title: Creating Decoherence-Free Subspaces with Strong and Fast Pulses

abstract:
  A decoherence-free subspace (DFS) isolates quantum information from
deleterious environmental interactions. We give explicit sequences of strong
and fast (``bang-bang'', BB) pulses that create the conditions allowing for the
existence of DFSs that support scalable, universal quantum computation. One
such example is the creation of the conditions for collective decoherence,
wherein all system particles are coupled in an identical manner to their
environment. The BB pulses needed for this are generated using only the
Heisenberg exchange interaction. In conjunction with previous results, this
shows that Heisenberg exchange is all by itself an enabler of universal fault
tolerant quantum computation on DFSs.


title:
Atom Lasers, Coherent States, and Coherence:II. Maximally Robust
  Ensembles of Pure States

abstract:
  As discussed in Wiseman and Vaccaro [quant-ph/9906125], the stationary state
of an optical or atom laser far above threshold is a mixture of coherent field
states with random phase, or, equivalently, a Poissonian mixture of number
states. We are interested in which, if either, of these descriptions of
$\rho_{ss}$, is more natural. In the preceding paper we concentrated upon
whether descriptions such as these are physically realizable (PR). In this
paper we investigate another relevant aspect of these ensembles, their
robustness. A robust ensemble is one for which the pure states that comprise it
survive relatively unchanged for a long time under the system evolution. We
determine numerically the most robust ensembles as a function of the parameters
in the laser model: the self-energy $\chi$ of the bosons in the laser mode, and
the excess phase noise $\nu$. We find that these most robust ensembles are PR
ensembles, or similar to PR ensembles, for all values of these parameters. In
the ideal laser limit ($\nu=\chi=0$), the most robust states are coherent
states. As the phase noise $\nu$ or phase dispersion $\chi$ is increased, the
most robust states become increasingly amplitude-squeezed. We find scaling laws
for these states. As the phase diffusion or dispersion becomes so large that
the laser output is no longer quantum coherent, the most robust states become
so squeezed that they cease to have a well-defined coherent amplitude. That is,
the quantum coherence of the laser output is manifest in the most robust PR
states having a well-defined coherent amplitude. This lends support to the idea
that robust PR ensembles are the most natural description of the state of the
laser mode. It also has interesting implications for atom lasers in particular,
for which phase dispersion due to self-interactions is expected to be large.


title:
Scalar charged particle in Weyl--Wigner--Moyal phase space. Constant
  magnetic field

abstract:
  A relativistic phase-space representation for a class of observables with
matrix-valued Weyl symbols proportional to the identity matrix
(charge-invariant observables)is proposed. We take into account the nontrivial
charge structure of the position and momentum operators. The evolution equation
coincides with its analog in relativistic quantum mechanics with nonlocal
Hamiltonian under conditions where particle-pair creation does not take place
(free particle and constant magnetic field). The differences in the equations
are connected with peculiarities of the constraints on the initial conditions.
An effective increase in coherence between eigenstates of the Hamiltonian is
found and possibilities of its experimental observation are discussed.


title:
Quantum key distribution with realistic states: photon-number statistics
  in the photon-number splitting attack

abstract:
  Quantum key distribution can be performed with practical signal sources such
as weak coherent pulses. One example of such a scheme is the Bennett-Brassard
protocol that can be implemented via polarization of the signals, or equivalent
signals. It turns out that the most powerful tool at the disposition of an
eavesdropper is the photon-number splitting attack. We show that this attack
can be extended in the relevant parameter regime such as to preserve the
Poissonian photon number distribution of the combination of the signal source
and the lossy channel.


title: In defence of naivete: The conceptual status of Lagrangian QFT

abstract:
  I analyse the conceptual and mathematical foundations of Lagrangian quantum
field theory (that is, the "naive" quantum field theory used in mainstream
physics, as opposed to algebraic quantum field theory). The objective is to see
whether Lagrangian quantum field theory has a sufficiently firm conceptual and
mathematical basis to be a legitimate object of foundational study, or whether
it is too ill-defined. The analysis covers renormalisation and infinities,
inequivalent representations, and the concept of localised states; the
conclusion is that Lagrangian QFT (at least as described here) is a perfectly
respectable physical theory, albeit somewhat different in certain respects from
most of those studied in foundational work.


title: Emergence of particles from bosonic quantum field theory

abstract:
  An examination is made of the way in which particles emerge from linear,
bosonic, massive quantum field theories. Two different constructions of the
one-particle subspace of such theories are given, both illustrating the
importance of the interplay between the quantum-mechanical linear structure and
the classical one. Some comments are made on the Newton-Wigner representation
of one-particle states, and on the relationship between the approach of this
paper and those of Segal, and of Haag and Ruelle.


title: Comments on the experimental disproof of Multisimultaneity

abstract:
  The recent Geneva experiment strikingly displays lawlike reversibility
together with quantum nonseparability. As in any probabilistic physics
correlation expresses interaction, and as Born's probability rules grafted upon
de Broglie's wave mechanics turn the probability scheme into the code of an
information transmitting telegraph, the Lorentz and CPT invariant transition
amplitude reversibly carries a zigzagging causation.


title:
Signal-Locality and Subquantum Information in Deterministic
  Hidden-Variables Theories

abstract:
  It is proven that any deterministic hidden-variables theory, that reproduces
quantum theory for a 'quantum equilibrium' distribution of hidden variables,
must predict the existence of instantaneous signals at the statistical level
for hypothetical 'nonequilibrium ensembles'. This 'signal-locality theorem'
generalises yet another feature of the pilot-wave theory of de Broglie and
Bohm, for which it is already known that signal-locality is true only in
equilibrium. Assuming certain symmetries, lower bounds are derived on the
'degree of nonlocality' of the singlet state, defined as the (equilibrium)
fraction of outcomes at one wing of an EPR-experiment that change in response
to a shift in the distant angular setting. It is shown by explicit calculation
that these bounds are satisfied by pilot-wave theory. The degree of nonlocality
is interpreted as the average number of bits of 'subquantum information'
transmitted superluminally, for an equilibrium ensemble. It is proposed that
this quantity might provide a novel measure of the entanglement of a quantum
state, and that the field of quantum information would benefit from a more
explicit hidden-variables approach. It is argued that the signal-locality
theorem supports the hypothesis, made elsewhere, that in the remote past the
universe relaxed to a state of statistical equilibrium at the hidden-variable
level, a state in which nonlocality happens to be masked by quantum noise.


title: From Monte Carlo to Quantum Computation

abstract:
  Quantum computing was so far mainly concerned with discrete problems.
  Recently, E. Novak and the author studied quantum algorithms for high
dimensional integration and dealt with the question, which advantages quantum
computing can bring over classical deterministic or randomized methods for this
type of problem.
  In this paper we give a short introduction to the basic ideas of quantum
computing and survey recent results on high dimensional integration. We discuss
connections to the Monte Carlo methology and compare the optimal error rates of
quantum algorithms to those of classical deterministic and randomized
algorithms.


title: Quantum Integration in Sobolev Classes

abstract:
  We study high dimensional integration in the quantum model of computation. We
develop quantum algorithms for integration of functions from Sobolev classes
$W^r_p([0,1]^d)$ and analyze their convergence rates. We also prove lower
bounds which show that the proposed algorithms are, in many cases, optimal
within the setting of quantum computing. This extends recent results of Novak
on integration of functions from H\"older classes.


title:
Conservation laws, uncertainty relations, and quantum limits of
  measurements

abstract:
  The uncertainty relation between the noise operator and the conserved
quantity leads to a bound for the accuracy of general measurements. The bound
extends the assertion by Wigner, Araki, and Yanase that conservation laws limit
the accuracy of ``repeatable'', or ``nondisturbing'', measurements to general
measurements, and improves the one previously obtained by Yanase for spin
measurements. The bound also sets an obstacle to making a small quantum
computer.


title:
Understanding Quantum Entanglement of Bipartite System Based on Bell
  Inequality

abstract:
  We present an alternative definition of quantum entanglement for bipartite
system based on Bell inequality and operators' noncommutativity. A state is
said to be entangled, if the maximum of CHSH expectation value $F_{\max}$ is
obtain by noncommutative measures on each particle of the bipartite system;
otherwise, the state is a disentangled state. A uniform measure quantifying the
degree of entanglement for any state of the bipartite system is also proposed.


title: Quantum Theory for the Binomial Model in Finance Theory

abstract:
  In this paper, a quantum model for the binomial market in finance is
proposed. We show that its risk-neutral world exhibits an intriguing structure
as a disk in the unit ball of ${\bf R}^3,$ whose radius is a function of the
risk-free interest rate with two thresholds which prevent arbitrage
opportunities from this quantum market. Furthermore, from the quantum
mechanical point of view we re-deduce the Cox-Ross-Rubinstein binomial option
pricing formula by considering Maxwell-Boltzmann statistics of the system of
$N$ distinguishable particles.


title: A model for the stochastic origins of Schrodinger's equation

abstract:
  A model for the motion of a charged particle in the vacuum is presented
which, although purely classical in concept, yields Schrodinger's equation as a
solution. It suggests that the origins of the peculiar and nonclassical
features of quantum mechanics are actually inherent in a statistical
description of the radiative reactive force.


title: Quantum Finance: The Finite Dimensional Case

abstract:
  In this paper, we present a quantum version of some portions of Mathematical
Finance, including theory of arbitrage, asset pricing, and optional
decomposition in financial markets based on finite dimensional quantum
probability spaces. As examples, the quantum model of binomial markets is
studied. We show that this quantum model ceases to pose the paradox which
appears in the classical model of the binomial market. Furthermore, we
re-deduce the Cox-Ross-Rubinstein binomial option pricing formula by
considering multi-period quantum binomial markets.


title: A Non-commutative Version of the Fundamental Theorem of Asset Pricing

abstract:
  In this note, a non-commutative analogue of the fundamental theorem of asset
pricing in mathematical finance is proved.


title: Charge in electric field in probability representation

abstract:
  Green function and linear integrals of motion for a charged particle moving
in electric field are discussed. Wigner function and tomogram of the ststionary
states of the charge are obtained. Connection of quantum propagators for
Schrodinger evolution equation, Moyal evolution equation and evolution equation
in tomographic probability representation for charge moving in electric field
is discussed.


title:
Experimental Realization of Br\"{u}schweiler's exponentially fast search
  algorithm in a homo-nuclear system

abstract:
  Compared with classical search algorithms, Grover quantum algorithm [ Phys.
Rev. Lett., 79, 325(1997)] achieves quadratic speedup and Bruschweiler hybrid
quantum algorithm [Phys. Rev. Lett., 85, 4815(2000)] achieves an exponential
speedup. In this paper, we report the experimental realization of the
Bruschweiler$ algorithm in a 3-qubit NMR ensemble system. The pulse sequences
are used for the algorithms and the measurement method used here is improved on
that used by Bruschweiler, namely, instead of quantitatively measuring the spin
projection of the ancilla bit, we utilize the shape of the ancilla bit
spectrum. By simply judging the downwardness or upwardness of the corresponding
peaks in an ancilla bit spectrum, the bit value of the marked state can be read
out, especially, the geometric nature of this read-out can make the results
more robust against errors.


title:
Fetching marked items from an unsorted database in NMR ensemble
  computing

abstract:
  Searching a marked item or several marked items from an unsorted database is
a very difficult mathematical problem. Using classical computer, it requires
$O(N=2^n)$ steps to find the target. Using a quantum computer, Grover's
algorithm uses $O(\sqrt{N=2^n})$ steps. In NMR ensemble computing,
Brushweiler's algorithm uses $\log N$ steps. In this Letter, we propose an
algorithm that fetches marked items in an unsorted database directly. It
requires only a single query. It can find a single marked item or multiple
number of items.


title:
Comment on ``One-Step Synthesis of Multiatom Greenberger-Horne-Zeilinger
  States'' [Shi-Biao Zheng, Phys. Rev. Lett. 87, 230404 (2001)]

abstract:
  We point out the relation between the work of Zheng and ours, APS [G.S.
Agarwal, R.R. Puri, and R.P. Singh, Phys. Rev. A 56, 2249 (2001)] and show the
important connection between the atomic cat state and the GHZ states.


title:
Stationary states of Jaynes-Cummings model with atomic center-of-mass
  quantum motion: direct comparison of standing-wave and
  counterpropagating-waves cases

abstract:
  The eigenstate problem of the Jaynes-Cummings model on the basis of complete
Hamiltonian, including the center-of -mass kinetic energy operator, is treated.
The energy spectrum and wave functions in standing-wave (SW)- and
counterpropagating waves (CPW)- cases are calculated and compared with each
other. It is shown that in CPW-case i) the atomic momentum distribution is
asymmetric and somewhat narrower in general; ii) the concept of quasimomentum
is not applicable and instead the ordinary momentum concerns the problem; iii)
atomic and photonic state distributions are self-consistent, and, in
consequence iiii) mean number of photons in the counterpropagating traveling
waves and mean atomic momentum match. Explicit analytic expressions for energy
eigenvalues and eigenfunctions are found in Tavis -Cummings-type approximation
[Phys. Rev. 170, 379(1968)] and is pointed, that it implies only the
bounded-like states for atomic center-of-mass motion. It is also shown that if
the recoil energy is taken into account, the Doppleron resonance is split into
two branches, one of which diverges to Bragg-like resonance in the high-order
range.


title:
Phase transitions in a one-dimensional multibarrier potential of finite
  range

abstract:
  We have previously studied properties of a one-dimensional potential with $N$
equally spaced identical barriers in a (fixed) finite interval for both finite
and infinite $N$. It was observed that scattering and spectral properties
depend sensitively on the ratio $c$ of spacing to width of the barriers (even
in the limit $N \to \infty$). We compute here the specific heat of an ensemble
of such systems and show that there is critical dependence on this parameter,
as well as on the temperature, strongly suggestive of phase transitions.


title: Towards a unification of physics and information theory

abstract:
  A common framework for quantum mechanics, thermodynamics and information
theory is presented. It is accomplished by reinterpreting the mathematical
formalism of Everett's many-worlds theory of quantum mechanics and augmenting
it to include preparation according to a given ensemble. The notion of
\emph{directed entanglement} is introduced through which both classical and
quantum communication over quantum channels are viewed as entanglement
transfer. This point is illustrated by proving the Holevo bound and quantum
data processing inequality relying exclusively on the properties of directed
entanglement. Within the model, quantum thermodynamic entropy is also related
to directed entanglement, and a simple proof of the second law of
thermodynamics is given.


title: Selected elevation in quantum tunneling

abstract:
  The tunneling through an opaque barrier with a strong oscillating component
is investigated. It is shown, that in the strong perturbations regime (in
contrast to the weak one), higher perturbations rate does not necessarily
improve the activation. In fact, in this regime two rival factors play a role,
and as a consequence, this tunneling system behaves like a sensitive
frequency-shifter device: for most incident particles' energies activation
occurs and the particles are energetically elevated, while for specific
energies activation is depressed and the transmission is very low. This effect
is unique to the strong perturbation regime, and it is totally absent in the
weak perturbation case. Moreover, it cannot be deduced even in the adiabatic
regime. It is conjectured that this mechanism can be used as a
frequency-dependent transistor, in which the device's transmission is governed
by the external field frequency.


title: Interaction cost of non-local gates

abstract:
  We introduce the interaction cost of a non-local gate as the minimal time of
interaction required to perform the gate when assisting the process with fast
local unitaries. This cost, of interest both in the areas of quantum control
and quantum information, depends on the specific interaction, and allows to
compare in an operationally meaningful manner any two non-local gates. In the
case of a two-qubit system, an analytical expression for the interaction cost
of any unitary operation given any coupling Hamiltonian is obtained. One gate
may be more time-consuming than another for any possible interaction. This
defines a partial order structure in the set of non-local gates, that compares
their degree of non-locality. We analytically characterize this partial order
in a region of the set of two-qubit gates.


title:
Geometric observation for the Bures fidelity between two states of a
  qubit

abstract:
  In this Brief Report, we present a geometric observation for the Bures
fidelity between two states of a qubit.


title: Steering a quantum system over a Schroedinger bridge

abstract:
  A new approach to the steering problem for quantum systems relying on
Nelson's stochastic mechanics and on the theory of Schroedinger bridges is
presented. The method is illustrated by working out a simple Gaussian example.


title:
Minimum-error discrimination between subsets of linearly dependent
  quantum states

abstract:
  A measurement strategy is developed for a new kind of hypothesis testing. It
assigns, with minimum probability of error, the state of a quantum system to
one or the other of two complementary subsets of a set of N given
non-orthogonal quantum states occurring with given a priori probabilities. A
general analytical solution is obtained for N states that are restricted to a
two-dimensional subspace of the Hilbert space of the system. The result for the
special case of three arbitrary but linearly dependent states is applied to a
variety of sets of three states that are symmetric and equally probable. It is
found that, in this case, the minimum error probability for distinguishing one
of the states from the other two is only about half as large as the minimum
error probability for distinguishing all three states individually.


title: Securing quantum bit commitment through reverse quantum communication

abstract:
  Einstein-Podolsky-Rosen- (EPR) and the more powerful Mayers-Lo-Chau attack
impose a serious constraint on quantum bit commitment (QBC). As a way to
circumvent them, it is proposed that the quantum system encoding the commitment
chosen by the committer (Alice) should be initially prepared in a seperable
quantum state known to and furnished by the acceptor (Bob), rather than Alice.
Classical communication is used to conclude the commitment phase and bind
Alice's subsequent unveiling. Such a class of secure protocols can be built
upon currently proposed QBC schemes impervious to a simple EPR attack. A
specific scheme based on the Brassard-Crepeau-Josza-Langlois protocol is
presented here as an example.


title:
The van der Waals Potential between Metastable Atoms and Solid Surfaces:
  Novel Diffraction Experiments versus Theory

abstract:
  Highly polarizable metastable He* ($\mathrm{2^3S}$) and Ne* ($\mathrm{2^3P}$)
atoms have been diffracted from a 100 nm period silicon nitride transmission
grating and the van der Waals coefficients $C_3$ for the interaction of the
excited atoms with the silicon nitride surface have been determined from the
diffraction intensities out to the 10th order. The results agree with
calculations based on the non-retarded Lifshitz formula.


title:
Semiclassical Quantization for the Spherically Symmetric Systems under
  an Aharonov-Bohm magnetic flux

abstract:
  The semiclassical quantization rule is derived for a system with a
spherically symmetric potential $V(r) \sim r^{\nu}$ $(-2<\nu <\infty)$ and an
Aharonov-Bohm magnetic flux. Numerical results are presented and compared with
known results for models with $\nu = -1,0,2,\infty$. It is shown that the
results provided by our method are in good agreement with previous results. One
expects that the semiclassical quantization rule shown in this paper will
provide a good approximation for all principle quantum number even the rule is
derived in the large principal quantum number limit $n \gg 1$. We also discuss
the power parameter $\nu $ dependence of the energy spectra pattern in this
paper.


title: The q-deformed Jaynes-Cummings Model and its q-Supercoherent States

abstract:
  In this paper, we have proposed a q-deformed Jaynes-Cummings(JC) model and
constructed the q-SuperCoherent States(q-SCSs) for the q-deformed JC model. We
have also discussed the properties of the q-supercoherent states and given the
completeness relation expression. The representation of the q-supercoherent
states for the q-deformed JC model is studied as well. PACS number(s): 03.65.Nk
Key Works: q-deformed JC model, q-supercoherent states,q-SCSs representation.


title:
Experimental realization of Shor's quantum factoring algorithm using
  nuclear magnetic resonance

abstract:
  The number of steps any classical computer requires in order to find the
prime factors of an $l$-digit integer $N$ increases exponentially with $l$, at
least using algorithms known at present. Factoring large integers is therefore
conjectured to be intractable classically, an observation underlying the
security of widely used cryptographic codes. Quantum computers, however, could
factor integers in only polynomial time, using Shor's quantum factoring
algorithm. Although important for the study of quantum computers, experimental
demonstration of this algorithm has proved elusive. Here we report an
implementation of the simplest instance of Shor's algorithm: factorization of
${N=15}$ (whose prime factors are 3 and 5). We use seven spin-1/2 nuclei in a
molecule as quantum bits, which can be manipulated with room temperature liquid
state nuclear magnetic resonance techniques. This method of using nuclei to
store quantum information is in principle scalable to many quantum bit systems,
but such scalability is not implied by the present work. The significance of
our work lies in the demonstration of experimental and theoretical techniques
for precise control and modelling of complex quantum computers. In particular,
we present a simple, parameter-free but predictive model of decoherence effects
in our system.


title: Some aspects of separability

abstract:
  We present three necessary separability criteria for bipartite mixed states,
the violation of each of these conditions is a sufficient condition for
entanglement. Some ideas on the issue of finding a necessary and sufficient
criterion of separability are also discussed.


title:
On a Supposed Conceptual Inadequacy of the Shannon Information in
  Quantum Mechanics

abstract:
  Recently, Brukner and Zeilinger (2001) have claimed that the Shannon
information is not well defined as a measure of information in quantum
mechanics, adducing arguments that seek to show that it is inextricably tied to
classical notions of measurement. It is shown here that these arguments do not
succeed: the Shannon information does not have problematic ties to classical
concepts. In a further argument, Brukner and Zeilinger compare the Shannon
information unfavourably to their preferred measure, I(p), with regard to the
definition of a notion of `total information content'. This argument is found
unconvincing and the relationship between individual measures of information
and notions of `total information content' investigated. We close by
considering the prospects of Zeilinger's Foundational Principle as a
foundational principle for quantum mechanics


title: Conservative Quantum Computing

abstract:
  Conservation laws limit the accuracy of physical implementations of
elementary quantum logic gates. If the computational basis is represented by a
component of spin and physical implementations obey the angular momentum
conservation law, any physically realizable unitary operators with size less
than n qubits cannot implement the controlled-NOT gate within the error
probability 1/(4n^2), where the size is defined as the total number of the
computational qubits and the ancilla qubits. An analogous limit for bosonic
ancillae is also obtained to show that the lower bound of the error probability
is inversely proportional to the average number of photons. Any set of
universal gates inevitably obeys a related limitation with error probability
O(1/n^2)$. To circumvent the above or related limitations yielded by
conservation laws, it is recommended that the computational basis should be
chosen as the one commuting with the additively conserved quantities.


title:
Resonances and spectral properties of detuned OPO pumped by fluctuating
  sources

abstract:
  Twin beam fluctuations are analyzed for detuned and mismatched OPO
configurations. Resonances and frequency responses to the quantum noise sources
(quantum and pump amplitude/phase fluctuations) are examined as functions of
cavity decay rates, excitation parameter and detuning. The dependence of self-
and mutual correlations of beam amplitudes and phases on detuning, mismatch and
damping parameters is discussed.


title: Demonstration of negative group delays in a simple electronic circuit

abstract:
  We present a simple electronic circuit which produces negative group delays
for base-band pulses. When a band-limited pulse is applied as the input, a
forwarded pulse appears at the output. The negative group delays in lumped
systems share the same mechanism with the superluminal light propagation, which
is recently demonstrated in an absorption-free, anomalous dispersive medium
[Wang et al., Nature 406, 277 (2000)]. In this circuit, the advance time more
than twenty percent of the pulse width can easily be achieved. The time
constants, which can be in the order of seconds, is slow enough to be observed
with the naked eye by looking at the lamps driven by the pulses.


title: Comment on "No-Signaling Condition and Quantum Dynamics"

abstract:
  This paper contains a criticism of the article: Ch. Simon, V. Buzek and N.
Gisin: ``No-Signaling Condition and Quantum Dynamics'', Phys. Rev. Lett. 87
(2001) 170405, containing a proposal of adoption into quantum mechanics (QM) a
new basic axiom. This axiom was declared to imply linearity of time evolution
in QM on the basis of kinematic assumptions only. It is shown why, under the
considered conditions, the axiom called ``no-signaling condition'' is not
effective.


title: Nodes in the Relativistic Quantum Trajectories and Photon's Trajectories

abstract:
  Through the constant potential and the linear potential, we establish the
existence of nodes for the relativistic quantum trajectories as the same way as
for the quantum trajectories. We establish the purely relativistic limit
$(\hbar \to 0)$ for these trajectories, and link the nodes to de Broglie's
wavelength.


title:
On gauge transformations of B\"acklund type and higher order nonlinear
  Schr\"odinger equations

abstract:
  We introduce a new, more general type of nonlinear gauge transformation in
nonrelativistic quantum mechanics that involves derivatives of the wave
function and belongs to the class of B\"acklund transformations. These
transformations satisfy certain reasonable, previously proposed requirements
for gauge transformations. Their application to the Schr\"odinger equation
results in higher order partial differential equations. As an example, we
derive a general family of 6th-order nonlinear Schr\"odinger equations, closed
under our nonlinear gauge group. We also introduce a new gauge invariant
current ${\bf \sigma}=\rho {\bf \nabla}\triangle \ln \rho $, where
$\rho=\bar\psi \psi$. We derive gauge invariant quantities, and characterize
the subclass of the 6th-order equations that is gauge equivalent to the free
Schr\"odinger equation. We relate our development to nonlinear equations
studied by Doebner and Goldin, and by Puszkarz.


title:
Flow equation approach to diagonal representation of an unbounded
  Hamiltonian with complex eigenvalues

abstract:
  The flow equation approach investigated by Wegner et al. is applied to an
unbounded Hamiltonian system with a generalization. We show that a well-known
quantized complex energy eigenvalues which is related to decay widths can be
given with this approach.


title: Supersymmetry and Brownian motion on supermanifolds

abstract:
  An anticommuting analogue of Brownian motion, corresponding to fermionic
quantum mechanics, is developed, and combined with classical Brownian motion to
give a generalised Feynman-Kac-It\^o formula for paths in geometric
supermanifolds. This formula is applied to give a rigorous version of the
proofs of the Atiyah-Singer index theorem based on supersymmetric quantum
mechanics. It is also shown how superpaths, parametrised by a commuting and an
anticommuting time variable, lead to a manifestly supersymmetric approach to
the index of the Dirac operator. After a discussion of the BFV approach to the
quantization of theories with symmetry, it is shown how the quantization of the
topological particle leads to the supersymmetric model introduced by Witten in
his study of Morse theory.


title: A lower bound on the quantum query complexity of read-once functions

abstract:
  We establish a lower bound of $\Omega{(\sqrt{n})}$ on the bounded-error
quantum query complexity of read-once Boolean functions, providing evidence for
the conjecture that $\Omega(\sqrt{D(f)})$ is a lower bound for all Boolean
functions. Our technique extends a result of Ambainis, based on the idea that
successful computation of a function requires ``decoherence'' of initially
coherently superposed inputs in the query register, having different values of
the function. The number of queries is bounded by comparing the required total
amount of decoherence of a judiciously selected set of input-output pairs to an
upper bound on the amount achievable in a single query step. We use an
extension of this result to general weights on input pairs, and general
superpositions of inputs.


title: Oblivious remote state preparation

abstract:
  We consider remote state preparation protocols for a set of pure states whose
projectors form a basis for operators acting on the input Hilbert space. If a
protocol (1) uses only forward communication and entanglement, (2)
deterministically prepares an exact copy of the state, and (3) does so
obliviously -- without leaking further information about the state to the
receiver -- then the protocol can be modified to require from the sender only a
single specimen of the state. Furthermore, the original protocol and the
modified protocol use the same amount of classical communication. Thus, under
the three conditions stated, remote state preparation requires at least as much
classical communication as teleportation, as Lo has conjectured [PRA 62 (2000)
012313], which is twice the expected classical communication cost of some
existing nonoblivious protocols.


title: U(2) invariant squeezing properties of pair coherent states

abstract:
  The U(2) invariant approach is delineated for the pair coherent states to
explore their squeezing properties. This approach is useful for a complete
analysis of the squeezing properties of these two-mode states. We use the
maximally compact subgroup U(2) of Sp(4,R) to mix the modes, thus allowing us
to search over all possible quadratures for squeezing. The variance matrix for
the pair coherent states turns out to be analytically diagonalisable, giving us
a handle over its least eigenvalue, through which we are able to pin down the
squeezing properties of these states. In order to explicitly demonstrate the
role played by U(2) transformations, we connect our results to the previous
analysis of squeezing for the pair coherent states.


title:
Quark-Parton Phase Transitions and the Entropy Problem in Quantum
  Mechanics

abstract:
  Since Feynman proposed his parton model in 1969, one of the most pressing
problems in high-energy physics has been whether partons are quarks. It is
shown that the quark model and the parton model are two different
manifestations of one covariant entity. The nature of transition from the
confined quarks to plasma-like partons is studied in terms of the entropy and
temperature coming from the time-separation variable. According to Einstein,
the time-separation variable exists wherever there is a spatial separation, but
it is not observed in the present form of quantum mechanics. It belongs to
Feynman's rest of the universe.


title:
Generation of any superposition of Dicke state of excitons in coupled
  quantum dots

abstract:
  We present a scheme to generate arbitrary superposition of the Dicke states
of excitons in optically driven quantum dots. This proposal is based on a
sequence of laser pulses, which are tuned appropriately to control transitions
on Dicke state. It is shown that N laser pulses are needed to generate
arbitrary superposition of the Dicke states of N quantum dots.


title: Information-theoretical meaning of quantum dynamical entropy

abstract:
  The theory of noncommutative dynamical entropy and quantum symbolic dynamics
for quantum dynamical systems is analised from the point of view of quantum
information theory. Using a general quantum dynamical system as a communication
channel one can define different classical capacities depending on the
character of resources applied for encoding and decoding procedures and on the
type of information sources. It is shown that for Bernoulli sources the
entanglement-assisted classical capacity, which is the largest one, is bounded
from above by the quantum dynamical entropy defined in terms of operational
partitions of unity. Stronger results are proved for the particular class of
quantum dynamical systems -- quantum Bernoulli shifts. Different classical
capacities are exactly computed and the entanglement-assisted one is equal to
the dynamical entropy in this case.


title: An unsharp logic from quantum computation

abstract:
  Logical gates studied in quantum computation suggest a natural logical
abstraction that gives rise to a new form of unsharp quantum logic. We study
the logical connectives corresponding to the following gates: the Toffoli gate,
the NOT and the squareroot of NOT (which admit of natural physical models).
This leads to a semantic characterization of a logic that we call computational
quantum logic CQL.


title: Qubit geometry and conformal mapping

abstract:
  Identifying the Bolch sphere with the Riemann sphere(the extended complex
plane), we obtain relations between single qubit unitary operations and
M\"{o}bius transformations on the extended complex plane.


title:
Relativistic precession and spin dynamics of an elliptic Rydberg wave
  packet

abstract:
  Time evolution of wave packets built from the eigenstates of the Dirac
equation for a hydrogenic system is considered. We investigate the space and
spin motion of wave packets which, in the non-relativistic limit, are
stationary states with a probability density distributed uniformly along the
classical, elliptical orbit (elliptic WP). We show that the precession of such
a WP, due to relativistic corrections to the energy eigenvalues, is strongly
correlated with the spin motion. We show also that the motion is universal for
all hydrogenic systems with an arbitrary value of the atomic number Z.


title: Algebraic treatment of the confluent Natanzon potentials

abstract:
  Using the so(2,1) Lie algebra and the Baker, Campbell and Hausdorff formulas,
the Green's function for the class of the confluent Natanzon potentials is
constructed straightforwardly. The bound-state energy spectrum is then
determined. Eventually, the three-dimensional harmonic potential, the
three-dimensional Coulomb potential and the Morse potential may all be
considered as particular cases.


title: Unspeakable quantum information

abstract:
  No verbal explanation can indicate a direction in space or the orientation of
a coordinate system. Only material objects can do it. In this article we
consider the use of a set of spin-\half particles in an entangled state for
indicating a direction, or a hydrogen atom in a Rydberg state for transmitting
a Cartesian frame. Optimal strategies are derived for the emission and
detection of the quantum signals.


title: Recovery Operator for Local Errors Generated by Gauge Multiplets

abstract:
  The components of a quantum computer are quantum subsystems which have a
complex internal structure. This structure is determined by short-range
interactions which are appropriately described in terms of local gauge fields
of the first kind. Any modification of their state would produce, in general, a
new type of internal error, called local error, in the quantum state of the
computer. We suggest that the general treatement of the local errors produced
by a gauge multiplet can be done in the framework of the Algebraic Quantum
Field Theory. A recovery operator is constructed from the first principles.


title:
Delayed - Choice Entanglement - Swapping with Vacuum-One Photon Quantum
  States

abstract:
  We report the experimental realization of a recently discovered quantum
information protocol by Asher Peres implying an apparent non-local quantum
mechanical retrodiction effect. The demonstration is carried out by applying a
novel quantum optical method by which each singlet entangled state is
physically implemented by a two-dimensional subspace of Fock states of a mode
of the electromagnetic field, specifically the space spanned by the vacuum and
the one photon state, along lines suggested recently by E. Knill et al., Nature
409, 46 (2001) and by M. Duan et al., Nature 414, 413 (2001). The successful
implementation of the new technique is expected to play an important role in
modern quantum information and communication and in EPR quantum non-locality
studies.


title:
Adiabatic Approximation in the Density Matrix Approach: Non-Degenerate
  Systems

abstract:
  We study the adiabatic limit in the density matrix approach for a quantum
system coupled to a weakly dissipative medium. The energy spectrum of the
quantum model is supposed to be non-degenerate. In the absence of dissipation,
the geometric phases for periodic Hamiltonians obtained previously by M.V.
Berry are recovered in the present approach. We determine the necessary
condition satisfied by the coefficients of the linear expansion of the
non-unitary part of the Liouvillian in order to the imaginary phases acquired
by the elements of the density matrix, due to dissipative effects, be
geometric. The results derived are model-independent. We apply them to spin 1/2
model coupled to reservoir at thermodynamic equilibrium.


title:
Equivalence of the Siegert-pseudostate and Lagrange-mesh R-matrix
  methods

abstract:
  Siegert pseudostates are purely outgoing states at some fixed point expanded
over a finite basis. With discretized variables, they provide an accurate
description of scattering in the s wave for short-range potentials with few
basis states. The R-matrix method combined with a Lagrange basis, i.e.
functions which vanish at all points of a mesh but one, leads to simple
mesh-like equations which also allow an accurate description of scattering.
These methods are shown to be exactly equivalent for any basis size, with or
without discretization. The comparison of their assumptions shows how to
accurately derive poles of the scattering matrix in the R-matrix formalism and
suggests how to extend the Siegert-pseudostate method to higher partial waves.
The different concepts are illustrated with the Bargmann potential and with the
centrifugal potential. A simplification of the R-matrix treatment can usefully
be extended to the Siegert-pseudostate method.


title:
Quantum Matching Theory (with new complexity theoretic, combinatorial
  and topological insights on the nature of the Quantum Entanglement)

abstract:
  Classical matching theory can be defined in terms of matrices with
nonnegative entries. The notion of Positive operator, central in Quantum
Theory, is a natural generalization of matrices with nonnegative entries. Based
on this point of view, we introduce a definition of perfect Quantum (operator)
matching . We show that the new notion inherits many "classical" properties,
but not all of them . This new notion goes somewhere beyound matroids . For
separable bipartite quantum states this new notion coinsides with the full rank
property of the intersection of two corresponding geometric matroids . In the
classical situation, permanents are naturally associated with perfects
matchings. We introduce an analog of permanents for positive operators, called
Quantum Permanent and show how this generalization of the permanent is related
to the Quantum Entanglement. Besides many other things, Quantum Permanents
provide new rational inequalities necessary for the separability of bipartite
quantum states . Using Quantum Permanents, we give deterministic poly-time
algorithm to solve Hidden Matroids Intersection Problem and indicate some
"classical" complexity difficulties associated with the Quantum Entanglement.
Finally, we prove that the weak membership problem for the convex set of
separable bipartite density matrices is NP-HARD.


title: Approximate quantum data storage and teleportation

abstract:
  In this paper we present an optimal protocol by which an unknown state on a
Hilbert space of dimension $N$ can be approximately stored in an
$M$-dimensional quantum system or be approximately teleported via an
$M$-dimensional quantum channel. The fidelity of our procedure is determined
for pure states as well as for mixed states and states which are entangled with
auxiliary quantum systems of varying Hilbert space dimension, and it is
compared with theoretical results for the maximally achievable fidelity.


title:
Geometric phases for neutral and charged particles in a time-dependent
  magnetic field

abstract:
  It is well known that any cyclic solution of a spin 1/2 neutral particle
moving in an arbitrary magnetic field has a nonadiabatic geometric phase
proportional to the solid angle subtended by the trace of the spin. For neutral
particles with higher spin, this is true for cyclic solutions with special
initial conditions. For more general cyclic solutions, however, this does not
hold. As an example, we consider the most general solutions of such particles
moving in a rotating magnetic field. If the parameters of the system are
appropriately chosen, all solutions are cyclic. The nonadiabatic geometric
phase and the solid angle are both calculated explicitly. It turns out that the
nonadiabatic geometric phase contains an extra term in addition to the one
proportional to the solid angle. The extra term vanishes automatically for spin
1/2. For higher spin, however, it depends on the initial condition. We also
consider the valence electron of an alkaline atom. For cyclic solutions with
special initial conditions in an arbitrary strong magnetic field, we prove that
the nonadiabatic geometric phase is a linear combination of the two solid
angles subtended by the traces of the orbit and spin angular momenta. For more
general cyclic solutions in a strong rotating magnetic field, the nonadiabatic
geometric phase also contains extra terms in addition to the linear
combination.


title: Pairwise entanglement in the XX model with a magnetic impurity

abstract:
  For a 3-qubit Heisenberg model in a uniform magnetic field, the pairwise
thermal entanglement of any two sites is identical due to the exchange symmetry
of sites. In this paper we consider the effect of a non-uniform magnetic field
on the Heisenberg model, modeling a magnetic impurity on one site. Since
pairwise entanglement is calculated by tracing out one of the three sites, the
entanglement clearly depends on which site the impurity is located. When the
impurity is located on the site which is traced out, that is, when it acts as
an external field of the pair, the entanglement can be enhanced to the maximal
value 1; while when the field acts on a site of the pair the corresponding
concurrence can only be increased from 1/3 to 2/3.


title: Young's experiment and the finiteness of information

abstract:
  Young's experiment is the quintessential quantum experiment. It is argued
here that quantum interference is a consequence of the finiteness of
information. The observer has the choice whether that information manifests
itself as path information or in the interference pattern or in both partially
to the extent defined by the finiteness of information.


title:
Arbitrary classical privicy amplification can be used for the quantum
  key distribution

abstract: The paper is withdrawn.


title: Fermionic entanglement in itinerant systems

abstract:
  We study pairwise quantum entanglement in systems of fermions itinerant in a
lattice from a second-quantized perspective. Entanglement in the
grand-canonical ensemble is studied, both for energy eigenstates and for the
thermal state. Relations between entanglement and superconducting correlations
are discussed in a BCS-like model and for $\eta$-pair superconductivity.


title: Heisenberg Evolution WKB and Symplectic Area Phases

abstract:
  The Schrodinger and Heisenberg evolution operators are represented in quantum
phase space by their Weyl symbols. Their semiclassical approximations are
constructed in the short and long time regimes. For both evolution problems,
the WKB representation is purely geometrical: the amplitudes are functions of a
Poisson bracket and the phase is the symplectic area of a region in phase space
bounded by trajectories and chords. A unified approach to the Schrodinger and
Heisenberg semiclassical evolutions is developed by introducing an extended
phase space. In this setting Maslov's pseudodifferential operator version of
WKB analysis applies and represents these two problems via a common higher
dimensional Schrodinger evolution, but with different extended Hamiltonians.
The evolution of a Lagrangian manifold in the extended phase space, defined by
initial data, controls the phase, amplitude and caustic behavior. The
symplectic area phases arise as a solution of a boundary condition problem.
Various applications and examples are considered.


title: Method for decoupling error correction from privacy amplification

abstract:
  Entanglement purification provides a unifying framework for proving the
security of quantum key distribution schemes. Nonetheless, up till now, a local
commutability constraint in the CSS code construction means that the error
correction and privacy amplification procedures of BB84 are not fully
decoupled. Here, I provide a method to decouple the two processes completely.
The method requires Alice and Bob to share some initial secret string and use
it to encrypt the bit-flip error syndrome using one-time-pad encryption. As an
application, I prove the unconditional security of the interactive Cascade
protocol, proposed by Brassard and Salvail for error correction, modified by
one-time-pad encryption of the error syndrome, and followed by the random
matrix protocol for privacy amplification. This is an efficient protocol in
terms of both computational power and key generation rate.


title: Quantum Adiabatic Evolution Algorithms versus Simulated Annealing

abstract:
  We explain why quantum adiabatic evolution and simulated annealing perform
similarly in certain examples of searching for the minimum of a cost function
of n bits. In these examples each bit is treated symmetrically so the cost
function depends only on the Hamming weight of the n bits. We also give two
examples, closely related to these, where the similarity breaks down in that
the quantum adiabatic algorithm succeeds in polynomial time whereas simulated
annealing requires exponential time.


title: Generation of arbitrary quantum state in a high-Q cavity

abstract:
  We present a scheme to generate arbitrary superposition of the Fock states in
a high-Q cavity. This proposal is based on a sequence of laser pulses, which
are tuned appropriately to control transitions on Fock state. It is shown that
N laser pulses are needed to generate a pure state with a phonon number limit
$N$.


title: Quantum Computation by Quantum Operations on Mixed States

abstract:
  Usually models for quantum computations deal with unitary gates on pure
states. In this paper we generalize the usual model. We consider a model of
quantum computations in which the state is an operator of density matrix and
the gates are quantum operations, not necessarily unitary. A mixed state
(operator of density matrix) of n two-level quantum systems is considered as an
element of $4^{n}$-dimensional operator Hilbert space. Unitary quantum gates
and nonunitary quantum operations for n-qubit system are considered as
generalized quantum gates acting on mixed state. In this paper we study
universality for quantum computations by quantum operations on mixed states.


title:
Parameter differentiation and quantum state decomposition for time
  varying Schroedinger equations

abstract:
  For the unitary operator, solution of the Schroedinger equation corresponding
to a time-varying Hamiltonian, the relation between the Magnus and the product
of exponentials expansions can be expressed in terms of a system of first order
differential equations in the parameters of the two expansions. A method is
proposed to compute such differential equations explicitly and in a closed
form.


title:
Quantum Cybernetics: A New Perspective for Nelson's Stochastic Theory,
  Nonlocality, and the Klein-Gordon Equation

abstract:
  The Klein-Gordon equation is shown to be equivalent to coupled partial
differential equations for a sub-quantum Brownian movement of a ''particle'',
which is both passively affected by, and actively affecting, a diffusion
process of its generally nonlocal environment. This indicates circularly
causal, or ''cybernetic'', relationships between ''particles'' and their
surroundings. Moreover, in the relativistic domain, the original stochastic
theory of Nelson is shown to hold as a limiting case only, i.e., for a
vanishing quantum potential.


title:
Heisenberg's Introduction of the `Collapse of the Wavepacket' into
  Quantum Mechanics

abstract:
  Heisenberg in 1929 introduced the "collapse of the wavepacket" into quantum
theory. We review here an experiment at Berkeley which demonstrated several
aspects of this idea. In this experiment, a pair of daughter photons was
produced in an entangled state, in which the sum of their two energies was
equal to the sharp energy of their parent photon, in the nonlinear optical
process of spontaneous parametric down-conversion. The wavepacket of one
daughter photon collapsed upon a measurement-at-a-distance of the other
daughter's energy, in such a way that the total energy of the two-photon system
was conserved. Heisenberg's energy-time uncertainty principle was also
demonstrated to hold in this experiment.


title: Quantum Parrondo's Games

abstract:
  Parrondo's Paradox arises when two losing games are combined to produce a
winning one. A history dependent quantum Parrondo game is studied where the
rotation operators that represent the toss of a classical biased coin are
replaced by general SU(2) operators to transform the game into the quantum
domain. In the initial state, a superposition of qubits can be used to couple
the games and produce interference leading to quite different payoffs to those
in the classical case.


title: Long Distance Quantum Key Distribution without Quantum Memory

abstract:
  The paper has been withdrawn by the author because the result obtained has
been reported earlier by other authors.


title:
Positive Operation Valued Measurement Based Multi-User Detection in
  DS-CDMA Systems

abstract:
  3G and 4G mobile are based on CDMA technology. In order to increase the
effectiveness of CDMA receivers large amount of effort is invested to develop
suitable multi-user detector techniques. However, at this moment there are only
suboptimal solutions available because of the rather high complexity of optimal
detectors. One of the possible receiver technologies can be the quantum
assisted computing devices which allows high level parallelism in computation.
The first commercial devices are estimated by 2004, which meets the advert of
3G and 4G systems. In this paper we introduce a novel quantum computation based
Quantum Multi-user detection (QMUD) algorithm, employing simple Positive
Operation Valued Measurement (POVM), which provides optimal solution. The
proposed algorithm is robust to any kind of noise.


title:
Classical states and decoherence by unitary evolution in the
  thermodynamic limit

abstract:
  It is shown how classical states, meant as states representing a classical
object, can be produced in the thermodynamic limit, retaining the unitary
evolution of quantum mechanics. Besides, using a simple model of a single spin
interacting with a spin-bath, it is seen how decoherence, with the off-diagonal
terms in the density matrix going to zero, can be obtained when the number of
the spins in the bath is taken to go formally to infinity. In this case,
indeed, the system appears to flop at a frequency being formally infinity that,
from a physical standpoint, can be proved equivalent to a time average.

categories: quant-ph cond-mat.str-el hep-th physics.atom-ph


title: Embezzling Entangled Quantum States

abstract:
  We show that in the presence of arbitrary catalysts, any pure bipartite
entangled state can be converted into any other to unlimited accuracy without
the use of any communication, quantum or classical.


title: General-Purpose Parallel Simulator for Quantum Computing

abstract:
  With current technologies, it seems to be very difficult to implement quantum
computers with many qubits. It is therefore of importance to simulate quantum
algorithms and circuits on the existing computers. However, for a large-size
problem, the simulation often requires more computational power than is
available from sequential processing. Therefore, the simulation methods using
parallel processing are required.
  We have developed a general-purpose simulator for quantum computing on the
parallel computer (Sun, Enterprise4500). It can deal with up-to 30 qubits. We
have performed Shor's factorization and Grover's database search by using the
simulator, and we analyzed robustness of the corresponding quantum circuits in
the presence of decoherence and operational errors. The corresponding results,
statistics and analyses are presented.


title: Mixed collective states of many spins

abstract:
  Mixed states of samples of spin s particles which are symmetric under
permutations of the particles are described in terms of their total collective
spin quantum numbers. We use this description to analyze the influence on spin
squeezing due to imperfect initial state preparation.


title: Engineering Entanglement between two cavity modes

abstract:
  We present scheme for generation of entanglement between different modes of
radiation field inside high-Q superconducting cavities. Our scheme is based on
the interaction of a three-level atom with the cavity field for pre-calculated
interaction times with each mode. This work enables us to generate complete set
of Bell basis states and GHZ state.


title: Trading by Quantum Rules - Quantum Anthropic Principle

abstract:
  This is a short review of the background and recent development in quantum
game theory and its possible application in economics and finance. The
intersection of science and society is discussed and Quantum Anthropic
Principle is put forward. The review is addressed to non-specialists.


title:
Bell-type inequalities for partial separability in N-particle systems
  and quantum mechanical violations

abstract:
  We derive N-particle Bell-type inequalities under the assumption of partial
separability, i.e. that the N-particle system is composed of subsystems which
may be correlated in any way (e.g. entangled) but which are uncorrelated with
respect to each other. These inequalities provide, upon violation,
experimentally accessible sufficient conditions for full N-particle
entanglement, i.e. for N-particle entanglement that cannot be reduced to
mixtures of states in which a smaller number of particles are entangled. The
inequalities are shown to be maximally violated by the N-particle
Greenberger-Horne-Zeilinger (GHZ) states.


title: Imperfect Detectors in Linear Optical Quantum Computers

abstract:
  We discuss the effects of imperfect photon detectors suffering from loss and
noise on the reliability of linear optical quantum computers. We show that for
a given detector efficiency, there is a maximum achievable success probability,
and that increasing the number of ancillary photons and detectors used for one
controlled sign flip gate beyond a critical point will decrease the probability
that the computer will function correctly. We have also performed simulations
of some small logic gates and estimate the efficiency and noise levels required
for the linear optical quantum computer to function properly.


title: Magnetic field effects in ultracold molecular collisions

abstract:
  We investigate the collisional stability of magnetically trapped ultracold
molecules, taking into account the influence of magnetic fields. We compute
elastic and spin-state-changing inelastic rate constants for collisions of the
prototype molecule $^{17}$O$_2$ with a $^3$He buffer gas as a function of the
magnetic field and the translational collision energy. We find that
spin-state-changing collisions are suppressed by Wigner's threshold laws as
long as the asymptotic Zeeman splitting between incident and final states does
not exceed the height of the centrifugal barrier in the exit channel. In
addition, we propose a useful one-parameter fitting formula that describes the
threshold behavior of the inelastic rates as a function of the field and
collision energy. Results show a semi-quantitative agreement of this formula
with the full quantum calculations, and suggest useful applications also to
different systems. As an example, we predict the low-energy rate constants
relevant to evaporative cooling of molecular oxygen.


title:
A family of sure-success quantum algorithms for solving a generalized
  Grover search problem

abstract:
  This work considers a generalization of Grover's search problem, viz., to
find any one element in a set of acceptable choices which constitute a fraction
f of the total number of choices in an unsorted data base. An infinite family
of sure-success quantum algorithms are introduced here to solve this problem,
each member for a different range of f. The nth member of this family involves
n queries of the data base, and so the lowest few members of this family should
be very convenient algorithms within their ranges of validity. The even member
{A}_{2n} of the family covers ever larger range of f for larger n, which is
expected to become the full range 0 <= f <= 1 in the limit n -->infinity.


title:
Holonomic control operators in quantum completely integrable Hamiltonian
  systems

abstract:
  We provide geometric quantization of a completely integrable Hamiltonian
system in the action-angle variables around an invariant torus with respect to
the angle polarization. The carrier space of this quantization is the
pre-Hilbert space of smooth complex functions on the torus. A Hamiltonian of a
completely integrable system in this carrier space has a countable spectrum. If
it is degenerate, its eigenvalues are countably degenerate. We study
nonadiabatic perturbations of this Hamiltonian by a term depending on classical
time-dependent parameters. It is originated by a connection on the parameter
space, and is linear in the temporal derivatives of parameters. One can choose
it commuting with a degenerate Hamiltonian of a completely integrable system.
Then the corresponding evolution operator acts in the eigenspaces of this
Hamiltonian, and is an operator of parallel displacement along a curve in the
parameter space.


title: Controlling Quantum Rotation With Light

abstract:
  Semiclassical catastrophes in the dynamics of a quantum rotor (molecule)
driven by a strong time-varying field are considered. We show that for strong
enough fields, a sharp peak in the rotor angular distribution can be achieved
via time-domain focusing phenomenon, followed by the formation of angular
rainbows and glory-like angular structures. Several scenarios leading to the
enhanced angular squeezing are proposed that use specially designed and
optimized sequences of pulses. The predicted effects can be observed in many
processes, ranging from molecular alignment (orientation) by laser fields to
heavy-ion collisions, and the squeezing of cold atoms in a pulsed optical
lattice.


title: Qudit Quantum State Tomography

abstract:
  Recently quantum tomography has been proposed as a fundamental tool for
prototyping a few qubit quantum device. It allows the complete reconstruction
of the state produced from a given input into the device. From this
reconstructed density matrix, relevant quantum information quantities such as
the degree of entanglement and entropy can be calculated. Generally orthogonal
measurements have been discussed for this tomographic reconstruction. In this
paper, we extend the tomographic reconstruction technique to two new regimes.
First we show how non-orthogonal measurement allow the reconstruction of the
state of the system provided the measurements span the Hilbert space. We then
detail how quantum state tomography can be performed for multi qudits with a
specific example illustrating how to achieve this in one and two qutrit
systems.


title:
Shor-Preskill Type Security-Proof for the Quantum Key Distribution
  without Public Announcement of Bases

abstract:
  We give a Shor-Preskill type security-proof to the quantum key distribution
without public announcement of bases [W.Y. Hwang et al., Phys. Lett. A 244, 489
(1998)]. First, we modify the Lo-Chau protocol once more so that it finally
reduces to the quantum key distribution without public announcement of bases.
Then we show how we can estimate the error rate in the code bits based on that
in the checked bits in the proposed protocol, that is the central point of the
proof. We discuss the problem of imperfect sources and that of large deviation
in the error rate distributions. We discuss when the bases sequence must be
discarded.


title:
Observation of off-diagonal geometric phase in polarized neutron
  interferometer experiments

abstract:
  Off-diagonal geometric phases acquired in the evolution of a spin-1/2 system
have been investigated by means of a polarized neutron interferometer. Final
counts with and without polarization analysis enable us to observe
simultaneously the off-diagonal and diagonal geometric phases in two detectors.
We have quantitatively measured the off-diagonal geometric phase for noncyclic
evolutions, confirming the theoretical predictions. We discuss the significance
of our experiment in terms of geometric phases (both diagonal and off-diagonal)
and in terms of the quantum erasing phenomenon.


title: Covariance approach to the free photon field

abstract:
  We introduce photon theory following the same principles as for introduction
of the quantum theory of a single particle, using a C*-algebraic approach based
on covariance systems. The basic symmetries are additivity of the fields and
additivity of test functions. We write down in explicit form a state of this
covariance system. It turns out to reproduce the traditional Fock
representation of the free photon field, with a Lorentz invariant vacuum.
Properties of smeared-out photons are discussed.


title: A Lower Bound on the Quantum Capacity of Channels with Correlated Errors

abstract:
  The highest fidelity of quantum error-correcting codes of length n and rate R
is proven to be lower bounded by 1 - exp [-n E(R)+ o(n)] for some function E(R)
on noisy quantum channels that are subject to not necessarily independent
errors. The E(R) is positive below some threshold R', which implies R' is a
lower bound on the quantum capacity. This work is an extension of the author's
previous works [M. Hamada, Phys. Rev. A, 65, 052305, 2002 (e-Print
quant-ph/0109114, LANL, 2001), and M. Hamada, submitted to IEEE Trans. Inf.
Theory, 2002 (e-Print quant-ph/0112103, LANL, 2001)], which presented the bound
for channels subject to independent errors, or channels modeled as tensor
products of copies of a completely positive linear map. The relation of the
channel class treated in this paper to those in the previous works are similar
to that of Markov chains to sequences of independent identically distributed
random variables.


title: Quantum Information Theory and Applications to Quantum Cryptography

abstract:
  Classical and quantum information theory are simply explained. To be more
specific it is clarified why Shannon entropy is used as measure of classical
information and after a brief review of quantum mechanics it is possible to
demonstrate why the density matrix is the main tool of quantum information
theory. Then von Neumann entropy is introduced and with its help a great
difference between classical and quantum information theory is presented:
quantum entanglement. Moreover an information theoretic interpretation of
quantum measurement is discussed. Data compression, error correction and noisy
channel transmission are simply demonstrated for both classical and quantum
cases. Finally using the above theory quantum cryptography is reviewed and the
possibility of a commercial device realizing it is explored.


title: Bell-type inequalities to detect true n-body non-separability

abstract:
  We analyze the structure of correlations among more than two quantum systems.
We introduce a classification of correlations based on the concept of
non-separability, which is different {\em a priori} from the concept of
entanglement. Generalizing a result of Svetlichny [Phys. Rev. D {\bf 35} (1987)
3066] on 3-particle correlations, we find an inequality for $n$-particle
correlations that holds under the most general separability condition and that
is violated by some quantum-mechanical states.


title:
Neutron Charge Radius Deduced from Interferometric Bragg Reflection
  Technique

abstract:
  The possibility of the determination of the neutron mean square charge radius
from high-precision thermal-neutron measurements of the nuclear scattering
length and of the scattering amplitudes of Bragg reflections is considered.
Making use of the same interferometric technique as Shull in 1968, the
scattering amplitudes of about eight higher-order Bragg reflections in silicon
could be measured without contamination problem. This would provide a value of
the neutron charge radius as precise as the disagreeing Argonne-Garching and
Dubna values, as well as a Debye-Waller factor of silicon ten times more
precise than presently available.


title: Magnon-mediated NMR quantum gates in a 1-D antiferromagnet

abstract:
  We propose a method of controlling a quantum logic gate in a solid-state NMR
quantum computer. A switchable inter-qubit coupling can be generated by using
the longitudinal component of the Suhl-Nakamura interaction induced by a local
singlet-triplet excitation in a 1-D antiferromagnet with a spin gap.


title: Entanglement and perfect quantum error correction

abstract:
  The entanglement of formation gives a necessary and sufficient condition for
the existence of a perfect quantum error correction procedure.


title:
Limitations of light delay and storage times in EIT experiments with
  condensates

abstract:
  We investigate the limitations arising from atomic collisions on the storage
and delay times of probe pulses in EIT experiments. We find that the atomic
collisions can be described by an effective decay rate that limits storage and
delay times. We calculate the momentum and temperature dependence of the decay
rate and find that it is necessary to excite atoms at a particular momentum
depending on temperature and spacing of the energy levels involved in order to
minimize the decoherence effects of atomic collisions.


title:
PT-symmetric non-polynomial oscillators and hyperbolic potential with
  two known real eigenvalues in a SUSY framework

abstract:
  Extending the supersymmetric method proposed by Tkachuk to the complex
domain, we obtain general expressions for superpotentials allowing generation
of quasi-exactly solvable PT-symmetric potentials with two known real
eigenvalues (the ground state and first-excited state energies). We construct
examples, namely those of complexified non-polynomial oscillators and of a
complexified hyperbolic potential, to demonstrate how our scheme works in
practice. For the former we provide a connection with the sl(2) method,
illustrating the comparative advantages of the supersymmetric one.


title: Experimental Implementation of the Quantum Baker's Map

abstract:
  This paper reports on the experimental implementation of the quantum baker's
map via a three bit nuclear magnetic resonance (NMR) quantum information
processor. The experiments tested the sensitivity of the quantum chaotic map to
perturbations. In the first experiment, the map was iterated forward and then
backwards to provide benchmarks for intrinsic errors and decoherence. In the
second set of experiments, the least significant qubit was perturbed in between
the iterations to test the sensitivity of the quantum chaotic map to applied
perturbations. These experiments are used to investigate previous predicted
properties of quantum chaotic dynamics.


title: Comment on an alleged refutation of non-locality

abstract:
  A recent claim (Deutsch and Hayden (2000)), that non-locality can be refuted
by considering the evolution of the system in the Heisenberg picture, is
denied. What they demonstrated was not the falsity of non-locality but the
no-superluminal-signalling principle.


title:
Kochen-Specker Obstruction for Position and Momentum Using a Single
  Degree of Freedom

abstract:
  It is shown that, given a reasonable continuity assumption regarding
possessed values, it is possible to construct a Kochen-Specker obstruction for
any coordinate and its conjugate momentum, demonstrating that at most one of
these two quantities can have a noncontextual value.


title: An approximate Fourier transform useful in quantum factoring

abstract:
  We define an approximate version of the Fourier transform on $2^L$ elements,
which is computationally attractive in a certain setting, and which may find
application to the problem of factoring integers with a quantum computer as is
currently under investigation by Peter Shor. (1994 IBM Internal Report)


title:
Errors due to Finite Rise/fall Times of Pulses in Superconducting Charge
  Qubits

abstract:
  We study numerically the dynamics of two-qubit gates with superconducting
charge qubits. The exact ratio of $E_J$ to $E_L$ and the corresponding
operation time are calculated in order to implement two-qubit gates. We
investigate the effect of finite rise/fall times of pulses in realization of
two-qubit gates. It is found that the error in implementing two-qubit gates
grows quadratically in rise/fall times of pulses.


title: Multipartite entanglement for entanglement teleportation

abstract:
  The scheme for entanglement teleportation is proposed to incorporate
multipartite entanglement of four qubits as a quantum channel. Based on the
invariance of entanglement teleportation under arbitrary two-qubit unitary
transformation, we derive relations of separabilities for joint measurements at
a sending station and for unitary operations at a receiving station. From the
relations of separabilities it is found that an inseparable quantum channel
always leads to a total teleportation of entanglement with an inseparable joint
measurement and/or a nonlocal unitary operation.


title: Quadratic Bell inequalities as tests for multipartite entanglement

abstract:
  This letter presents quantum mechanical inequalities which distinguish, for
systems of $N$ spin-$\half$ particles ($N>2$), between fully entangled states
and states in which at most $N-1$ particles are entangled. These inequalities
are stronger than those obtained by Gisin and Bechmann-Pasquinucci [Phys.\
Lett. A {\bf 246}, 1 (1998)] and by Seevinck and Svetlichny [quant-ph/0201046].


title: Quantum Characterization of a Werner-like Mixture

abstract:
  We introduce a Werner-like mixture [R. F. Werner, Phys. Rev. A {\bf 40}, 4277
(1989)] by considering two correlated but different degrees of freedom, one
with discrete variables and the other with continuous variables. We evaluate
the mixedness of this state, and its degree of entanglement establishing its
usefulness for quantum information processing like quantum teleportation. Then,
we provide its tomographic characterization. Finally, we show how such a
mixture can be generated and measured in a trapped system like one electron in
a Penning trap.


title:
Sensitivity to Initial Conditions in Quantum Dynamics: an Analytical
  Semiclassical Expansion

abstract:
  We construct a class of systems for which quantum dynamics can be expanded
around a mean field approximation with essentially classical content.
  The modulus of the quantum overlap of mean field states naturally introduces
a classical distance between classical phase points. Using this fact we
analytically show that the time rate of change (trc) of two neighbouring
classical trajectories is directly proportional to the trc of quantum
correlations. Coherence loss and nonlocality effects appear as corrections to
mean field dynamics and we show that they can be given in terms of classical
trajectories and generalized actions. This result is a first step in the
connection between quantum and classically chaotic dynamics in the same sense
of semiclassical expansions for the density of states. We apply the results to
the nonintegrable (classically chaotic) version of the N-atom Jaynes-Cummings
model.


title: Countering Quantum Noise with Supplementary Classical Information

abstract:
  We consider situations in which i) Alice wishes to send quantum information
to Bob via a noisy quantum channel, ii) Alice has a classical description of
the states she wishes to send and iii) Alice can make use of a finite amount of
noiseless classical information. After setting up the problem in general, we
focus attention on one specific scenario in which Alice sends a known qubit
down a depolarizing channel along with a noiseless cbit. We describe a protocol
which we conjecture is optimal and calculate the average fidelity obtained. A
surprising amount of structure is revealed even for this simple case which
suggests that relationships between quantum and classical information could in
general be very intricate.


title: Minimum-error discrimination between three mirror-symmetric states

abstract:
  We present the optimal measurement strategy for distinguishing between three
quantum states exhibiting a mirror symmetry. The three states live in a
two-dimensional Hilbert space, and are thus overcomplete. By mirror symmetry we
understand that the transformation {|+> -> |+>, |-> -> -|->} leaves the set of
states invariant. The obtained measurement strategy minimizes the error
probability. An experimental realization for polarized photons, realizable with
current technology, is suggested.


title:
Dispersion cancellation and non-classical noise reduction for large
  photon-number states

abstract:
  Nonlocal dispersion cancellation is generalized to frequency-entangled states
with large photon number N. We show that the same entangled states can
simultaneously exhibit a factor of 1/sqrt(N) reduction in noise below the
classical shot noise limit in precise timing applications, as was previously
suggested by Giovannetti, Lloyd and Maccone (Nature v412 (2001) p417). The
quantum-mechanical noise reduction can be destroyed by a relatively small
amount of uncompensated dispersion and entangled states of this kind have
larger timing uncertainties than the corresponding classical states in that
case. Similar results were obtained for correlated states, anti-correlated
states, and frequency-entangled coherent states, which shows that these effects
are a fundamental result of entanglement.


title: Propagators of the Jaynes-Cummings model in open systems

abstract:
  We present a propagator formalism to investigate the scattering of photons by
a cavity QED system that consists of a single two-level atom dressed by a leaky
optical cavity field. We establish a diagrammatic method to construct the
propagator analytically. This allows us to determine the quantum state of the
scattered photons for an arbitrary incident photon packet. As an application,
we explicitly solve the problem of a single-photon packet scattered by an
initially excited atom.


title:
A local variable model for entanglement swapping exploiting the
  detection loophole

abstract:
  In an entanglement swapping process two initially uncorrelated qubits become
entangled, without any direct interaction. We present a model using local
variables aiming at reproducing this remarkable process, under the realistic
assumption of finite detection efficiencies. The model assumes that the local
variables describing the two qubits are initially completely uncorrelated.
Nevertheless, we show that once conditioned on the Bell measurement result, the
local variables bear enough correlation to simulate quantum measurement results
with correlation very close to the quantum prediction. When only a partial Bell
measurement is simulated, as carried out is all experiments so far, then the
model recovers analytically the quantum prediction.


title:
Evolution of a qubit under the influence of a succession of unsharp
  measurements

abstract:
  We investigate the evolution of a single qubit subject to a continuous
unitary dynamics and an additional interrupting influence which occurs
periodically. One may imagine a dynamically evolving closed quantum system
which becomes open at certain times. The interrupting influence is represented
by an operation, which is assumed to equivalently describe a non-selective
unsharp measurement. It may be decomposed into a positive operator, which in
case of a measurement represents the pure measurement part, followed by an
unitary back-action operator. Equations of motion for the state evolution are
derived in the form of difference equations. It is shown that the 'free'
Hamiltonian is completed by an averaged Hamiltonian, which goes back to the
back-action. The positive operator specifies a decoherence rate and results in
a decoherence term. The continuum limit to a master equation is performed. The
selective evolution is discussed and correcting higher order terms are worked
out in an Appendix.


title: All Entanglements in a Multipartite System

abstract:
  For a multipartite system, we sort out all possible entanglements, each of
which is among a set of subsystems. Each entanglement can be measured by a
generalized relative entropy of entanglement, which is conserved on average
under reversible local operations and classical communication (LOCC) defined
for all the parties. Then we derive a series of inequalities of different
entanglements that have to be satisfied by any pure state which can be
generated by reversible LOCC from the set of all GHZ-like states.


title: Can a quantum measurement be cancelled in a very short period of time?

abstract:
  A test is suggested for whether the obtaining of certain information, and
then deleting it too quickly to be retained, constitutes a quantum measurement
of that information.


title: Bohmian picture of Rydberg atoms

abstract:
  Unlike the previous theoretical results based on standard quantum mechanics
that has established the nearly elliptical shapes for the centre-of-mass motion
using numerical simulations, we show analytically that the Bohmian trajectories
in Rydberg atoms are nearly elliptical.


title:
Quantum Computers and Quantum Computer Languages: Quantum Assembly
  Language and Quantum C Language

abstract:
  We show a representation of Quantum Computers defines Quantum Turing Machines
with associated Quantum Grammars. We then create examples of Quantum Grammars.
Lastly we develop an algebraic approach to high level Quantum Languages using
Quantum Assembly language and Quantum C language as examples.


title:
Problems in realization of large-scale ensemble silicon-based NMR
  quantum computers

abstract:
  Problems in realization of silicon-based solid-state NMR quantum computer
with ensemble addressing to qubits are considered. It is presented the
extension of Kane's scheme to ensemble approach version with strip gates. For
the initialization of nuclear quantum states it is proposed to use the
solid-state effect in ENDOR technique whereby the nuclear spins can be
practically fully polarized or, that is the same, indirect cooled to the spin
temperature less than ~ 1 mK. It is suggested the possible planar silicon
topology of such ensemble quantum computer and shown that the measurement with
standard NMR methods signal of L ~ 10^3 qubit system may be achieved for a
number of ensemble components N >= 10^5. As another variant of ensemble silicon
quantum computer the gateless architecture of cellular-automaton is also
considered. The decoherence of quantum states in the ensemble quantum computers
and ways of its suppression is also discussed.


title: Quantum mechanics from a Heisenberg-type equality

abstract:
  The usual Heisenberg uncertainty relation for position and momentum may be
replaced by an exact equality, for suitably chosen measures of position and
momentum uncertainty. This "exact" uncertainty relation is valid for_all_ pure
states, and is sufficiently strong to provide an axiomatic basis for moving
from classical mechanics to quantum mechanics. In particular, the assumption of
a nonclassical momentum fluctuation, having a strength which scales inversely
with uncertainty in position, leads from the classical equations of motion to
the Schroedinger equation.


title: Fibre bundle formulation of relativistic quantum mechanics

abstract:
  We propose a fibre bundle formulation of the mathematical base of
relativistic quantum mechanics. At the present stage the bundle form of the
theory is equivalent to its conventional one, but it admits new types of
generalizations in different directions. In the bundle description the
wavefunctions are replaced with (state) sections (covariant approach) or
liftings of paths (equivalently: sections along paths) (time-dependent
approach) of a suitably chosen vector bundle over space-time whose (standard)
fibre is the space of the wavefunctions. Now the quantum evolution is described
as a linear transportation of the state sections/liftings in the (total) bundle
space. The equations of these transportations turn to be the bundle versions of
the corresponding relativistic wave equations. Connections between the
(retarded) Green functions of these equations and the evolution operators and
transports are found. Especially the Dirac and Klein-Gordon equations are
considered.


title:
Entanglement between external degrees of freedom of atoms via Bragg
  deflection

abstract:
  We suggest that atoms undergoing Bragg deflection from a cavity field
introduce entanglement between their external degrees of freedom. The atoms
interact with an electromagnetic cavity field which is far detuned from atomic
transition frequency and is in superposition state. We provide a set of
experimental parameters in order to perform the suggested experiment within the
frame work of the presently available technology.


title: Demonstration of the Lateral Casimir Force

abstract:
  The lateral Casimir force between a sinusoidally corrugated gold coated plate
and large sphere was measured for surface separations between 0.2 $\mu$m to 0.3
$\mu$m using an atomic force microscope. The measured force shows the required
periodicity corresponding to the corrugations. It also exhibits the necessary
inverse fourth power distance dependence. The obtained results are shown to be
in good agreement with a complete theory taking into account the imperfectness
of the boundary metal. This demonstration opens new opportunities for the use
of the Casimir effect for lateral translation in microelectromechanical
systems.


title: Quantum Chaos, Irreversibility, dissipation and dephasing

abstract:
  The main idea of "Quantum Chaos" studies is that Quantum Mechanics introduces
two energy scales into the study of chaotic systems: One is obviously the mean
level spacing $\Delta\propto\hbar^d$, where $d$ is the dimensionality; The
other is $\Delta_b\propto\hbar$, which is known as the non-universal energy
scale, or as the bandwidth, or as the Thouless energy. Associated with these
two energy scales are two special quantum-mechanical (QM) regimes in the theory
of driven system. These are the QM adiabatic regime, and the QM
non-perturbative regime respectively. Otherwise Fermi golden rule applies, and
linear response theory can be trusted. Demonstrations of this general idea,
that had been published in 1999, have appeared in studies of wavepacket
dynamics, survival probability, dissipation, quantum irreversibility, fidelity
and dephasing.


title: Squeezing of Atoms in a Pulsed Optical Lattice

abstract:
  We study the process of squeezing of an ensemble of cold atoms in a pulsed
optical lattice. The problem is treated both classically and
quantum-mechanically under various thermal conditions. We show that a dramatic
compression of the atomic density near the minima of the optical potential can
be achieved with a proper pulsing of the lattice. Several strategies leading to
the enhanced atomic squeezing are suggested, compared and optimized.


title:
On matrix elements of phase-angular momentum commutator in Hilbert space
  of arbitrary dimensions

abstract:
  We discuss correspondence between the predictions of quantum theories for
rotation angle formulated in infinite and finite dimensional Hilbert spaces,
taking as example, the calculation of matrix elements of phase-angular momentum
commutator. A new derivation of the matrix elements is presented in infinite
space, making use of a unitary transformation that maps from the state space of
periodic functions to non-periodic functions, over which the spectrum of
angular momentum operator is in general, fractional. The approach can be
applied to finite dimensional Hilbert space also, for which identical matrix
elements are obtained.


title: A Pedestrian Introduction to Gamow Vectors

abstract:
  The Gamow vector description of resonances is compared with the S-matrix and
the Green function descriptions using the example of the square barrier
potential. By imposing different boundary conditions on the time independent
Schrodinger equation, we obtain either eigenvectors corresponding to real
eigenvalues and the physical spectrum or eigenvectors corresponding to complex
eigenvalues (Gamow vectors) and the resonance spectrum. We show that the poles
of the S matrix are the same as the poles of the Green function and are the
complex eigenvalues of the Schrodinger equation subject to a purely outgoing
boundary condition. The intrinsic time asymmetry of the purely outgoing
boundary condition is discussed. Finally, we show that the probability of
detecting the decay within a shell around the origin of the decaying state
follows an exponential law if the Gamow vector (resonance) contribution to this
probability is the only contribution that is taken into account.


title: Coherent medium as a polarization splitter of pulses

abstract:
  We show how one can use the anisotropic properties of a coherent medium to
separate temporally the two polarization components of a linearly polarized
pulse. This is achieved by applying a control field such that one component of
the pulse becomes ultraslow while the other component's group velocity is
almost unaffected by the medium. We present analytical and numerical results to
support the functioning of such a coherent medium as a polarization splitter of
pulses.


title: Towards a Coherent Theory of Physics and Mathematics

abstract:
  As an approach to a Theory of Everything a framework for developing a
coherent theory of mathematics and physics together is described. The main
characteristic of such a theory is discussed: the theory must be valid and and
sufficiently strong, and it must maximally describe its own validity and
sufficient strength. The mathematical logical definition of validity is used,
and sufficient strength is seen to be a necessary and useful concept. The
requirement of maximal description of its own validity and sufficient strength
may be useful to reject candidate coherent theories for which the description
is less than maximal. Other aspects of a coherent theory discussed include
universal applicability, the relation to the anthropic principle, and possible
uniqueness. It is suggested that the basic properties of the physical and
mathematical universes are entwined with and emerge with a coherent theory.
Support for this includes the indirect reality status of properties of very
small or very large far away systems compared to moderate sized nearby systems.
Discussion of the necessary physical nature of language includes physical
models of language and a proof that the meaning content of expressions of any
axiomatizable theory seems to be independent of the algorithmic complexity of
the theory. G\"{o}del maps seem to be less useful for a coherent theory than
for purely mathematical theories because all symbols and words of any language
musthave representations as states of physical systems already in the domain of
a coherent theory.


title:
Continuous variable quantum teleportation with a finite-basis
  entanglement resource

abstract:
  Entanglement is a crucial resource in quantum information theory. We
investigate the use of different forms of entangled states in continuous
variable quantum teleportation, specifically the use of a finite-basis
entanglement resource. We also consider the continuous variable teleportation
of finite-basis states, such as qubits, and present results that point to the
possibility of an efficient conditional scheme for continuous variable
teleportation of such states with near-unit fidelity using finite-basis
entanglement.


title: Quantum Hidden Subgroup Problems: A Mathematical Perspective

abstract:
  The ultimate objective of this paper is to create a stepping stone to the
development of new quantum algorithms. The strategy chosen is to begin by
focusing on the class of abelian quantum hidden subgroup algorithms, i.e., the
class of abelian algorithms of the Shor/Simon genre. Our strategy is to make
this class of algorithms as mathematically transparent as possible. By the
phrase "mathematically transparent" we mean to expose, to bring to the surface,
and to make explicit the concealed mathematical structures that are inherently
and fundamentally a part of such algorithms. In so doing, we create symbolic
abelian quantum hidden subgroup algorithms that are analogous to the those
symbolic algorithms found within such software packages as Axiom, Cayley,
Maple, Mathematica, and Magma.
  As a spin-off of this effort, we create three different generalizations of
Shor's quantum factoring algorithm to free abelian groups of finite rank. We
refer to these algorithms as wandering (or vintage Z_Q) Shor algorithms. They
are essentially quantum algorithms on free abelian groups A of finite rank n
which, with each iteration, first select a random cyclic direct summand Z of
the group A and then apply one iteration of the standard Shor algorithm to
produce a random character of the "approximating" finite group A=Z_Q, called
the group probe. These characters are then in turn used to find either the
order P of a maximal cyclic subgroup Z_P of the hidden quotient group H_phi, or
the entire hidden quotient group H_phi. An integral part of these wandering
quantum algorithms is the selection of a very special random transversal, which
we refer to as a Shor transversal. The algorithmic time complexity of the first
of these wandering Shor algorithms is found to be O(n^2(lgQ)^3(lglgQ)^(n+1)).


title: How do two observers pool their knowledge about a quantum system?

abstract:
  In the theory of classical statistical inference one can derive a simple rule
by which two or more observers may combine {\em independently} obtained states
of knowledge together to form a new state of knowledge, which is the state
which would be possessed by someone having the combined information of both
observers. Moreover, this combined state of knowledge can be found without
reference to the manner in which the respective observers obtained their
information. However, in this note we show that in general this is not possible
for quantum states of knowledge; in order to combine two quantum states of
knowledge to obtain the state resulting from the combined information of both
observers, these observers must also possess information about how their
respective states of knowledge were obtained. Nevertheless, we emphasize this
does not preclude the possibility that a unique, well motivated rule for
combining quantum states of knowledge without reference to a measurement
history could be found. We examine both the direct quantum analogue of the
classical problem, and that of quantum state-estimation, which corresponds to a
variant in which the observers share a specific kind of prior information.


title: Quantum multimeters: A programmable state discriminator

abstract:
  We discuss a possibility to build a programmable quantum measurement device
(a "quantum multimeter"). That is, a device that would be able to perform
various desired generalized, positive operator value measure (POVM)
measurements depending on a quantum state of a "program register". As an
example, we present a "universal state discriminator". It serves for the
unambiguous discrimination of a pair of known non-orthogonal states (from a
certain set). If the two states are changed the apparatus can be switched via
the choice of the program register to discriminate the new pair of states
unambiguously. The proper POVM is determined by the state of an auxiliary
quantum system. The probability of successful discrimination is not optimal for
all pairs of non-orthogonal states from the given set. However, for some
subsets it can be very close to the optimal value.


title: Heisenberg's Uncertainty Relations and Quantum Optics

abstract:
  We present a brief review of the impact of the Heisenberg uncertainty
relations on quantum optics. In particular we demonstrate how almost all
coherent and nonclassical states of quantum optics can be derived from
uncertainty relations.


title:
Two families of superintegrable and isospectral potentials in two
  dimensions

abstract:
  As an extension of the intertwining operator idea, an algebraic method which
provides a link between supersymmetric quantum mechanics and quantum
(super)integrability is introduced. By realization of the method in two
dimensions, two infinite families of superintegrable and isospectral stationary
potentials are generated. The method makes it possible to perform Darboux
transformations in such a way that, in addition to the isospectral property,
they acquire the superintegrability preserving property. Symmetry generators
are second and fourth order in derivatives and all potentials are isospectral
with one of the Smorodinsky-Winternitz potentials. Explicit expressions of the
potentials, their dynamical symmetry generators and the algebra they obey as
well as their degenerate spectra and corresponding normalizable states are
presented.


title: A General Approach of Quasi-Exactly Solvable Schroedinger Equations

abstract:
  We construct a general algorithm generating the analytic eigenfunctions as
well as eigenvalues of one-dimensional stationary Schroedinger Hamiltonians.
Both exact and quasi-exact Hamiltonians enter our formalism but we focus on
quasi-exact interactions for which no such general approach has been considered
before. In particular we concentrate on a generalized sextic oscillator but
also on the Lame and the screened Coulomb potentials.