on these maps. The
importance of the main physical requirement, that the basic arithmetic
operations are efficiently implementable, is discussed. This conditions states
that there exist physically realizable Hamiltonians that can implement the
basic arithmetic operations and that the space-time and thermodynamic resources
required are polynomial in L.


title: From Einstein Nonlocality to Von Neumann Reality

abstract:
  Recent nonlocality results support a new picture of reality built on the
ideas of John von Neumanm


title: Decoherence, Quantum Zeno Effect, and the Efficacy of Mental Effort

abstract:
  Recent theoretical and experimental papers support the prevailing opinion
that large warm systems will rapidly lose quantum coherence, and that classical
properties will emerge. This rapid loss of coherence would naturally be
expected to block any critical role for quantum theory in explaining the
interaction between our conscious experiences and the physical activities of
our brains. However, there is a quantum theory of mind in which the efficacy of
mental effort is not affected by decoherence effects. In this theory the
effects of mental action on brain activity is achieved by a Quantum Zeno Effect
that is not weakened by decoherence. The theory is based on a relativistic
version of von Neumann's quantum theory. It encompasses all the predictions of
Copenhagen quantum theory, which include all the validated predictions of
classical physical theory. In addition, it forges two-way dynamical links
between the physical and experiential aspects of nature. The theory has
significant explanatory power.


title:
Functional relations in Stokes multipliers - Fun with $x^6 + \alpha x^2$
  potential-

abstract:
  We consider eigenvalue problems in quantum mechanics in one dimension.
Hamiltonians contain a class of double well potential terms, x^6 + \alpha x^2,
for example . The space coordinate is continued to a complex plane and the
connection problem of fundamental system of solutions is considered. A hidden
U_q(\hat{gl}(2|1)) structure arises in "fusion relations" of Stokes
multipliers. With this observation, we derive coupled nonlinear integral
equations which characterize the spectral properties of both \pm \alpha
potentials simultaneously. equations.


title:
Correlations of measurement information and noise in quantum
  measurements with finite resolution

abstract:
  The original purpose of measurements is to provide us with information about
a previously unknown physical property of the system observed. In the Hilbert
space formalism of quantum mechanics, this physical meaning of measurement
information is not immediately apparent. In order to study the relationship
between the Hilbert space coherence of the quantum state and the measurement
information obtained in the laboratory, we introduce a generalized measurement
postulate for finite resolution measurements. With this measurement model,
correlations between non-commuting observables can be investigated. These
experimentally accessible correlations reveal nonclassical features in their
dependence on the operator ordering, reflecting the particular measurement
context by which they are determined.


title:
Universal construction of unitary transformation of quantum computation
  with one- and two-body interactions

abstract:
  Any unitary transformation of quantum computational networks is explicitly
decomposed, in an exact and unified form, into a sequence of a limited number
of one-qubit quantum gates and the two-qubit diagonal gates that have diagonal
unitary representation in usual computational basis. This decomposition may be
simplified greatly with the help of the properties of the finite-dimensional
multiple-quantum operator algebra spaces of a quantum system and the specific
properties of a given quantum algorithm. As elementary building blocks of
quantum computation, the two-qubit diagonal gates and one-qubit gates may be
constructed physically with one- and two-body interactions in a two-state
quantum system and hence could be conveniently realized experimentally. The
present work will be helpful for implementing generally any N-qubit quantum
computation in those feasible two-state quantum systems and determining
conveniently the time evolution of these systems in course of quantum
computation.


title: Duality and Anholonomy in Quantum Mechanics of 1D Contact Interactions

abstract:
  We study systems with parity invariant contact interactions in one dimension.
The model analyzed is the simplest nontrivial one --- a quantum wire with a
point defect --- and yet is shown to exhibit exotic phenomena, such as strong
vs weak coupling duality and spiral anholonomy in the spectral flow. The
structure underlying these phenomena is SU(2), which arises as accidental
symmetry for a particular class of interactions.


title: All Teleportation and Dense Coding Schemes

abstract:
  We establish a one-to-one correspondence between (1) quantum teleportation
schemes, (2) dense coding schemes, (3) orthonormal bases of maximally entangled
vectors, (4) orthonormal bases of unitary operators with respect to the
Hilbert-Schmidt scalar product, and (5) depolarizing operations, whose Kraus
operators can be chosen to be unitary. The teleportation and dense coding
schemes are assumed to be ``tight'' in the sense that all Hilbert spaces
involved have the same finite dimension d, and the classical channel involved
distinguishes d^2 signals. A general construction procedure for orthonormal
bases of unitaries, involving Latin Squares and complex Hadamard Matrices is
also presented.


title: Reply to a review of photon-exchange interactions by Opatrny and Kurizki

abstract:
  In a recent review article, Opatrny and Kurizki [submitted to Fortschr.
Phys., e-print quant-ph/0003010] discussed a number of issues related to the
feasibility of quantum computation based on photon-exchange interactions. This
Reply summarizes my view of each of the issues and the overall prospects for
quantum computing based on photon-exchange interactions.


title: Communication Capacity of Quantum Computation

abstract:
  By considering quantum computation as a communication process, we relate its
efficiency to a communication capacity. This formalism allows us to rederive
lower bounds on the complexity of search algorithms. It also enables us to link
the mixedness of a quantum computer to its efficiency. We discuss the
implications of our results for quantum measurement.


title:
Welcher Weg Experiments and the Orthodox Bohr's Complementarity
  Principle

abstract:
  In its most orthodox form, Bohr's Complementarity Principle states that a
quanton (a quantum system consisting of a Boson or Fermion) can either behave
as a particle or as wave, but never simultaneosuly as both. A less orthodox
interpretation of this Principle is the ``duality condition'' embodied in a
mathematical inequality due to Englert [B-G Englert, Phys. Rev. Lett., Vol. 77,
2154 (1996)] which allows wave and particle attributes to co-exist, but
postulates that a stronger manifestation of the particle nature leads to a
weaker manifestation of the wave nature and vice versa. In this Letter, we show
that some recent {\it welcher weg} ("which path") experiments in
interferometers and similar set-ups, that claim to have validated, or
invalidated, the Complementarity Principle, actually shed no light on the
orthodox interpretation. They may have instead validated the weaker duality
condition, but even that is not completely obvious. We propose simple
modifications to these experiments which we believe can test the orthodox
Complementarity Principle and also shed light on the nature of wavefunction
collapse and quantum erasure.


title:
On the nature of continuous physical quantities in classical and quantum
  mechanics

abstract:
  Within the traditional Hilbert space formalism of quantum mechanics, it is
not possible to describe a particle as possessing, simultaneously, a sharp
position value and a sharp momentum value. Is it possible, though, to describe
a particle as possessing just a sharp position value (or just a sharp momentum
value)? Some, such as Teller (Journal of Philosophy, 1979), have thought that
the answer to this question is No -- that the status of individual continuous
quantities is very different in quantum mechanics than in classical mechanics.
On the contrary, I shall show that the same subtle issues arise with respect to
continuous quantities in classical and quantum mechanics; and that it is, after
all, possible to describe a particle as possessing a sharp position value
without altering the standard formalism of quantum mechanics.


title: Causality, delocalization and positivity of energy

abstract:
  In a series of interesting papers G. C. Hegerfeldt has shown that quantum
systems with positive energy initially localized in a finite region,
immediately develop infinite tails. In our paper Hegerfeldt's theorem is
analysed using quantum and classical wave packets. We show that Hegerfeldt's
conclusion remains valid in classical physics. No violation of Einstein's
causality is ever involved. Using only positive frequencies, complex wave
packets are constructed which at $t = 0$ are real and finitely localized and
which, furthemore, are superpositions of two nonlocal wave packets. The
nonlocality is initially cancelled by destructive interference. However this
cancellation becomes incomplete at arbitrary times immediately afterwards. In
agreement with relativity the two nonlocal wave packets move with the velocity
of light, in opposite directions.


title:
A Magnetic Resonance Force Microscopy Quantum Computer with Tellurium
  Donors in Silicon

abstract:
  We propose a magnetic resonance force microscopy (MRFM)-based nuclear spin
quantum computer using tellurium impurities in silicon. This approach to
quantum computing combines the well-developed silicon technology with expected
advances in MRFM.


title:
Dynamics of Nonlocality for A Two-Mode Squeezed State in Thermal
  Environment

abstract:
  We investigate the time evolution of nonlocality for a two-mode squeezed
state in the thermal environment. The initial two-mode pure squeezed state is
nonlocal with a stronger nonlocality for a larger degree of squeezing. It is
found that the larger the degree of initial squeezing is, the more rapidly the
squeezed state loses its nonlocality. We explain this by the rapid destruction
of quantum coherence for the strongly squeezed state.


title:
Transfer of nonclassical features in quantum teleportation via a mixed
  quantum channel

abstract:
  Quantum teleportation of a continuous-variable state is studied for the
quantum channel of a two-mode squeezed vacuum influenced by a thermal
environment. Each mode of the squeezed vacuum is assumed to undergo the same
thermal influence. It is found that when the mixed two-mode squeezed vacuum for
the quantum channel is separable, any nonclassical features, which may be
imposed in an original unknown state, cannot be transferred to a receiving
station. A two-mode Gaussian state, one of which is a mixed two-mode squeezed
vacuum, is separable if and only if a positive well-defined $P$ function can be
assigned to it. The fidelity of teleportation is considered in terms of the
noise factor given by the imperfect channel. It is found that quantum
teleportation may give more noise than direct transmission of a field under the
thermal environment, which is due to the fragile nature of quantum entanglement
of the quantum channel.


title:
Subnormal operators regarded as generalized observables and
  compound-system-type normal extension related to su(1,1)

abstract:
  In this paper, subnormal operators, not necessarily bounded, are discussed as
generalized observables. In order to describe not only the information about
the probability distribution of the output data of their measurement but also a
framework of their implementations, we introduce a new concept
compound-system-type normal extension, and we derive the compound-system-type
normal extension of a subnormal operator, which is defined from an irreducible
unitary representation of the algebra su(1,1). The squeezed states are
characterized as the eigenvectors of an operator from this viewpoint, and the
squeezed states in multi-particle systems are shown to be the eigenvectors of
the adjoints of these subnormal operators under a representation. The affine
coherent states are discussed in the same context, as well.


title: The f-conditioned Phase Transform

abstract:
  We present a quantum algorithm for the f-conditioned phase transform which
does not require any initialization of ancillary register. We also develop a
quantum algorithm that can solve the generalized Deutsch-Jozsa problem by a
single evaluation of a function.


title:
The Coulomb - harmonic oscillator correspondence in PT-symmetric quantum
  mechanics

abstract:
  We show that and how the Coulomb potential can be regularized and solved
exactly at the imaginary couplings. The new spectrum of energies is real and
bounded as expected, but its explicit form proves totally different from the
usual real-coupling case.


title: Complete quantum teleportation with a Kerr nonlinearity

abstract:
  We present a scheme for the quantum teleportation of the polarization state
of a photon employing a cross-Kerr medium. The experimental feasibility of the
scheme is discussed and we show that, using the recently demonstrated ultraslow
light propagation in cold atomic media, our proposal can be realized with
presently available technology.