title:
Renormalisation in Quantum Mechanics, Quantum Instantons and Quantum
  Chaos

abstract:
  We suggest how to construct non-perturbatively a renormalized action in
quantum mechanics. We discuss similarties and differences with the standard
effective action. We propose that the new quantum action is suitable to define
and compute quantum instantons and quantum chaos.


title: Searching a Database under Decoherence

abstract:
  We report on the effects of a simple decoherence model on the quantum search
algorithm. Despite its simplicity, the decoherence model is an instructive
model that can genuinely imitate realistic noisy environment in many
situations. As one would expect, as the size of the database gets larger, the
effects of decoherence on the efficiency of the quantum search algorithm cannot
be ignored. Moreover, with decoherence, it may not be useful to iterate beyond
the first maxima in the probability distribution of the search entry.
Surprisingly, we also find that the number of iterations for maximum
probability of the search entry reduces with decoherence.


title: Testing Quantum Dynamics in Genetic Information Processing

abstract:
  Does quantum dynamics play a role in DNA replication? What type of tests
would reveal that? Some statistical checks that distinguish classical and
quantum dynamics in DNA replication are proposed.


title:
Efficient bipartite quantum state purification in arbitrary dimensional
  Hilbert spaces

abstract:
  A new purification scheme is proposed which applies to arbitrary dimensional
bipartite quantum systems. It is based on the repeated application of a special
class of nonlinear quantum maps and a single, local unitary operation. This
special class of nonlinear quantum maps is generated in a natural way by a
hermitian generalized XOR-gate. The proposed purification scheme offers two
major advantages, namely it does not require local depolarization operations at
each step of the purification procedure and it purifies more efficiently than
other know purification schemes.


title: Irreversibility in asymptotic manipulations of entanglement

abstract:
  We show that the process of entanglement distillation is irreversible by
showing that the entanglement cost of a bound entangled state is finite. Such
irreversibility remains even if extra pure entanglement is loaned to assist the
distillation process.


title:
Storing quantum dynamics in quantum states: stochastic programmable gate
  for U(1) operations

abstract:
  We show how quantum dynamics can be captured in the state of a quantum
system, in such a way that the system can be used to stochastically perform, at
a later time, the stored transformation perfectly on some other quantum system.
Thus programmable quantum gates for quantum information processing are feasible
if some probability of failure -that we show to decrease exponentially with the
size of the storing resources- is allowed.


title: Quasiprobability and Probability Distributions for Spin 1/2 States

abstract:
  We develop a Radon like transformation, in which $P$ quasiprobability
distribution for spin 1/2 states is written in terms the tomographic
probability distribution $w$.


title: Bell's theorem for general N-qubit states

abstract:
  We derive a single general Bell inequality which is a necessary and
sufficient condition for the correlation function for N particles to be
describable in a local and realistic picture, for the case in which
measurements on each particle can be chosen between two arbitrary dichotomic
observables. We also derive a necessary and sufficient condition for an
arbitrary N-qubit mixed state to violate this inequality. This condition is a
generalization and reformulation of the Horodeccy family condition for two
qubits.


title: Universal state inversion and concurrence in arbitrary dimensions

abstract:
  Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for
the entanglement of formation of two qubits in terms of what he calls the
concurrence of the joint density operator. Wootters's concurrence is defined
with the help of the superoperator that flips the spin of a qubit. We
generalize the spin-flip superoperator to a "universal inverter," which acts on
quantum systems of arbitrary dimension, and we introduce the corresponding
concurrence for joint pure states of (D1 X D2) bipartite quantum systems. The
universal inverter, which is a positive, but not completely positive
superoperator, is closely related to the completely positive universal-NOT
superoperator, the quantum analogue of a classical NOT gate. We present a
physical realization of the universal-NOT superoperator.


title: Interference due to Coherence Swapping

abstract:
  We propose a method called `coherence swapping' which enables us to create
superposition of a particle in two distinct paths, which is fed with initially
incoherent, independent radiations. This phenomenon is also present for the
charged particles, and can be used to swap the effect of flux line due to
Aharonov-Bohm effect. We propose an optical version of the experimental set-up
to test the coherence swapping. The phenomenon, which is simpler than
entanglement swapping or teleportation, raises some fundamental questions about
true nature of wave-particle duality, and also opens up the possibility of
studying the quantum erasure from a new angle.


title:
Comment on: Breakdown of Bohr's Correspondence Principle by: Bo Gao
  Phys. Rev. Lett. 83, 4225 (1999)

abstract:
  Gao applied LeRoy and Bernstein semi-classical analysis for the energy levels
in a potential of the form -C/r^n to sequences of scaled energy differences
progressing towards low lying states and found a better agreement with the
semi-classical prediction. We checked that for the energy levels obtained by
Stwalley et al. with the same potential, the agreement with the semi-classical
approximation is better for higher vibrational quantum numbers in agreement
with Bohr's correspondence principle.


title: Causal and localizable quantum operations

abstract:
  We examine constraints on quantum operations imposed by relativistic
causality. A bipartite superoperator is said to be localizable if it can be
implemented by two parties (Alice and Bob) who share entanglement but do not
communicate; it is causal if the superoperator does not convey information from
Alice to Bob or from Bob to Alice. We characterize the general structure of
causal complete measurement superoperators, and exhibit examples that are
causal but not localizable. We construct another class of causal bipartite
superoperators that are not localizable by invoking bounds on the strength of
correlations among the parts of a quantum system. A bipartite superoperator is
said to be semilocalizable if it can be implemented with one-way quantum
communication from Alice to Bob, and it is semicausal if it conveys no
information from Bob to Alice. We show that all semicausal complete measurement
superoperators are semilocalizable, and we establish a general criterion for
semicausality. In the multipartite case, we observe that a measurement
superoperator that projects onto the eigenspaces of a stabilizer code is
localizable.


title: A robust verification of the quantum nature of light

abstract:
  We present a conditional experiment involving a parametric amplifier and an
avalanche photodetector to generate highly nonclassical states of the radiation
field. The nonclassicality is robust against amplifier gain, detector
efficiency and dark counts. At the output all the generalized Wigner functions
have negative values, and this is exploited in order to reveal the
nonclassicality through quantum homodyne tomography.


title: Slow light in three-level cold atoms: a numerical analysis

abstract:
  We investigate theoretically the slow group velocity of a pulse probe laser
propagating through a cold sample and interacting with atoms in a three-level
$\Lambda$ configuration having losses towards external states. The EIT
phenomenon produces very small group velocities for the probe pulse in presence
of a strong coupling field even in presence of the population losses, as in an
open three-level system. The group velocity and the transmission of the pulses
are examined numerically as functions of several parameters, the adiabatic
transfer, the loss rate, the modification of the atomic velocity produced
within the cold sample. The conditions for a more efficient pulse transmission
through the cold atomic sample are specified.


title: Remotely prepared entanglement: a quantum web page

abstract:
  In quantum teleportation, an unknown quantum state is transmitted from one
party to another using only local operations and classical communication, at
the cost of shared entanglement. Is it possible similarly, using an $N$ party
entangled state, to have the state retrievable by {\it any} of the $N-1$
possible receivers? If the receivers cooperate, and share a suitable state,
this can be done reliably. The $N$ party GHZ is one such state; I derive a
large class of such states, and show that they are in general not equivalent to
the GHZ. I also briefly discuss the problem where the parties do not cooperate,
and the relationship to multipartite entanglement quantification. I define a
new set of entanglement monotones, the entanglements of preparation.


title: Quantum mechanics and consciousness: fact and fiction

abstract:
  This article was written in response to a request from an editor of American
Vedantist. It is shown that the idea that consciousness is essential to
understanding quantum mechanics arises from logical fallacies. This may be
welcome news to those who share the author's annoyance at consciousness being
dragged into discussions of physics, but beware: The same fallacies may
underlie the reader's own way of making sense of quantum mechanics. The article
ends up embracing a Vedantic world view, for two reasons. For one, such a world
view seems to the author to be the most sensible alternative to a materialistic
one. For another, quantum mechanics is inconsistent with a materialistic world
view but makes perfect sense within a Vedantic framework of thought.


title: Quantum teleportation of entangled coherent states

abstract:
  We propose a simple scheme for the quantum teleportation of both bipartite
and multipartite entangled coherent states with the successful probability 1/2.
The scheme is based on only linear optical devices such as beam splitters and
phase shifters, and two-mode photon number measurements. The quantum channels
described by multipartite maximally entangled coherent states are readily made
by the beam splitters and phase shifters.


title: The Paradoxes of the Interaction-Free Measurement

abstract:
  Interaction-free measurements introduced by Elitzur and Vaidman [Found. Phys.
23, 987 (1993)] allow finding infinitely fragile objects without destroying
them. Paradoxical features of these and related measurements are discussed. The
resolution of the paradoxes in the framework of the Many-Worlds Interpretation
is proposed.


title:
Lie-type transformations and effective Hamiltonians in nonlinear quantum
  optics: applications to multilevel systems

abstract:
  We reelaborate on a general method for diagonalizing a wide class of
nonlinear Hamiltonians describing different quantum optical models. This method
makes use of a nonlinear deformation of the usual su(2) algebra and when some
physical parameter, dictated by the particular model under consideration,
becomes small, it gives a diagonal effective Hamiltonian that describes
correctly the dynamics for arbitrary states and long times. We extend the
technique to $N$-level atomic systems interacting with quantum fields, finding
the corresponding effective Hamiltonians when the condition of $k$-photon
resonance is fulfilled.


title: Parametric Potential Determination by the Canonical Function Method

abstract:
  The canonical function method (CFM) is a powerful means for solving the
Radial Schrodinger Equation. The mathematical difficulty of the RSE lies in the
fact it is a singular boundary value problem. The CFM turns it into a regular
initial value problem and allows the full determination of the spectrum of the
Schrodinger operator without calculating the eigenfunctions. Following the
parametrisation suggested by Klapisch and Green, Sellin and Zachor we develop a
CFM to optimise the potential parameters in order to reproduce the experimental
Quantum Defect results for various Rydberg series of He, Ne and Ar as evaluated
from Moore's data.


title: Quantum phase gate with a selective interaction

abstract:
  We present a proposal for implementing quantum phase gates using selective
interactions. We analize selectivity and the possibility to implement these
gates in two particular systems, namely, trapped ions and Cavity QED.


title: The EPR Experiment: A Prelude to Bohr's Reply to EPR

abstract:
  Recent work on Bohr's reply to EPR has helped improve our understanding of
Bohr's reply, but further work is needed. In this paper I do two things towards
that end. First, I make some elementary points about EPR's argument, which help
to clear the air of some minor criticisms of Bohr's reply. Second, I argue that
Bohr's thought experiment is a reasonable realization of EPR's argument, and I
briefly suggest how to understand that experiment. I finish with a brief remark
about Bohm's version of the experiment, and its relation to Bohr's.


title: Quantum Pushdown Automata

abstract:
  Quantum finite automata, as well as quantum pushdown automata (QPA) were
first introduced by C. Moore and J. P. Crutchfield. In this paper we introduce
the notion of QPA in a non-equivalent way, including unitarity criteria, by
using the definition of quantum finite automata of Kondacs and Watrous. It is
established that the unitarity criteria of QPA are not equivalent to the
corresponding unitarity criteria of quantum Turing machines. We show that QPA
can recognize every regular language. Finally we present some simple languages
recognized by QPA, not recognizable by deterministic pushdown automata.


title: Quantum Liouville-space trajectories for dissipative systems

abstract:
  In this paper we present a new quantum-trajectory based treatment of quantum
dynamics suitable for dissipative systems. Starting from a de Broglie/Bohm-like
representation of the quantum density matrix, we derive and define quantum
equations-of-motion for Liouville-space trajectories for a generalized system
coupled to a dissipative environment. Our theory includes a vector potential
which mixes forward and backwards propagating components and non-local quantum
potential which continuously produces coherences in the system. These
trajectories are then used to propagate an adaptive Lagrangian grid which
carries the density matrix, $\rho(x,y)$, and the action, $A(x,y)$, thereby
providing a complete hydrodynamic-like description of the dynamics.


title:
Electron g-factor Engineering in III-V Semiconductors for Quantum
  Communications

abstract:
  An entanglement-preserving photo-detector converts photon polarization to
electron spin. Up and down spin must respond equally to oppositely polarized
photons, creating a requirement for degenerate spin energies, ge=0 for
electrons. We present a plot of ge-factor versus lattice constant, analogous to
bandgap versus lattice constant, that can be used for g-factor engineering of
III-V alloys and quantum wells


title:
Interference of resonances and the double-pole of the S-matrix in a
  double well system

abstract:
  We discuss the interaction between two resonant states in a quantum
double-well structure. The behaviour of the resonant states depends on the
coupling between the wells, i.e. the height and width of the barrier that
separates them. We distinguish a region with resonant tunneling and a region
where the two resonances repel each other. The transition between the two
regions is marked by a double pole of the S-matrix.


title:
Quantum Key Distribution and Quantum Authentication Based on Entangled
  State

abstract:
  Using the previously shared Einstein-Podolsky-Rosen pairs, a proposal which
can be used to distribute a quantum key and identify the user's identification
simultaneously is presented. In this scheme, two local unitary operations and
the Bell state measurement are used. Combined with quantum memories, a
cryptographic network is proposed. One advantage is no classical communication
is needed, which make the scheme more secure. The secure analysis of this
scheme is shown.


title: Signatures of the Pair-Coherent State

abstract:
  We explore in detail the possibility of generating a pair-coherent state in
the non-degenerate parametric oscillator when decoherence is included. Such
states are predicted in the transient regime in parametric oscillation where
the pump mode is adiabatically eliminated. Two specific signatures are examined
to indicate whether the state of interest has been generated, the Schrodinger
cat state - like signatures, and the fidelity. Solutions in a transient regime
reveal interference fringes which are indicative of the formation of a
Schrodinger cat state. The fidelity indicates the purity of our prepared state
compared to the ideal pair-coherent state.


title: A novel quantum key distribution scheme with orthogonal product states

abstract:
  The general conditions for the orthogonal product states of the multi-state
systems to be used in quantum key distribution (QKD) are proposed, and a novel
QKD scheme with orthogonal product states in the 3x3 Hilbert space is
presented. We show that this protocol has many distinct features such as great
capacity, high efficiency. The generalization to nxn systems is also discussed
and a fancy limitation for the eavesdropper's success probability is reached.


title: Gravitational decoherence of planetary motions

abstract:
  We study the effect of the scattering of gravitational waves on planetary
motions, say the motion of the Moon around the Earth. Though this effect has a
negligible influence on dissipation, it dominates fluctuations and the
associated decoherence mechanism, due to the very high effective temperature of
the background of gravitational waves in our galactic environment.


title:
Faint laser quantum key distribution: Eavesdropping exploiting
  multiphoton pulses

abstract:
  The technological possibilities of a realistic eavesdropper are discussed.
Two eavesdropping strategies taking profit of multiphoton pulses in faint laser
QKD are presented. We conclude that, as long as storage of Qubits is
technically impossible, faint laser QKD is not limited by this security issue,
but mostly by the detector noise.


title: Discussion on spin-flip synchrotron radiation

abstract:
  Quantum spin-flip transitions are of great importance in the synchrotron
radiation theory. For better understanding of the nature of this phenomenon, it
is necessary to except the effects connected with the electric charge radiation
from observation. This fact explains the suggested choice of the spin-flip
radiation model in the form of radiation of the electric neutral Dirac-Pauli
particle moving in the homogeneous magnetic field. It is known that in this
case, the total radiation in the quantum theory is conditioned by spin-flip
transitions. The idea is that spin-flip radiation is represented as a
nonstationary process connected with spin precession. We shall shown how to
construct a solution of the classical equation of the spin precession in the
BMT theory having the exact solution of the Dirac-Pauli equation.Thus, one will
find the connection of the quantum spin-flip transitions with classical spin
precession.


title: Statistical distinguishability between unitary operations

abstract:
  The problem of distinguishing two unitary transformations, or quantum gates,
is analyzed and a function reflecting their statistical distinguishability is
found. Given two unitary operations, $U_1$ and $U_2$, it is proved that there
always exists a finite number $N$ such that $U_1^{\otimes N}$ and $U_2^{\otimes
N}$ are perfectly distinguishable, although they were not in the single-copy
case. This result can be extended to any finite set of unitary transformations.
Finally, a fidelity for one-qubit gates, which satisfies many useful properties
from the point of view of quantum information theory, is presented.


title: Unusual bound or localized states

abstract:
  We summarize unusual bound or localized states in quantum mechanics. Our
guide through these intriguing phenomena is the classical physics of the
upside-down pendulum. Taking advantage of the analogy between the corresponding
Newton's equation of motion and the time-independent Schr\"{o}dinger equation,
we discuss the zero-energy ground state in a three-dimensional, spatially
oscillating, potential. Moreover, we focus on the effect of the attractive
quantum anti-centrifugal potential that only occurs in a two-dimensional
situation.


title:
Interpretations of quantum mechanics, and interpretations of violation
  of Bell's inequality

abstract:
  The discussion of the foundations of quantum mechanics is complicated by the
fact that a number of different issues are closely entangled. Three of these
issues are i) the interpretation of probability, ii) the choice between realist
and empiricist interpretations of the mathematical formalism of quantum
mechanics, iii) the distinction between measurement and preparation. It will be
demonstrated that an interpretation of violation of Bell's inequality by
quantum mechanics as evidence of non-locality of the quantum world is a
consequence of a particular choice between these alternatives. Also a
distinction must be drawn between two forms of realism, viz. a) realist
interpretations of quantum mechanics, b) the possibility of hidden-variables
(sub-quantum) theories.


title: Two-qubit catalysis in a four-state pure bipartite system

abstract:
  We consider a four-state pure bipartite system consisting of four qubits
shared among two parties using the same Schmidt basis, two qubits per party. In
some cases, transformation between two known pure states may not be possible
using LOCC transformations but may be possible with the addition of a two-qubit
catalyst. We provide a necessary and sufficient condition for this to occur.


title: Faster Database search in Quantum Computing

abstract: The paper has been withdrawn


title: Schrodinger equation from an exact uncertainty principle

abstract:
  An exact uncertainty principle, formulated as the assumption that a classical
ensemble is subject to random momentum fluctuations of a strength which is
determined by and scales inversely with uncertainty in position, leads from the
classical equations of motion to the Schrodinger equation. Thus there is an
exact formulation of the uncertainty principle which precisely captures the
essence of what is "quantum" about quantum mechanics.


title: State Preparation in Quantum Optics

abstract:
  In quantum information and communication, optical schemes provide simple and
intuitive experimental implementations. Of particular importance is quantum
state preparation. In this thesis, the creation of polarisation entanglement
using a particular class of optical circuits is studied. I give a mathematical
description of this class of circuits in terms of Hermite polynomials. In this
context, single photon resolution and single photon sensitivity detectors are
discussed and compared with detector cascading. In addition, I study
applications of state preparation such as quantum teleportation and quantum
lithography.


title: Bohmian trajectories for photons

abstract:
  The first examples of Bohmian trajectories for photons have been worked out
for simple situations, using the Kemmer-Duffin-Harishchandra formalism.


title: Effects of anisotropy on thermal entanglement

abstract:
  We study the thermal entanglement in the two-qubit anisotropic XXZ model and
the Heisenberg model with Dzyaloshinski-Moriya (DM) interactions. The DM
interaction is another kind of anisotropic antisymmetric exchange interaction.
The effects of these two kinds of anisotropies on the thermal entanglement are
studied in detail for both the antiferromagnetic and ferromagnetic cases.


title: Optimal local discrimination of two multipartite pure states

abstract:
  In a recent paper, Walgate et. al. demonstrated that any two orthogonal
multipartite pure states can be optimally distinguished using only local
operations. We utilise their result to show that this is true for any two
multiparty pure states, in the sense of inconclusive discrimination. There are
also certain regimes of conclusive discrimination for which the same also
applies, although we can only conjecture that the result is true for all
conclusive regimes. We also discuss a class of states that can be distinguished
locally according to any discrimination measure, as they can be locally
recreated in the hands of one party. A consequence of this is that any two
maximally entangled states can always be optimally discriminated locally,
according to any figure of merit.


title:
Conditional large Fock state preparation and field state reconstruction
  in Cavity QED

abstract:
  We propose a scheme for producing large Fock states in Cavity QED via the
implementation of a highly selective atom-field interaction. It is based on
Raman excitation of a three-level atom by a classical field and a quantized
field mode. Selectivity appears when one tunes to resonance a specific
transition inside a chosen atom-field subspace, while other transitions remain
dispersive, as a consequence of the field dependent electronic energy shifts.
We show that this scheme can be also employed for reconstructing, in a new and
efficient way, the Wigner function of the cavity field state.


title:
Correlation induced collapse of many-body systems with zero-range
  potentials

abstract:
  The zero-range potential is customarily employed in various mean-field
calculations of many-body systems in atomic and nuclear physics within,
correspondingly, Gross-Pitaevskii and Skyrme-Hartree-Fock approach. We argue,
however, that a many-body system with zero-range potentials is unstable against
clusterization into collapsed three-body subsystems. We show that neither the
density dependence of the potential nor an additional repulsive three-body
potential can prevent this unexpected correlational collapse if the potentials
are of zero range. Therefore the zero-range potential can only be used in
many-body calculations where all three-body correlations are explicitly
excluded.


title:
3D input-output relations of quantized light at dispersing and absorbing
  multilayer dielectric plates

abstract:
  The theory developed by Gruner and Welsch [Phys. Rev. A 54, 1661 (1996)] for
calculating the 1D input-output relations of the quantized electromagnetic
field at dispersing and absorbing dielectric (multilayer) plates is generalized
to the three-dimensional case. First a general recipe for the derivation of the
reflection and transmission coefficients at an arbitrary body that separates
two half spaces from each other is presented. The general theory is then
applied to the case of planar multilayer structures, for which the Green tensor
is well-known.


title: Phase-Conjugated Inputs Quantum Cloning Machines

abstract:
  A quantum cloning machine is introduced that yields $M$ identical optimal
clones from $N$ replicas of a coherent state and $N'$ replicas of its phase
conjugate. It also optimally produces $M'=M+N'-N$ phase-conjugated clones at no
cost. For well chosen input asymmetries $N'/(N+N')$, this machine is shown to
provide better cloning fidelities than the standard $(N+N') \to M$ cloner. The
special cases of the optimal balanced cloner ($N=N'$) and the optimal
measurement ($M=\infty$) are investigated.


title:
Quantum complexities of ordered searching, sorting, and element
  distinctness

abstract:
  We consider the quantum complexities of the following three problems:
searching an ordered list, sorting an un-ordered list, and deciding whether the
numbers in a list are all distinct. Letting N be the number of elements in the
input list, we prove a lower bound of \frac{1}{\pi}(\ln(N)-1) accesses to the
list elements for ordered searching, a lower bound of \Omega(N\log{N}) binary
comparisons for sorting, and a lower bound of \Omega(\sqrt{N}\log{N}) binary
comparisons for element distinctness. The previously best known lower bounds
are {1/12}\log_2(N) - O(1) due to Ambainis, \Omega(N), and \Omega(\sqrt{N}),
respectively. Our proofs are based on a weighted all-pairs inner product
argument.
  In addition to our lower bound results, we give a quantum algorithm for
ordered searching using roughly 0.631 \log_2(N) oracle accesses. Our algorithm
uses a quantum routine for traversing through a binary search tree faster than
classically, and it is of a nature very different from a faster algorithm due
to Farhi, Goldstone, Gutmann, and Sipser.


title: Verifying Atom Entanglement Schemes by Testing Bell's Inequality

abstract:
  Recent experiments to test Bell's inequality using entangled photons and ions
aimed at tests of basic quantum mechanical principles. Interesting results have
been obtained and many loopholes could be closed. In this paper we want to
point out that tests of Bell's inequality also play an important role in
verifying atom entanglement schemes. We describe as an example a scheme to
prepare arbitrary entangled states of N two-level atoms using a leaky optical
cavity and a scheme to entangle atoms inside a photonic crystal. During the
state preparation no photons are emitted and observing a violation of Bell's
inequality is the only way to test whether a scheme works with a high precision
or not.


title:
Bell's inequality and a strict assessment of the concept of
  ``possession''

abstract:
  It is argued that the concept of ``physical quantities possessed by the
system'' is both redundant and inappropriate. We have examined two versions of
the concept of ``possessed values'': one identical with the observed values and
the other non-identical. Assuming the existence of such ``physical quantities
possessed by the system'' and subjecting it to the framework of Bell theorem
under very generous condition allowing even certain form of ``nonlocality'',
one can still arrive at the proper Bell's inequality. With the experimental
falsification of Bell's inequality, we conclude that the concept of ``possessed
values'' finds no place in proper physical reasoning.


title: A Superdecay of an excited atom placed near ''Left-Handed'' sphere

abstract:
  The influence of a microsphere having a simultaneously negative permittivity
and permeability (Left-Handed Sphere) on the decay rate of the allowed and
forbidden transitions is considered. It is found, that in contrast to usual
(Right-Handed) materials it is possible to increase the decay rate by several
orders of magnitude even in the case of a sphere of small radii. This
enhancement is due to the fact that there exist a new type of resonance modes
(LH surface modes). The analytical expressions for resonance frequencies and
associated quality factors of the new modes are found.


title: Efficient quantum computing insensitive to phase errors

abstract:
  We show that certain computational algorithms can be simulated on a quantum
computer with exponential efficiency and be insensitive to phase errors. Our
explicit algorithm simulates accurately the classical chaotic dynamics for
exponentially many orbits even when the quantum fidelity drops to zero. Such
phase-insensitive algorithms open new possibilities for computation on
realistic quantum computers.


title: Sending Signals to Space-Like Separated Regions

abstract:
  Two recent works suggest a possibility of sending signals to a space-like
separated region, contrary to the spirit of special relativity. In the first
work [J. Grunhaus, S. Popescu, and D. Rohrlich, Phys. Rev. A 53, 3781 (1996)]
it has been shown that sending signals to particular union of space-like
separated region cannot cause causality paradoxes. Another work [Y. Aharonov
and L. Vaidman, Phys. Rev. A 61, 052108 (2000)] showed that the relative phase
of quantum superposition of a particle in two separate locations can be
measured locally. Together with the possibility of changing the relative phase
in a nonlocal way using potential effect we, apparently, have a method of
sending signals to space-like separated regions. These arguments are critically
analyzed in this paper.


title:
From Classical to Quantum Mechanics: "How to translate physical ideas
  into mathematical language"

abstract:
  In this paper, we investigate the connection between Classical and Quantum
Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics
(a system is described by a state in a Hilbert space, observables are
self-adjoint operators and so on) - Quantum Mechanics properly that specifies
the Hilbert space, the Heisenberg rule, the free Hamiltonian... We show that
General Quantum Axiomatics (up to a supplementary "axiom of classicity") can be
used as a non-standard mathematical ground to formulate all the ideas and
equations of ordinary Classical Statistical Mechanics. So the question of a
"true quantization" with "h" must be seen as an independent problem not
directly related with quantum formalism. Moreover, this non-standard
formulation of Classical Mechanics exhibits a new kind of operation with no
classical counterpart: this operation is related to the "quantization process",
and we show why quantization physically depends on group theory (Galileo
group). This analytical procedure of quantization replaces the "correspondence
principle" (or canonical quantization) and allows to map Classical Mechanics
into Quantum Mechanics, giving all operators of Quantum Mechanics and
Schrodinger equation. Moreover spins for particles are naturally generated,
including an approximation of their interaction with magnetic fields. We find
also that this approach gives a natural semi-classical formalism: some exact
quantum results are obtained only using classical-like formula. So this
procedure has the nice property of enlightening in a more comprehensible way
both logical and analytical connection between classical and quantum pictures.


title:
Atomic motion in magneto-optical double-well potentials: A new testing
  ground for quantum chaos

abstract:
  We have identified ultra-cold atoms in magneto-optical double-well potentials
as a very clean setting in which to study the quantum and classical dynamics of
a nonlinear system with multiple degrees of freedom. In this system,
entanglement at the quantum level and chaos at the classical level arise from
nonseparable couplings between the atomic spin and its center of mass motion.
The main features of the chaotic dynamics are analyzed using action-angle
variables and Poincare surfaces of section. We show that for the initial state
prepared in current experiments [D. J. Haycock et al., Phys. Rev. Lett. 85,
3365 (2000)], the classical and quantum dynamics diverge, and the observed
experimental dynamics are best described by quantum mechanics. Furthermore, the
motion corresponds to tunneling through a dynamical potential barrier. The
coupling between the spin and the motional subsystems, which are very different
in nature from one another, leads to new questions regarding the transition
from regular quantum dynamics to chaotic classical motion.


title: Recent Results in Trapped-Ion Quantum Computing

abstract:
  We review recent experiments on entanglement, Bell's inequality, and
decoherence-free subspaces in a quantum register of trapped \be ions. We have
demonstrated entanglement of up to four ions using the technique of M{\o}lmer
and S{\o}rensen. This method produces the state |down down> + |up up> for two
ions and the state |down down down down> + |up up up up> for four ions. We
generate the entanglement deterministically in each shot of the experiment.
Measurements on the two-ion entangled state violates Bell's inequality at the
$8\sigma$ level. Because of the high detector efficiency of our apparatus, this
experiment closes the detector loophole for Bell's inequality measurements for
the first time. This measurement is also the first violation of Bell's
inequality by massive particles that does not implicitly assume results from
quantum mechanics. Finally, we have demonstrated reversible encoding of an
arbitrary qubit, originally contained in one ion, into a decoherence-free
subspace (DFS) of two ions. The DFS-encoded qubit resists applied collective
dephasing noise and retains coherence under ambient conditions 3.6 times longer
than does an unencoded qubit. The encoding method, which uses single-ion gates
and the two-ion entangling gate, demonstrates all the elements required for
two-qubit universal quantum logic.


title:
Modified de Broglie-Bohm approach closer to classical Hamilton-Jacobi
  theory

abstract:
  A modified de Broglie-Bohm (dBB) approach to quantum mechanics is presented.
In this new deterministic theory, the problem of zero velocity for bound states
does not appear. Also this approach is equivalent to standard quantum mechanics
when averages of dynamical variables are taken, in exactly the same way as in
the original dBB theory.


title: Unconventional decay law for excited states in closed many-body systems

abstract:
  We study the time evolution of an initially excited many-body state in a
finite system of interacting Fermi-particles in the situation when the
interaction gives rise to the ``chaotic'' structure of compound states. This
situation is generic for highly excited many-particle states in quantum
systems, such as heavy nuclei, complex atoms, quantum dots, spin systems, and
quantum computers. For a strong interaction the leading term for the return
probability $W(t)$ has the form $W(t)\simeq \exp (-\Delta_E^2t^2)$ with
$\Delta_E^2$ as the variance of the strength function. The conventional
exponential linear dependence $W(t)=C\exp (-\Gamma t)$ formally arises for a
very large time. However, the prefactor $C$ turns out to be exponentially
large, thus resulting in a strong difference from the conventional estimate for
$W(t)$.

categories: quant-ph cond-mat.stat-mech nlin.CD nucl-th physics.atom-ph


title: Design of an RSFQ Control Circuit to Observe MQC on an rf-SQUID

abstract:
  We believe that the best chance to observe macroscopic quantum coherence
(MQC) in a rf-SQUID qubit is to use on-chip RSFQ digital circuits for
preparing, evolving and reading out the qubit's quantum state. This approach
allows experiments to be conducted on a very short time scale (sub-nanosecond)
without the use of large bandwidth control lines that would couple
environmental degrees of freedom to the qubit thus contributing to its
decoherence. In this paper we present our design of a RSFQ digital control
circuit for demonstrating MQC in a rf-SQUID. We assess some of the key
practical issues in the circuit design including the achievement of the
necessary flux bias stability. We present an "active" isolation structure to be
used to increase coherence times. The structure decouples the SQUID from
external degrees of freedom, and then couples it to the output measurement
circuitry when required, all under the active control of RSFQ circuits.
Research supported in part by ARO grant # DAAG55-98-1-0367.


title: A "Tipping Pulse" Scheme for rf-SQUID Qubits

abstract:
  We introduce a technique to control the macroscopic quantum state of an rf
SQUID qubit. We propose to employ a stream of single flux quantum (SFQ) pulses
magnetically coupled to the qubit junction to momentarily suppresses its
critical current. This effectively lowers the barrier in the double-well
rf-SQUID potential thereby increasing the tunneling oscillation frequency
between the wells. By carefully choosing the time interval between SFQ pulses
one may accelerate the interwell tunneling rate. Thus it is possible to place
the qubit into a chosen superposition of flux states and then effectively to
freeze the qubit state. We present both numerical simulations and analytical
time-dependent perturbation theory calculations that demonstrate the technique.
Using this strategy one may control the quantum state of the rf-SQUID in a way
analogous to the \pi pulses in other qubit schemes. Research supported in part
by ARO grant # DAAG55-98-1-0367.


title: On first-order scaling intertwining in quantum mechanics

abstract:
  We generalize the standard first-order intertwining relationship of
supersymmetric quantum mechanics in order to include simultaneous scaling
transformations in both the original Hamiltonian and the intertwining operator.
It is argued that in this way one can generate potentials with more interesting
spectra than those obtained by means of the standard first-order intertwining
technique and, as an outcome, a simple engineering procedure is presented. The
harmonic oscillator potential is used in order to illustrate the previous
statements. Moreover, a matrix representation of the scaled intertwining
relationship is sketched up allowing for higher-dimensional generalizations in
the case of separable potentials


title: The quantum absolute phase observable

abstract:
  Defining the observable ${\bf \phi}$ canonically conjugate to the number
observable ${\bf N}$ has long been an open problem in quantum theory. Here we
show how to define the absolute phase observable ${\bf \Phi}\equiv |{\bf\phi}|$
by suitably restricting the Hilbert space of $x$ and $p$ like variables. This
${\bf \Phi}$ is actually the absolute value of the phase and has the correct
classical limit. A correction to the ``cosine'' ${\bf C}$ and ``sine'' ${\bf
S}$ operators of Carruthers and Nieto is obtained.


title:
Generating Complex Potentials with Real Eigenvalues in Supersymmetric
  Quantum Mechanics

abstract:
  In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians,
we analyze three sets of complex potentials with real spectra, recently derived
by a potential algebraic approach based upon the complex Lie algebra sl(2, C).
This extends to the complex domain the well-known relationship between SUSYQM
and potential algebras for Hermitian Hamiltonians, resulting from their common
link with the factorization method and Darboux transformations. In the same
framework, we also generate for the first time a pair of elliptic partner
potentials of Weierstrass $\wp$ type, one of them being real and the other
imaginary and PT symmetric. The latter turns out to be quasiexactly solvable
with one known eigenvalue corresponding to a bound state. When the Weierstrass
function degenerates to a hyperbolic one, the imaginary potential becomes PT
non-symmetric and its known eigenvalue corresponds to an unbound state.


title: The Role of Relative Entropy in Quantum Information Theory

abstract:
  Quantum mechanics and information theory are among the most important
scientific discoveries of the last century. Although these two areas initially
developed separately it has emerged that they are in fact intimately related.
In this review I will show how quantum information theory extends traditional
information theory by exploring the limits imposed by quantum, rather than
classical mechanics on information storage and transmission. The derivation of
many key results uniquely differentiates this review from the "usual"
presentation in that they are shown to follow logically from one crucial
property of relative entropy. Within the review optimal bounds on the speed-up
that quantum computers can achieve over their classical counter-parts are
outlined using information theoretic arguments. In addition important
implications of quantum information theory to thermodynamics and quantum
measurement are intermittently discussed. A number of simple examples and
derivations including quantum super-dense coding, quantum teleportation,
Deutsch's and Grover's algorithms are also included.


title:
Peculiarities of the Weyl - Wigner - Moyal formalism for scalar charged
  particles

abstract:
  A description of scalar charged particles, based on the Feshbach-Villars
formalism, is proposed. Particles are described by an object that is a Wigner
function in usual coordinates and momenta and a density matrix in the charge
variable. It is possible to introduce the usual Wigner function for a large
class of dynamical variables. Such an approach explicitly contains a measuring
device frame. From our point of view it corresponds to the Copenhagen
interpretation of quantum mechanics. It is shown how physical properties of
such particles depend on the definition of the coordinate operator. The
evolution equation for the Wigner function of a single-charge state in the
classical limit coincides with the Liouville equation. Localization
peculiarities manifest themselves in specific constraints on possible initial
conditions.


title: Optomechanical scheme for the detection of weak impulsive forces

abstract:
  We show that a cooling scheme and an appropriate quantum nonstationary
strategy can be used to improve the signal to noise ratio for the
optomechanical detection of weak impulsive forces.


title: Information losses in continuous variable quantum teleportation

abstract:
  It is shown that the information losses due to the limited fidelity of
continuous variable quantum teleportation are equivalent to the losses induced
by a beam splitter of appropriate reflectivity.


title:
Observations of a doubly driven V system probed to a fourth level in
  laser-cooled rubidium

abstract:
  Observations of a doubly driven V system probed to a fourth level in an N
configuration are reported. A dressed state analysis is also presented. The
expected three-peak spectrum is explored in a cold rubidium sample in a
magneto-optic trap. Good agreement is found between the dressed state theory
and the experimental spectra once light shifts and uncoupled absorptions in the
rubidium system are taken into account.


title: Structure of Probabilistic Information and Quantum Laws

abstract:
  In quantum experiments the acquisition and representation of basic
experimental information is governed by the multinomial probability
distribution. There exist unique random variables, whose standard deviation
becomes asymptotically invariant of physical conditions. Representing all
information by means of such random variables gives the quantum mechanical
probability amplitude and a real alternative. For predictions, the linear
evolution law (Schrodinger or Dirac equation) turns out to be the only way to
extend the invariance property of the standard deviation to the predicted
quantities. This indicates that quantum theory originates in the structure of
gaining pure, probabilistic information, without any mechanical underpinning.


title: Nonlinear Qubit Transformations

abstract:
  We generalise our previous results of universal linear manipulations [Phys.
Rev. A63, 032304 (2001)] to investigate three types of nonlinear qubit
transformations using measurement and quantum based schemes. Firstly, nonlinear
rotations are studied. We rotate different parts of a Bloch sphere in opposite
directions about the z-axis. The second transformation is a map which sends a
qubit to its orthogonal state (which we define as ORTHOG). We consider the case
when the ORTHOG is applied to only a partial area of a Bloch sphere. We also
study nonlinear general transformation, i.e. (theta,phi)->(theta-alpha,phi),
again, applied only to part of the Bloch sphere. In order to achieve these
three operations, we consider different measurement preparations and derive the
optimal average (instead of universal) quantum unitary transformations. We also
introduce a simple method for a qubit measurement and its application to other
cases.


title: Concept of unified local field theory and nonlocality of matter

abstract:
  The concept of unified local field theory is considered. According to this
concept the quantum description and the classical one must be the levels for
investigation of some world solution of the unified field model. It is shown
that in the framework of the unified local field theory there are nonlocal
correlations between space separate events. Thus the experiments of Aspect type
for testing of the Bell inequalities and for showing of the nonlocal
correlations do not reject a possibility for description of matter with the
unified local field theory. Advantages of such theory for new technologies are
considered.


title:
Floydian trajectories for stationary systems: a modification for bound
  states

abstract:
  The Floydian trajectory method of quantum mechanics and the appearance of
microstates of the Schr\"{o}dinger equation are reviewed and contrasted with
the Bohm interpretation of quantum mechanics. The kinematic equation of
Floydian trajectories is analysed in detail and a new definition of the
variational derivative of kinetic energy with respect to total energy is
proposed for which Floydian trajectories have an explicit time dependence with
a frequency equal to the beat frequency between adjacent pairs of energy
eigenstates in the case of bound systems. In the case of unbound systems,
Floydian and Bohmian trajectories are found to be related by a local
transformation of time which is determined by the quantum potential.


title: Unveiled reality: comment on d'Espagnat's note on measurement

abstract:
  According to d'Espagnat we must choose between nonlinear breaks in quantum
state evolution and weak objectivity. In this comment it is shown that this
choice is forced on us by an inconsistent pseudo-realistic interpretation of
quantum states. A strongly objective one-world interpretation of linear quantum
mechanics is presented. It is argued that the weak objectivity favored by
d'Espagnat is, in fact, inconsistent with quantum mechanics.


title: Quantum reversibility and a new model of quantum automaton

abstract:
  This article is an attempt to generalize the classical theory of reversible
computing, principally developed by Bennet [IBM J. Res. Develop., 17(1973)] and
by Fredkin and Toffoli [Internat. J. Theoret. Phys., 21(1982)], to the quantum
case. This is a fundamental step towards the construction of a quantum computer
because a time efficient quantum computation is a reversible physical process.
The paper is organized as follows. The first section reviews the classical
theory of reversible computing. In the second section it is showed that the
designs used in the classical framework to decrease the consumption of space
cannot be generalized to the quantum case; it is also suggested that quantum
computing is generally more demanding of space than classical computing. In the
last section a new model of fully quantum and reversible automaton is proposed.
The computational power of this automaton is at least equal to that of
classical automata. Some conclusion are drawn in the last section.


title: On the grounding of spin effects in theory of synchrotron radiation

abstract:
  The problem of the uniqueness in the introduction of spin operators in the
synchrotron radiation theory is discussed. For this purpose we give the
invariant spin projections on the basis of the spin projections in the rest
frame. The spin equations are used to construct the integrals of motion in the
presence of the external electromagnetic field.


title: Is the Thomas precession a source of SR power?

abstract:
  The structural composition and the properties of the first quantum
spin-orientation-dependent correction to synchrotron radiation power are
discussed. On the basis of spin mass renormalization it is shown that, in the
conventional sence, the Thomas precession is not a source of relativistic
radiation. This conclusion is in agreement with well-known statements on the
spin dependence of mass and purely kinematic origin of Thomas precession.


title:
Spin-orbital motion and Thomas precession in the classical and quantum
  theories

abstract:
  The motion of a magnetic spin particle in electromagnetic fields is
considered on the basis of general principles of the classical relativistic
theory. Alternative approaches in derivation of the equations of charge motion
and spin precession, the problem of noncollinearity of the momentum and
velocity of a particle with spin, the origin and the meaning of Thomas
precession in dynamics of the spin particle are also considered. The
correspondence principle in the spin theory is discussed.


title: Quantum Kolmogorov Complexity Based on Classical Descriptions

abstract:
  We develop a theory of the algorithmic information in bits contained in an
individual pure quantum state. This extends classical Kolmogorov complexity to
the quantum domain retaining classical descriptions. Quantum Kolmogorov
complexity coincides with the classical Kolmogorov complexity on the classical
domain. Quantum Kolmogorov complexity is upper bounded and can be effectively
approximated from above under certain conditions. With high probability a
quantum object is incompressible. Upper- and lower bounds of the quantum
complexity of multiple copies of individual pure quantum states are derived and
may shed some light on the no-cloning properties of quantum states. In the
quantum situation complexity is not sub-additive. We discuss some relations
with ``no-cloning'' and ``approximate cloning'' properties.


title: Non-Sequential Behavior of the Wave Function

abstract:
  An experiment is presented in which the alleged progression of a photon's
wave function is ``measured'' by a row of superposed atoms. The photon's wave
function affects only one out of the atoms, regardless of its position within
the row, thereby manifesting not only non-local but also non-sequential
characteristics. It also turns out that, out of n atoms, each one has a
probability which is higher than the normal 1/n to be the single affected one.


title:
Addendum to "Nonlinear quantum evolution with maximal entropy
  production"

abstract:
  The author calls attention to previous work with related results, which has
escaped scrutiny before the publication of the article "Nonlinear quantum
evolution with maximal entropy production", Phys.Rev.A63, 022105 (2001).


title:
Explicit summation of the constituent WKB series and new approximate
  wave functions

abstract:
  The independent solutions of the one-dimensional Schr\"odinger equation are
approximated by means of the explicit summation of the leading constituent WKB
series. The continuous matching of the particular solutions gives the uniformly
valid analytical approximation to the wave functions. A detailed numerical
verification of the proposed approximation is performed for some exactly
solvable problems arising from different kinds of potentials.


title:
Ghost Diffraction: Causal Explanation via Correlated Trajectory
  Calculations

abstract:
  We use trajectory calculations to successfully explain two-photon "ghost"
diffraction, a phenomenon previously explained via quantum mechanical
entanglement. The diffraction patterns are accumulated one photon pair at a
time. The calculations are based on initial correlation of the trajectories in
the crystal source and a trajectory-wave ordering interaction with a variant
generator inherent in its structure. Details are presented in comparison with
ordinary diffraction calculated with the same trajectory model.


title: Position eigenstates and the Statistical Axiom of Quantum Mechanics

abstract:
  Quantum mechanics postulates the existence of states determined by a particle
position at a single time. This very concept, in conjunction with
superposition, induces much of the quantum-mechanical structure. In particular,
it implies the time evolution to obey the Schroedinger equation, and it can be
used to complete a truely basic derivation of the statistical axiom as recently
proposed by Deutsch.


title:
A Method for Deriving the Dirac Equation from the Relativistic Newton's
  Second Law

abstract:
  The derivation becomes possible when we find a new formalism which connects
the relativistic mechanics with the quantum mechanics. In this paper, we
explore the quantum wave nature from the Newtonian mechanics by using a
concept: velocity field. At first, we rewrite the relativistic Newton's second
law as a field equation in terms of the velocity field, which directly reveals
a new relationship connecting to the quantum mechanics. Next, we show that the
Dirac equation can be derived from the field equation in a rigorous and
consistent manner.


title: Separability and entanglement in 2x2xN composite quantum systems

abstract:
  We investigate separability and entanglement of mixed states in ${\cal
C}^2\otimes{\cal C}^2\otimes{\cal C}^N$ three party quantum systems. We show
that all states with positive partial transposes that have rank $\le N$ are
separable. For the 3 qubit case (N=2) we prove that all states $\rho$ that have
positive partial transposes and rank 3 are separable. We provide also
constructive separability checks for the states $\rho$ that have the sum of the
rank of $\rho$ and the ranks of partial transposes with respect to all
subsystems smaller than 15N-1.


title: Minimal Absorption Measurements

abstract:
  We show that it is not possible to discriminate two close transparencies
without a certain number of photons being absorbed. We extend this to the
discrimination of patterns of transparency (images).


title: A computable measure of entanglement

abstract:
  We present a measure of entanglement that can be computed effectively for any
mixed state of an arbitrary bipartite system. We show that it does not increase
under local manipulations of the system, and use it to obtain a bound on the
teleportation capacity and on the distillable entanglement of mixed states.


title: Quantum Interrogation and the Safer X-ray

abstract:
  We investigate quantum interrogation techniques which allow imaging
information about semi-transparent objects to be obtained with lower absorption
rates than standard classical methods. We show that a gain proportional to log
N can be obtained when searching for defects in an array of N pixels, if it is
known that at most M of the pixels can have transparencies different from a
predetermined theoretical value. A logarithmic gain can also be obtained when
searching for infrequently occurring large structures in arrays.


title: The Bell Inequality and Entanglement

abstract:
  Entanglement is a critical resource used in many current quantum information
schemes. As such entanglement has been extensively studied in two qubit systems
and its entanglement nature has been exhibited by violations of the Bell
inequality. Can the amount of violation of the Bell inequality be used to
quantify the degree of entanglement. What do Bell inequalities indicate about
the nature of entanglement?


title:
A Linear Programming Approach to Attainable Cram\'{e}r-Rao type Bounds
  and Randomness Condition II

abstract:
  The author studies the Cram\'{e}r-Rao type bound by a linear programming
approach. By this approach, he found a necessary and sufficient condition that
the Cram\'{e}r-Rao type bound is attained by a random measurement. In a spin
1/2 system, this condition is satisfied.


title: Teleportation of a state in view of the quantum theory of measurement

abstract:
  We give a description of the teleportation of an unknown quantum state which
takes into account the action of the measuring device and manifestly avoids any
reference to the postulate of the state vector collapse.


title: Grover search with pairs of trapped ions

abstract:
  The desired interference required for quantum computing may be modified by
the wave function oscillations for the implementation of quantum
algorithms[Phys.Rev.Lett.84(2000)1615]. To diminish such detrimental effect, we
propose a scheme with trapped ion-pairs being qubits and apply the scheme to
the Grover search. It can be found that our scheme can not only carry out a
full Grover search, but also meet the requirement for the scalable hot-ion
quantum computing. Moreover, the ion-pair qubits in our scheme are more robust
against the decoherence and the dissipation caused by the environment than
single-particle qubits proposed before.


title: Low-Entanglement Remote State Preparation

abstract:
  An upper bound on the low-entanglement remote state preparation (RSP) ebits
vs. bits tradeoff curve (Bennett et al.,quant-ph/0006044) is found using
techniques of classical information theory. We prove our coding scheme to be
optimal amongst an important class of protocols, and conjecture the bound to be
tight.


title:
On a linear optical implementation of non local product states and on
  their indistinguishability

abstract:
  In a recent paper Bennett et al.[Phys. Rev.A 59, 1070 (1999)] have shown the
existence of a basis of product states of a bipartite system with manifest
non-local properties. In particular these states cannot be completely
discriminated by means of bilocal measurements. In this paper we propose an
optical realization of these states and we will show that they cannot be
completely discriminate by means of a global measurement using only optical
linear elements, conditional transformation and auxiliary photons.


title: The no-signaling condition and quantum dynamics

abstract:
  We show that the basic dynamical rules of quantum physics can be derived from
its static properties and the condition that superluminal communication is
forbidden. More precisely, the fact that the dynamics has to be described by
linear completely positive maps on density matrices is derived from the
following assumptions: (1) physical states are described by rays in a Hilbert
space, (2) probabilities for measurement outcomes at any given time are
calculated according to the usual trace rule, (3) superluminal communication is
excluded. This result also constrains possible non-linear modifications of
quantum physics.


title: A single mode realization of SU(1,1)

abstract:
  A single mode realization of SU(1,1) algebra is proposed. This realization
makes it possible to reduce the problem of two nonlinear interacting
oscillators to the problem of free moving particle.


title: A Physical Explanation for Tilde System in Thermo Field Dynamics

abstract:
  For a two-body quantum system, any pure state can be represented by a
biorthogonal expression by means of Schmidt decomposition. Using this in the
composite system which include a thermodynamic system and its surroundings, it
is found that the tilde system in thermo field dynamics is just the
surroundings of the real system.


title:
Bateman's dual system revisited: I. Quantization, geometric phase and
  relation with the ground-state energy of the linear harmonic oscillator

abstract:
  By using the Feynman-Hibbs prescription for the evolution amplitude, we
quantize the system of a damped harmonic oscillator coupled to its
time-reversed image, known as Bateman's dual system.
  The time-dependent quantum states of such a system are constructed and
discussed entirely in the framework of the classical theory.
  The corresponding geometric (Pancharatnam) phase is calculated and found to
be directly related to the ground-state energy of the 1D linear harmonic
oscillator to which the 2D system reduces under appropriate constraint.


title: Quantum Zeno Effect in Trapped Ions

abstract:
  A "continuous measurement" Quantum Zeno Effect (QZE) in the context of
trapped ions is predicted. We describe the physical system and study its exact
time evolution showing the appearance of Zeno Phenomena. New indicators for the
occurrence of QZE in oscillatory systems are proposed and carefully discussed.


title: Shannon entropy and blackbody radiation

abstract: A response to criticism of the author's previous paper quant-ph/0002084.


title:
Comments on "On Bohm trajectories in two-particle interference devices"
  by L. Marchildon

abstract: Marchildon's arguments against my earlier work are refuted.


title: Extending the Fisher metric to density matrices

abstract:
  Chentsov studied Riemannian metrics on the set of probability measures from
the point of view of decision theory. He proved that up to a constant factor
the Fisher information is the only metric which is monotone under stochastic
transformations. The present paper deals with monotone metrics on the space of
finite density matrices on the basis motivated by quantum mechanics. A
characterization of those metrics is given in terms of operator monotone
functions. Several concrete metrics are constructed and analyzed, in
particular, instead of the uniqueness in the probabilistic case, there is a
large class of monotone metrics. Some of those appeared already in the physics
literature a long time ago. A limiting procedure to pure states is discussed as
well.


title: Necessary And Sufficient Condition of Separability of Any System

abstract:
  The necessary and sufficient condition of separability of a mixed state of
any systems is presented, which is practical in judging the separability of a
mixed state. This paper also presents a method of finding the disentangled
decomposition of a separable mixed state.


title: An Ergodic Theorem for Quantum Counting Processes

abstract:
  For a quantum-mechanical counting process we show ergodicity, under the
condition that the underlying open quantum system approaches equilibrium in the
time mean. This implies equality of time average and ensemble average for
correlation functions of the detection current to all orders and with
probability 1.


title: Cutoff dependence and Lorentz invariance of the Casimir effect

abstract:
  The Casimir force between two conducting planes is considered in both the
electromagnetic and scalar field cases. This is done by the usual summation
over energy eigenmodes of the system as well as by a calculation of the stress
tensor in the region between the planes. The latter case requires that careful
attention be given to singular operator products, an issue which is
accommodated here by invoking the point separation method in conjunction with a
scalar cutoff. This is shown to yield cutoff dependent and divergent
contributions to the Casimir pressure which are dependent on the separation
parameters, but entirely consistent with Lorentz covariance. Averaging over the
point splitting parameters allows finite results to be obtained, but fails to
yield a unique Casimir force.


title: Entanglement Simulations of Shor's Algorithm

abstract:
  We demonstrate that, in the case of Shor's algorithm for factoring, highly
mixed states will allow efficient quantum computation, indeed factorization can
be achieved efficiently with just one initial pure qubit and a supply of
initally maximally mixed qubits (S. Parker and M. B. Plenio, Phys. Rev. Lett.
85, 3049 (2000)) . This leads us to ask how this affects the entanglement in
the algorithm. We thus investigate the behaviour of entanglement in Shor's
algorithm for small numbers of qubits by classical computer simulation of the
quantum computer at different stages of the algorithm. We find that
entanglement is an intrinsic part of the algorithm and that the entanglement
through the algorithm appears to be closely related to the amount of mixing.
Furthermore, if the computer is in a highly mixed state any attempt to remove
entanglement by further mixing of the algorithm results in a significant
decrease in its efficiency.


title: Thermal concurrence mixing in a 1D Ising model

abstract:
  We investigate the entanglement arising naturally in a 1D Ising chain in a
magnetic field in an arbitrary direction. We find that for different
temperatures, different orientations of the magnetic field give maximum
entanglement. In the high temperature limit, this optimal orientation
corresponds to the magnetic field being perpendicular to the Ising orientation
(z direction). In the low temperature limit, we find that varying the angle of
the magnetic field very slightly from the z direction leads to a rapid rise in
entanglement. We also find that the orientation of the magnetic field for
maximum entanglement varies with the field amplitude. Furthermore, we have
derived a simple rule for the mixing of concurrences (a measure of
entanglement) due to mixing of pure states satisfying certain conditions.


title:
Proof of unconditional security of six-state quantum key distribution
  scheme

abstract:
  We prove the unconditional security of the standard six-state scheme for
quantum key distribution (QKD). We demonstrate its unconditional security up to
a bit error rate of 12.7 percents, by allowing only one-way classical
communications in the error correction/privacy amplification procedure between
Alice and Bob. This shows a clear advantage of the six-state scheme over
another standard scheme---BB84, which has been proven to be secure up to only
about 11 percents, if only one-way classical communications are allowed. Our
proof technique is a generalization of that of Shor-Preskill's proof of
security of BB84. We show that a advantage of the six-state scheme lies in the
Alice and Bob's ability to establish rigorously from their test sample the
non-trivial mutual information between the bit-flip and phase error patterns. A
modified version of the degenerate quantum codes studied by DiVincenzo, Shor
and Smolin is employed in our proof.


title: Bell's Inequality: More Tests Are Needed

abstract:
  According to recent reports, the last loopholes in testing Bell's inequality
are closed. It is argued that the really important task in this field has not
been tackled yet and that the leading experiments claiming to close locality
and detection efficiency loopholes, although making a very significant
progress, have conceptual drawbacks.


title: Encoded Universality in Physical Implementations of a Quantum Computer

abstract:
  We revisit the question of universality in quantum computing and propose a
new paradigm. Instead of forcing a physical system to enact a predetermined set
of universal gates (e.g., single-qubit operations and CNOT), we focus on the
intrinsic ability of a system to act as a universal quantum computer using only
its naturally available interactions. A key element of this approach is the
realization that the fungible nature of quantum information allows for
universal manipulations using quantum information encoded in a subspace of the
full system Hilbert space, as an alternative to using physical qubits directly.
Starting with the interactions intrinsic to the physical system, we show how to
determine the possible universality resulting from these interactions over an
encoded subspace. We outline a general Lie-algebraic framework which can be
used to find the encoding for universality and give several examples relevant
to solid-state quantum computing.


title: Probabilistic manipulation of entangled photons

abstract:
  We propose probabilistic controlled-NOT and controlled-phase gates for qubits
stored in the polarization of photons. The gates are composed of linear optics
and photon detectors, and consume polarization entangled photon pairs. The
fraction of the successful operation is only limited by the efficiency of the
Bell-state measurement. The gates work correctly under the use of imperfect
detectors and lossy transmission of photons. Combined with single-qubit gates,
they can be used for producing arbitrary polarization states and for designing
various quantum measurements.


title: Theory of Pseudomodes in Quantum Optical Processes

abstract:
  This paper deals with non-Markovian behaviour in atomic systems coupled to a
structured reservoir of quantum EM field modes, with particular relevance to
atoms interacting with the field in high Q cavities or photonic band gap
materials. In cases such as the former, we show that the pseudo mode theory for
single quantum reservoir excitations can be obtained by applying the Fano
diagonalisation method to a system in which the atomic transitions are coupled
to a discrete set of (cavity) quasimodes, which in turn are coupled to a
continuum set of (external) quasimodes with slowly varying coupling constants
and continuum mode density. Each pseudomode can be identified with a discrete
quasimode, which gives structure to the actual reservoir of true modes via the
expressions for the equivalent atom-true mode coupling constants. The quasimode
theory enables cases of multiple excitation of the reservoir to now be treated
via Markovian master equations for the atom-discrete quasimode system.
Applications of the theory to one, two and many discrete quasimodes are made.
For a simple photonic band gap model, where the reservoir structure is
associated with the true mode density rather than the coupling constants, the
single quantum excitation case appears to be equivalent to a case with two
discrete quasimodes.


title: Quantum Supearrivals

abstract:
  A curious effect is uncovered by calculating the it time evolving probability
of reflection of a Gaussian wave packet from a rectangular potential barrier
while it is perturbed by reducing its height. A time interval is found during
which this probability of reflection is larger (``superarrivals'') than in the
unperturbed case. This nonclassical effect can be explained by requiring a wave
function to act as a ``field'' through which an action, induced by the
perturbation of the boundary condition, propagates at a speed depending upon
the rate of reducing the barrier height.


title:
Generation of Continuous Variable Einstein-Podolsky-Rosen Entanglement
  via the Kerr Nonlinearity in an Optical Fibre

abstract:
  We report on the generation of a continuous variable Einstein-Podolsky-Rosen
(EPR) entanglement using an optical fibre interferometer. The Kerr nonlinearity
in the fibre is exploited for the generation of two independent squeezed beams.
These interfere at a beam splitter and EPR entanglement is obtained between the
output beams. The correlation of the amplitude (phase) quadratures are measured
to be 4.0+-0.2 (4.0+-0.4) dB below the quantum noise limit. The sum criterion
for these squeezing variances 0.80+-0.03 < 2 verifies the nonseparability of
the state. The product of the inferred uncertainties for one beam 0.64+-0.08 is
well below the EPR limit of unity.


title:
Comment on: Necessary and sufficient condition of separability of any
  system

abstract:
  In a recent paper (quant-ph/0102133) Chen, Liang, Li and Huang suggest a
necessary and sufficient separability criterion, which is supposedly practical
in judging the separability of any mixed state. In this note we briefly
recapitulate their main result and show that it is a reformulation of the
problem rather than a practical criterion.


title: Remark On Quantum Battle of The Sexes Game

abstract:
  Recently Quantum Battle of The Sexes Game has been studied by Luca Marinatto
and Tullio Weber. Yet some important problems exist in their scheme. Here we
propose a new scheme to quantize Battle of The Sexes Game, and this scheme will
truly remove the dilemma that exists in the classical form of the game.


title: Mixed State Entanglement: Manipulating Polarisation-Entangled Photons

abstract:
  There has been much discussion recently regarding entanglement
transformations in terms of local filtering operations and whether the optimal
entanglement for an arbitrary two-qubit state could be realised. We introduce
an experimentally realisable scheme for manipulating the entanglement of an
arbitrary state of two polarisation entangled qubits. This scheme is then used
to provide some perspective to the mathematical concepts inherent in this field
with respect to a laboratory environment. Specifically, we look at how to
extract enhanced entanglement from systems with a fixed rank and in the case
where the rank of the density operator for the state can be reduced, show how
the state can be made arbitrarily close to a maximally entangled pure state. In
this context we also discuss bounds on entanglement in mixed states.


title: Quantum enhanced positioning and clock synchronization

abstract:
  A wide variety of positioning and ranging procedures are based on repeatedly
sending electromagnetic pulses through space and measuring their time of
arrival. This paper shows that quantum entanglement and squeezing can be
employed to overcome the classical power/bandwidth limits on these procedures,
enhancing their accuracy. Frequency entangled pulses could be used to construct
quantum positioning systems (QPS), to perform clock synchronization, or to do
ranging (quantum radar): all of these techniques exhibit a similar enhancement
compared with analogous protocols that use classical light. Quantum
entanglement and squeezing have been exploited in the context of
interferometry, frequency measurements, lithography, and algorithms. Here, the
problem of positioning a party (say Alice) with respect to a fixed array of
reference points will be analyzed.


title:
Control of Non-Resonant Effects in a Nuclear Spin Quantum Computer with
  a Large Number of Qubits

abstract:
  We discuss how to simulate simple quantum logic operations with a large
number of qubits. These simulations are needed for experimental testing of
scalable solid-state quantum computers. Quantum logic for remote qubits is
simulated in a spin chain. Analytical estimates are presented for possible
correlated errors caused by non-resonant transitions. A range of parameters is
given in which non-resonant effects can be minimized.


title: Solid-State Quantum Computer Based on Scanning Tunneling Microscopy

abstract:
  We propose a solid-state nuclear spin quantum computer based on application
of scanning tunneling microscopy (STM) and well-developed silicon technology.
It requires the measurement of tunneling current modulation caused by the
Larmor precession of a single electron spin.
  Our envisioned STM quantum computer would operate at the high magnetic field
($\sim 10$T) and at low temperature $\sim 1$K.


title: Onset of Chaos in a Model of Quantum Computation

abstract:
  We show that a magnetic field gradient can suppress the onset of quantum
chaos in a nuclear spin chain quantum computer.


title: Analysis of nonperturbative fluctuations in a triple-well potential

abstract:
  We consider the quantum tunneling phenomenon in a well-behaved triple-well
potential. As required by the semiclassical approximation we take into account
the quadratic fluctuations over the instanton which represents as usual the
localised finite-action solution of the euclidean equation of motion. The
determinants of the quadratic differential operators at issue are evaluated by
means of the Gelfang-Yaglom method. In doing so the explicit computation of the
conventional ratio of determinants takes as reference the harmonic oscillator
whose frequency is the average of the individual frequencies derived from the
non-equivalent minima of the potential. Eventually the physical effects of the
multi-instanton configurations are included in this approach. As a matter of
fact we obtain information about the energies of the ground-state and the two
first excited levels of the discrete spectrum at issue.


title: Introduction to Grassmann Manifolds and Quantum Computation

abstract:
  Geometrical aspects of quantum computing are reviewed elementarily for
non-experts and/or graduate students who are interested in both Geometry and
Quantum Computation.
  In the first half we show how to treat Grassmann manifolds which are very
important examples of manifolds in Mathematics and Physics. Some of their
applications to Quantum Computation and its efficiency problems are shown in
the second half. An interesting current topic of Holonomic Quantum Computation
is also covered.
  In the Appendix some related advanced topics are discussed.


title: Dirac particles in a rotating magnetic field

abstract:
  We study a relativistic charged Dirac particle moving in a rotating magnetic
field. By using a time-dependent unitary transformation, the Dirac equation
with the time-dependent Hamiltonian can be reduced to a Dirac-like equation
with a time-independent effective Hamiltonian. Eigenstates of the effective
Hamiltonian correspond to cyclic solutions of the original Dirac equation. The
nonadiabatic geometric phase of a cyclic solution can be expressed in terms of
the expectation value of the component of the total angular momentum along the
rotating axis, regardless of whether the solution is explictly available. For a
slowly rotating magnetic field, the eigenvalue problem of the effective
Hamiltonian is solved approximately and the geometric phases are calculated.
The same problem for a charged or neutral Dirac particle with an anomalous
magnetic moment is discussed briefly.


title: Scattering by a contact potential in three and lower dimensions

abstract:
  We consider the scattering of nonrelativistic particles in three dimensions
by a contact potential $\Omega\hbar^2\delta(r)/ 2\mu r^\alpha$ which is defined
as the $a\to 0$ limit of $\Omega\hbar^2\delta(r-a)/2\mu r^\alpha$. It is
surprising that it gives a nonvanishing cross section when $\alpha=1$ and
$\Omega=-1$. When the contact potential is approached by a spherical square
well potential instead of the above spherical shell one, one obtains basically
the same result except that the parameter $\Omega$ that gives a nonvanishing
cross section is different. Similar problems in two and one dimensions are
studied and results of the same nature are obtained.


title:
Simulation of Einstein-Podolsky-Rosen experiments in a local hidden
  variables model with limited efficiency and coherence

abstract:
  We simulate correlation measurements of entangled photons numerically. The
model employed is strictly local. The correlation is determined by its
classical expression with one decisive difference: we sum up coincidences for
each pair individually. We analyze the effects of decoherence, detector
efficiency and polarizer thresholds in detail. The Bell inequalities are
violated in these simulations. The violation depends crucially on the threshold
of the polarizer switches and can reach a value of 2.0 in the limiting case.
Existing experiments can be fully accounted for by limited coherence and
non-ideal detector switches. It seems thus safe to conclude that the Bell
inequalities are no suitable criterium to decide on the nonlocality issue.


title:
Tunneling and Traversal of Ultra-cold Atoms through Vacuum Induced
  Potentials

abstract:
  We examine the passage of ultra-cold two-level atoms through the potential
produced by the vacuum of the cavity field. The peak of the transmitted wave
packet generally occurs at the instant given by the expression for phase time
even if that instant is earlier than the instant at which incident wave
packet's peak enters the cavity and thus the phase time can be considered as
the appropriate measure of the time required for the atom to traverse the
cavity. We show that the phase tunneling time for ultra-cold atoms could be
both super - and sub - classical time and we show how this behaviour can be
understood in terms of the momentum dependence of the phase of transmission
amplitude. The passage of the atom through the cavity is unique as it involves
a coherent addition of the transition amplitudes corresponding to both barrier
and well. New features such as the splitting of the wave packet arise from the
entanglement between the center of mass motion and the electronic as well as
field states in the cavity.


title: Boundary of the Set of Separable States

abstract:
  The set of all separable quantum states is compact and convex. We focus on
the two-qubit quanum system and study the boundary of the set. Then we give the
criterion to determine whether a separable state is on the boundary. Some
straightforward geometrical interpretations for entanglement are based on the
concept and presented subsequently.


title: Carbon--The First Frontier of Information Processing

abstract:
  Information is often encoded as an aperiodic chain of building blocks. Modern
digital computers use bits as the building blocks, but in general the choice of
building blocks depends on the nature of the information to be encoded. What
are the optimal building blocks to encode structural information? This can be
analysed by substituting the operations of addition and multiplication of
conventional arithmetic with translation and rotation. It is argued that at the
molecular level, the best component for encoding discretised structural
information is carbon. Living organisms discovered this billions of years ago,
and used carbon as the back-bone for constructing proteins that function
according to their structure. Structural analysis of polypeptide chains shows
that an efficient and versatile structural language of 20 building blocks is
needed to implement all the tasks carried out by proteins. Properties of amino
acids indicate that the present triplet genetic code was preceded by a more
primitive one, coding for 10 amino acids using two nucleotide bases.

categories: quant-ph cond-mat physics.bio-ph q-bio.BM


title: Integral equations of scattering in one dimension

abstract:
  A self-contained discussion of integral equations of scattering is presented
in the case of centrally-symmetric potentials in one dimension, which will
facilitate the understanding of more complex scattering integral equations in
two and three dimensions. The present discussion illustrates in a simple
fashion the concept of partial-wave decomposition, Green's function,
Lippmann-Schwinger integral equations of scattering for wave function and
transition operator, optical theorem and unitarity relation. We illustrate the
present approach with a Dirac delta potential.


title:
Relativistic Restrictions on the Distinguishability of Orthogonal
  Quantum States

abstract:
  We analyze the restrictions on the distinguishability of quantum states
imposed by special relativity. An explicit expression relating the error
probability for distinguishing between two orthogonal single-photon states with
the time $T$ elapsed from the start of the measurement procedure until the
measurement result is obtained by the observer.


title: An example of the difference between quantum and classical random walks

abstract:
  In this note, we discuss a general definition of quantum random walks on
graphs and illustrate with a simple graph the possibility of very different
behavior between a classical random walk and its quantum analogue. In this
graph, propagation between a particular pair of nodes is exponentially faster
in the quantum case.


title: Distinguishing n Hamiltonians on C^n by a single measurement

abstract:
  If an experimentalist wants to decide which one of n possible Hamiltonians
acting on an n dimensional Hilbert space is present, he can conjugate the time
evolution by an appropriate sequence of known unitary transformations in such a
way that the different Hamiltonians result in mutual orthogonal final states.
We present a general scheme providing such a sequence.


title: Quantum control without access to the controlling interaction

abstract:
  In our model a fixed Hamiltonian acts on the joint Hilbert space of a quantum
system and its controller. We show under which conditions measurements, state
preparations, and unitary implementations on the system can be performed by
quantum operations on the controller only.
  It turns out that a measurement of the observable A and an implementation of
the one-parameter group exp(iAr) can be performed by almost the same sequence
of control operations. Furthermore measurement procedures for A+B, for (AB+BA),
and for i[A,B] can be constructed from measurements of A and B. This shows that
the algebraic structure of the set of observables can be explained by the Lie
group structure of the unitary evolutions on the joint Hilbert space of the
measuring device and the measured system.
  A spin chain model with nearest neighborhood coupling shows that the border
line between controller and system can be shifted consistently.


title: Resource reduction via repeaters in entanglement distribution

abstract:
  We show that the amount of entanglement needed as an initial resource to set
up a certain final amount of entanglement between two ends of a noisy channel
can be reduced in certain cases by using quantum repeaters. Our investigation
(for various channels) considers cases when a large number of entangled pairs
are transmitted through the channel using known asymptotic results and
conjectured bounds on distillable entanglement.


title: Quantum Entanglement of Photons in Doubled q-Fock Space

abstract:
  A doubled q-Fock space is constructed by introducing an idle mode system dual
to the physical one under consideration. The quantum entanglements of photons
in the squeezed states and thermal states based on the doubled q-Fock space are
discussed.


title: Classification of mixed three-qubit states

abstract:
  We introduce a classification of mixed three-qubit states, in which we define
the classes of separable, biseparable, W- and GHZ-states. These classes are
successively embedded into each other. We show that contrary to pure W-type
states, the mixed W-class is not of measure zero. We construct witness
operators that detect the class of a mixed state. We discuss the conjecture
that all entangled states with positive partial transpose (PPTES) belong to the
W-class. Finally, we present a new family of PPTES "edge" states with maximal
ranks.


title:
Generation of correlated photons in controlled spatial modes by
  down-conversion in nonlinear waveguides

abstract:
  We report the observation of correlated photon pairs generated by spontaneous
parametric down-conversion in a quasi-phase matched KTiOPO4 nonlinear
waveguide. The highest ratio of coincidence to single photon count rates
observed in the 830 nm wavelength region exceeds 18%. This makes nonlinear
waveguides a promising source of correlated photons for metrology and quantum
information processing applications. We also discuss possibilities of
controlling the spatial characteristics of the down-converted photons produced
in multimode waveguide structures.


title: Relativity of pure states entanglement

abstract:
  Entanglement of any pure state of an N times N bi-partite quantum system may
be characterized by the vector of coefficients arising by its Schmidt
decomposition. We analyze various measures of entanglement derived from the
generalized entropies of the vector of Schmidt coefficients. For N >= 3 they
generate different ordering in the set of pure states and for some states their
ordering depends on the measure of entanglement used. This odd-looking property
is acceptable, since these incomparable states cannot be transformed to each
other with unit efficiency by any local operation. In analogy to special
relativity the set of pure states equivalent under local unitaries has a causal
structure so that at each point the set splits into three parts: the 'Future',
the 'Past' and the set of noncomparable states.


title:
Einstein-separability, time related hidden parameters for correlated
  spins, and the theorem of Bell

abstract:
  We analyze the assumptions that are made in the proofs of Bell-type
inequalities for the results of Einstein-Podolsky-Rosen type of experiments. We
find that the introduction of time-like random variables permits the
construction of a broader mathematical model which accounts for all
correlations of variables that are contained in the time dependent parameter
set of the backward light cone. It also permits to obtain the quantum result
for the spin pair correlation, a result that contradicts Bell's inequality. Two
key features of our mathematical model are (i) the introduction of time
operators that are indexed by the measurement settings and appear in addition
to Bell's source parameters and (ii) the related introduction of a probability
measure for all parameters that does depend on the analyzer settings. Using the
theory of B-splines, we then show that this probability measure can be
constructed as a linear combination of setting dependent subspace product
measures and that the construction guarantees Einstein-separability.


title: Scattering in quantum tubes

abstract:
  It is possible to fabricate mesoscopic structures where at least one of the
dimensions is of the order of de Broglie wavelength for cold electrons. By
using semiconductors, composed of more than one material combined with a metal
slip-gate, two-dimensional quantum tubes may be built. We present a method for
predicting the transmission of low-temperature electrons in such a tube. This
problem is mathematically related to the transmission of acoustic or
electromagnetic waves in a two-dimensional duct. The tube is asymptotically
straight with a constant cross-section. Propagation properties for complicated
tubes can be synthesised from corresponding results for more simple tubes by
the so-called Building Block Method. Conformal mapping techniques are then
applied to transform the simple tube with curvature and varying cross-section
to a straight, constant cross-section, tube with variable refractive index.
Stable formulations for the scattering operators in terms of ordinary
differential equations are formulated by wave splitting using an invariant
imbedding technique. The mathematical framework is also generalised to handle
tubes with edges, which are of large technical interest. The numerical method
consists of using a standard MATLAB ordinary differential equation solver for
the truncated reflection and transmission matrices in a Fourier sine basis. It
is proved that the numerical scheme converges with increasing truncation.


title: Virtual Quantum Subsystems

abstract:
  The physical resources available to access and manipulate the degrees of
freedom of a quantum system define the set $\cal A$ of operationally relevant
observables. The algebraic structure of $\cal A$ selects a preferred tensor
product structure i.e., a partition into subsystems. The notion of compoundness
for quantum system is accordingly relativized. Universal control over virtual
subsystems can be achieved by using quantum noncommutative holonomies


title:
Nonclassical Interference Effects In The Radiation From Coherently
  Driven Uncorrelated Atoms

abstract:
  We demonstrate the existence of new nonclassical correlations in the
radiation of two atoms, which are coherently driven by a continuous laser
source. The photon-photon-correlations of the fluorescence light show a spatial
interferene pattern not present in a classical treatment. A feature of the new
phenomenon is, that bunched and antibunched light is emitted in different
spatial directions. The calculations are performed analytically. It is pointed
out, that the correlations are induced by state reduction due to the
measurement process when the detection of the photons does not distinguish
between the atoms. It is interesting to note, that the phenomena show up even
without any interatomic interaction.


title: State and dynamical parameter estimation for open quantum systems

abstract:
  Following the evolution of an open quantum system requires full knowledge of
its dynamics. In this paper we consider open quantum systems for which the
Hamiltonian is ``uncertain''. In particular, we treat in detail a simple system
similar to that considered by Mabuchi [Quant. Semiclass. Opt. 8, 1103 (1996)]:
a radiatively damped atom driven by an unknown Rabi frequency $\Omega$ (as
would occur for an atom at an unknown point in a standing light wave). By
measuring the environment of the system, knowledge about the system state, and
about the uncertain dynamical parameter, can be acquired. We find that these
two sorts of knowledge acquisition (quantified by the posterior distribution
for $\Omega$, and the conditional purity of the system, respectively) are quite
distinct processes, which are not strongly correlated. Also, the quality and
quantity of knowledge gain depend strongly on the type of monitoring scheme. We
compare five different detection schemes (direct, adaptive, homodyne of the $x$
quadrature, homodyne of the $y$ quadrature, and heterodyne) using four
different measures of the knowledge gain (Shannon information about $\Omega$,
variance in $\Omega$, long-time system purity, and short-time system purity).


title:
Monitoring the Dipole-Dipole Interaction via Quantum Jumps of Individual
  Atoms

abstract:
  The emission characteristics in the fluorescence of two laser-driven
dipole-dipole-interacting three level atoms is investigated. When the light
from both atoms is detected separately a correlation of the emission processes
is observed in dependence of the dipole-dipole interaction. This opens the
possibility to investigate the dipole-dipole interaction through the emission
behavior. We present Monte-Carlo simulations which are in good agreement with
the analytic solutions.


title:
Absorption-free optical control of spin systems:the quantum Zeno effect
  in optical pumping

abstract:
  We show that atomic spin motion can be controlled by circularly polarized
light without light absorption in the strong pumping limit. In this limit, the
pumping light, which drives the empty spin state, destroys the Zeeman coherence
effectively and freezes the coherent transition via the quantum Zeno effect. It
is verified experimentally that the amount of light absorption decreases
asymptotically to zero as the incident light intensity is increased.


title: Two-photon diffraction and quantum lithography

abstract:
  We report a proof-of-principle experimental demonstration of quantum
lithography. Utilizing the entangled nature of a two-photon state, the
experimental results have bettered the classical diffraction limit by a factor
of two. This is a quantum mechanical two-photon phenomenon but not a violation
of the uncertainty principle.


title: Applications of the nilpotent Dirac state vector

abstract:
  The nilpotent version of the Dirac equation is applied to the baryon
wavefunction, the strong interaction potential, electroweak mixing, and Dirac
and Klein-Gordon propagators. The results are used to interpret a
quaternion-vector model of particle structures.


title: Generalized stochastic Schroedinger equations for state vector collapse

abstract:
  A number of authors have proposed stochastic versions of the Schr\"odinger
equation, either as effective evolution equations for open quantum systems or
as alternative theories with an intrinsic collapse mechanism. We discuss here
two directions for generalization of these equations. First, we study a general
class of norm preserving stochastic evolution equations, and show that even
after making several specializations, there is an infinity of possible
stochastic Schr\"odinger equations for which state vector collapse is provable.
Second, we explore the problem of formulating a relativistic stochastic
Schr\"odinger equation, using a manifestly covariant equation for a quantum
field system based on the interaction picture of Tomonaga and Schwinger. The
stochastic noise term in this equation can couple to any local scalar density
that commutes with the interaction energy density, and leads to collapse onto
spatially localized eigenstates. However, as found in a similar model by
Pearle, the equation predicts an infinite rate of energy nonconservation
proportional to $\delta^3(\vec 0)$, arising from the local double commutator in
the drift term.