title:
A finite-dimensional representation of the quantum angular momentum
  operator

abstract:
  A useful finite-dimensional matrix representation of the derivative of
periodic functions is obtained by using some elementary facts of trigonometric
interpolation. This NxN matrix becomes a projection of the angular derivative
into polynomial subspaces of finite dimension and it can be interpreted as a
generator of discrete rotations associated to the z-component of the projection
of the angular momentum operator in such subspaces, inheriting thus some
properties of the continuum operator. The group associated to these discrete
rotations is the cyclic group of order N. Since the square of the quantum
angular momentum L^2 is associated to a partial differential boundary value
problem in the angular variables $\theta$ and $\phi$ whose solution is given in
terms of the spherical harmonics, we can project such a differential equation
to obtain an eigenvalue matrix problem of finite dimension by extending to
several variables a projection technique for solving numerically two point
boundary value problems and using the matrix representation of the angular
derivative found before. The eigenvalues of the matrix representing L^2 are
found to have the exact form n(n+1), counting the degeneracy, and the
eigenvectors are found to coincide exactly with the corresponding spherical
harmonics evaluated at a certain set of points.


title: An Intutive Paragidm for Quantum Mechanics

abstract:
  Use is made of a relativistic kinematic modulation effect to compliment
imagery from Stochastic Electrodynamics to provide intuitive paradigms for
Quantum Mechanics. Based on these paradigms, resolutions for epistemological
problems vexing conventional interpretations of Quantum Mechanics are proposed
and discussed.


title:
Finite resolution measurement of the non-classical polarization
  statistics of entangled photon pairs

abstract:
  By limiting the resolution of quantum measurements, the measurement induced
changes of the quantum state can be reduced, permitting subsequent measurements
of variables that do not commute with the initially measured property. It is
then possible to experimentally determine correlations between non-commuting
variables. The application of this method to the polarization statistics of
entangled photon pairs reveals that negative conditional probabilities between
non-orthogonal polarization components are responsible for the violation of
Bell's inequalities. Such negative probabilities can also be observed in finite
resolution measurements of the polarization of a single photon. The violation
of Bell's inequalities therefore originates from local properties of the
quantum statistics of single photon polarization.


title: Symmetry, Duality and Anholonomy of Point Interactions in One Dimension

abstract:
  We analyze the spectral structure of the one dimensional quantum mechanical
system with point interaction, which is known to be parametrized by the group
U(2). Based on the classification of the interactions in terms of symmetries,
we show, on a general ground, how the fermion-boson duality and the spectral
anholonomy recently discovered can arise. A vital role is played by a hidden
su(2) formed by a certain set of discrete transformations, which becomes a
symmetry if the point interaction belongs to a distinguished U(1) subfamily in
which all states are doubly degenerate. Within the U(1), there is a particular
interaction which admits the interpretation of the system as a supersymmetric
Witten model.


title: Quantum Complexity of Integration

abstract:
  It is known that quantum computers yield a speed-up for certain discrete
problems. Here we want to know whether quantum computers are useful for
continuous problems. We study the computation of the integral of functions from
the classical Hoelder classes with d variables. The optimal orders for the
complexity of deterministic and (general) randomized methods are known. We
obtain the respective optimal orders for quantum algorithms and also for
restricted Monte Carlo (only coin tossing instead of general random numbers).
To summarize the results one can say that (1) there is an exponential speed-up
of quantum algorithms over deterministic (classical) algorithms, if the
smoothness is small; (2) there is a (roughly) quadratic speed-up of quantum
algorithms over randomized classical methods, if the smoothness is small.


title: Solvable PT symmetric Hamiltonians

abstract:
  Brief review is given of my recent results on solvable models within the so
called PT symmetric version of quantum mechanics.


title: Quantum theory without Hilbert spaces

abstract:
  Quantum theory does not only predict probabilities, but also relative phases
for any experiment, that involves measurements of an ensemble of systems at
different moments of time. We argue, that any operational formulation of
quantum theory needs an algebra of observables and an object that incorporates
the information about relative phases and probabilities. The latter is the
(de)coherence functional, introduced by the consistent histories approach to
quantum theory. The acceptance of relative phases as a primitive ingredient of
any quantum theory, liberates us from the need to use a Hilbert space and
non-commutative observables. It is shown, that quantum phenomena are adequately
described by a theory of relative phases and non-additive probabilities on the
classical phase space. The only difference lies on the type of observables that
correspond to sharp measurements. This class of theories does not suffer from
the consequences of Bell's theorem (it is not a theory of Kolmogorov
probabilities) and Kochen- Specker's theorem (it has distributive "logic"). We
discuss its predictability properties, the meaning of the classical limit and
attempt to see if it can be experimentally distinguished from standard quantum
theory. Our construction is operational and statistical, in the spirit of
Kopenhagen, but makes plausible the existence of a realist, geometric theory
for individual quantum systems.


title:
Comment on: "A quantum approach to static games of complete
  information''

abstract:
  Recently Marinatto and Weber introduced an interesting new scheme for
quantizing games, and applied their scheme to the famous game 'Battle of the
Sexes'. In this Comment we make two observations: (a) the overall quantization
scheme is fundamentally very similar to a previous scheme proposed by Eisert et
al., and (b) in contrast to a main claim of the paper, the quantum Battle of
the Sexes game does not have a unique solution - a similar dilemma exists in
both the classical and the quantum versions.


title: Quantum reference systems: reconciling locality with quantum mechanics

abstract:
  The status of locality in quantum mechanics is analyzed from a nonstandard
point of view. It is assumed that quantum states are relative, they depend on
and are defined with respect to some bigger physical system which contains the
former system as a subsystem. Hence, the bigger system acts as a reference
system. It is shown that quantum mechanics can be reformulated in accordance
with this new physical assumption. There is an important consequence of this
dependence: states may not be comparable, i.e., they cannot be checked by
suitable measurements simultaneously. This special circumstance is fully
reflected mathematically by the theory. Especially, it is shown that certain
joint probabilities (or the corresponding combined events) which play a vital
role in any proof of Bell's theorem do not exist. The conclusion is that the
principle of locality is fully valid in quantum mechanics, and one has to give
up instead of locality an intuitively natural-looking feature of realism,
namely, the comparability of existing states.


title: Quantum codes from cyclic codes over GF(4^m)

abstract:
  We provide a construction for quantum codes (hermitian-self-orthogonal codes
over GF(4)) starting from cyclic codes over GF(4^m). We also provide examples
of these codes some of which meet the known bounds for quantum codes.


title:
Infrared generation in low-dimensional semiconductor heterostructures
  via quantum coherence

abstract:
  A new scheme for infrared generation without population inversion between
subbands in quantum-well and quantum-dot lasers is presented and documented by
detailed calculations. The scheme is based on the simultaneous generation at
three frequencies: optical lasing at the two interband transitions which take
place simultaneously, in the same active region, and serve as the coherent
drive for the IR field. This mechanism for frequency down-conversion does not
rely upon any ad hoc assumptions of long-lived coherences in the semiconductor
active medium. And it should work efficiently at room temperature with
injection current pumping. For optimized waveguide and cavity parameters, the
intrinsic efficiency of the down-conversion process can reach the limiting
quantum value corresponding to one infrared photon per one optical photon. Due
to the parametric nature of IR generation, the proposed inversionless scheme is
especially promising for long-wavelength (far- infrared) operation.


title: Decoherence within a single atom

abstract:
  An "almost diagonal" reduced density matrix (in coordinate representation) is
usually a result of environment induced decoherence and is considered the sign
of classical behavior. We point out that the proton of a ground state hydrogen
atom can possess such a density matrix. We demonstrate on this example that an
"almost diagonal" reduced density matrix may derive from an interaction with a
low number of degrees of freedom (in our case with a single electron) which
play the role of the environment. We also show that decoherence effects in our
example can only be observed if the interaction with the measuring device is
significantly faster than the interaction with the environment (the electron).
In the opposite case, when the interaction with the environment is significant
during the measurement process, coherence is restored.
  Finally, we propose a neutron scattering experiment on cold He atoms to
observe decoherence which shows up as an additional contribution to the
differential scattering cross section.


title: Coherent State Path Integrals without Resolutions of Unity

abstract:
  From the very beginning, coherent state path integrals have always relied on
a coherent state resolution of unity for their construction. By choosing an
inadmissible fiducial vector, a set of ``coherent states'' spans the same space
but loses its resolution of unity, and for that reason has been called a set of
weak coherent states. Despite having no resolution of unity, it is nevertheless
shown how the propagator in such a basis may admit a phase-space path integral
representation in essentially the same form as if it had a resolution of unity.
Our examples are toy models of similar situations that arise in current studies
of quantum gravity.


title:
Coherent oscillation in a linear quantum system coupled to a thermal
  bath

abstract:
  We consider the time development of the density matrix for a system coupled
to a thermal bath, in models that go beyond the standard two-level systems
through addition of an energy excitation degree of freedom and through the
possibility of the replacement of the spin algebra by a more complex algebra.
We find conditions under which increasing the coupling to the bath above a
certain level decreases the rate of entropy production, and in which the
limiting behavior is a dissipationless sinusoidal oscillation that could be
interpreted as the synchronization of many modes of the uncoupled system.


title: The asymptotic entanglement cost of preparing a quantum state

abstract:
  We give a detailed proof of the conjecture that the asymptotic entanglement
cost of preparing a bipartite state \rho is equal to the regularized
entanglement of formation of \rho.


title: Quantum Mechanics and the Cookie Cutter Paradigm

abstract:
  What has so far prevented us from decrypting quantum mechanics is the Cookie
Cutter Paradigm, according to which the world's synchronic multiplicity derives
from surfaces that carve up space in the manner of three-dimensional cookie
cutters. This insidious notion is shown to be rooted in our neurophysiological
make-up. An effort is made to liberate the physical world from this innate
fallacy.


title: NMR Quantum Computation

abstract:
  In this article I will describe how NMR techniques may be used to build
simple quantum information processing devices, such as small quantum computers,
and show how these techniques are related to more conventional NMR experiments.


title:
Decoherence, Correlation, and Entanglement in a Pair of Coupled Quantum
  Dissipative Oscillators

abstract:
  A pair of coupled quantum dissipative oscillators, serving as a model for a
nanosystem, is here described by the Lindblad equation. Its dynamic evolution
is shown to exhibit the features of decoherence (spatial extent of quantum
behavior), correlation (spatial scale over which the system localizes to its
physical dimensions), and entanglement (a special quantum feature making its
appearance first in such bipartite systems) as a function of the coupling
constants of the Lindblad equation. One interesting feature emerging out of
this calculation is that the entanglement may exhibit revivals in time. An
initially entangled state need not remain so for all time and may exhibit
regions of nonentanglement. Interpreting the parameters of the Lindblad theory
as environmental features in certain experimental situations, this model
calculation gives us clues to possible control of decoherence, correlation, and
entanglement. We indicate possible interpretation of the Lindblad parameters as
control parameters in more general contexts of some recent experiments.


title: On the class of languages recognizable by 1-way quantum finite automata

abstract:
  It is an open problem to characterize the class of languages recognized by
quantum finite automata (QFA). We examine some necessary and some sufficient
conditions for a (regular) language to be recognizable by a QFA. For a subclass
of regular languages we get a condition which is necessary and sufficient.
  Also, we prove that the class of languages recognizable by a QFA is not
closed under union or any other binary Boolean operation where both arguments
are significant.


title: Quantum computing of quantum chaos and imperfection effects

abstract:
  We study numerically the imperfection effects in the quantum computing of the
kicked rotator model in the regime of quantum chaos. It is shown that there are
two types of physical characteristics: for one of them the quantum computation
errors grow exponentially with the number of qubits in the computer while for
the other the growth is polynomial. Certain similarity between classical and
quantum computing errors is also discussed.


title:
Eavesdropper's Optimal Information in Variations of Bennett-Brassard
  1984 Quantum Key Distribution in the Coherent Attacks

abstract:
  We calculate eavesdropper's optimal information on raw bits in
Bennett-Brassard 1984 quantum key distribution (BB84 QKD) and six-state scheme
in coherent attacks, using a formula by Lo and Chau [Science 283 (1999) 2050]
with single photon assumption. We find that eavesdropper's optimal information
in QKD without public announcement of bases [Phys. Lett. A 244 (1998) 489] is
the same as that of a corresponding QKD WITH it in the coherent attack. We
observe a sum-rule concerning each party's information.


title: The Einstein-Podolsky-Rosen state maximally violates Bell's inequalities

abstract:
  In their well-known argument against the completeness of quantum theory,
Einstein, Podolsky, and Rosen (EPR) made use of a state that strictly
correlates the positions and momenta of two particles. We prove the existence
and uniqueness of the EPR state as a normalized, positive linear functional of
the Weyl algebra for two degrees of freedom. We then show that the EPR state
maximally violates Bell's inequalities.


title: Remarks on the semi-classical theory of three state system

abstract:
  The semi-classical solution of the three state system is considered to study
the population inversion at and away from resonance. At resonance, it is shown
that if the system is initially populated either in the upper or in the lower
level, then the population oscillation occurs in a way which is quite different
from that if it is initially populated in the middle state. At off resonance,
there is gradual suppression of the population in the excited states and in the
asymptotic limit of the detuning, the system returns to its initial state.


title:
The definition of a random sequence of qubits: from Noncommutative
  Algorithmic Probability Theory to Quantum Algorithmic Information Theory and
  back

abstract:
  The issue of defining a random sequence of qubits is studied in the framework
of Algorithmic Free Probability Theory.Its connection with Quantum Algorithmic
Information Theory is shown


title:
Hadamard Products of Product Operators and the Design of
  Gradient-Diffusion Experiments for Simulating Decoherence by NMR Spectroscopy

abstract:
  An extension of the product operator formalism of NMR is introduced, which
uses the Hadamard matrix product to describe many simple spin 1/2 relaxation
processes. The utility of this formalism is illustrated by deriving NMR
gradient-diffusion experiments to simulate several decoherence models of
interest in quantum information processing, along with their Lindblad and Kraus
representations. Gradient-diffusion experiments are also described for several
more complex forms of decoherence, including the well-known collective
isotropic model. Finally, it is shown that the Hadamard formalism gives a
concise representation of decoherence with arbitrary correlations among the
fluctuating fields at the different spins involved, and that this can be
applied to both decoherence (T2) as well as nonadiabatic relaxation (T1)
processes.


title: Particle on a polygon: Quantum Mechanics

abstract:
  We study the quantization of a model proposed by Newton to explain
centripetal force namely, that of a particle moving on a regular polygon. The
exact eigenvalues and eigenfunctions are obtained. The quantum mechanics of a
particle moving on a circle and in an infinite potential well are derived as
limiting cases.


title:
Basic Properties of Coherent and Generalized Coherent Operators
  Revisited

abstract:
  In this letter we make a brief review of some basic properties (the matrix
elements, the trace, the Glauber formula) of coherent operators and study the
corresponding ones for generalized coherent operators based on Lie algebra
su(1,1). We also propose some problems.


title:
Comment on the paper ``Decoherence and the theory of continuous quantum
  measurements'', by M. B. Mensky, Phys. Usp. 41, 923 (1998),
  arXiv:quant-ph/9812017v2

abstract:
  In quant-ph/9812017v2 M.B. Mensky reviewed our application of the restricted
path integral approach to quantum measurements of energy. In this comment we
point out that Mensky's assessment of our results is incorrect.


title: Experimental requirements for quantum communication complexity protocols

abstract:
  I present a simple two-party quantum communication complexity protocol with
higher success rate than the best possible classical protocol for the same
task. The quantum protocol is shown to be equivalent to a quantum non-locality
test, except that it is not necessary to close the locality loophole. I derive
bounds for the detector efficiency and background count rates necessary for an
experimental implementation and show that they are close to what can be
currently achieved using ion trap technology. I also analyze the requirements
for a three-party protocol and show that they are less demanding than those for
the two-party protocol. The results can be interpreted as sufficient
experimental conditions for quantum non-locality tests using two or three
entangled qubits.


title: General procedure of solving the time-dependent Schr\"odinger equation

abstract:
  A nonperturbative procedure of solving the time-dependent Schr\"odinger
equation, called the multi-projection approach or phase dynamics of quantum
mechanics, is derived and illustrated. In addition to introducing a method with
that time-dependent systems become solvable (under the assumption that
corresponding time-independent systems are solvable), the new approach unveils
several misconcepts related to the usual wavefunction expansion and the
standard perturbation theory.


title:
Violations of Bell Inequalities for Measurements with Macroscopic
  Uncertainties: What does it Mean to Violate Macroscopic Local Realism?

abstract:
  We suggest to test the premise of ``macroscopic local realism'' which is
sufficient to derive Bell inequalities when measurements of photon number are
only accurate to an uncertainty of order $n$ photons, where $n$ is macroscopic.
Macroscopic local realism is only sufficient to imply, in the context of the
original Einstein-Podolsky-Rosen argument, fuzzy ``elements of reality'' which
have a macroscopic indeterminacy. We show therefore how the violation of local
realism in the presence of macroscopic uncertainties implies the failure of
``macroscopic local realism''. Quantum states violating this macroscopic local
realism are presented.


title: A Variational Expansion for the Free Energy of a Bosonic System

abstract:
  In this paper, a variational perturbation scheme for nonrelativistic
many-Fermion systems is generalized to a Bosonic system. By calculating the
free energy of an anharmonic oscillator model, we investigated this variational
expansion scheme for its efficiency. Using the modified Feynman rules for the
diagrams, we obtained the analytical expression of the free energy up to the
fourth order. Our numerical results at various orders are compared with the
exact and other relevant results.


title: Feynman's Entropy and Decoherence Mechanism

abstract:
  If we reduce coherence in a given quantum system, the result is an increase
in entropy. Does this necessarily convert this quantum system into a classical
system? The answer to this question is No. The decrease of coherence means more
uncertainty. This does not seem to make the system closer to classical system
where there are no uncertainties. We examine the problem using two coupled
harmonic oscillators where we make observations on one of them while the other
oscillator is assumed to be unobservable or to be in Feynman's rest of the
universe. Our ignorance about the rest of the universe causes an increase in
entropy. However, does the system act like a classical system? The answer is
again No. When and how does this system appear like a classical system? It is
shown that this paradox can be resolved only if measurements are taken along
the normal coordinates. It is also shown that Feynman's parton picture is one
concrete physical example of this decoherence mechanism.


title:
Interpreting the time of decay measurement: phenomenological
  significance of the Bohm model

abstract:
  We point out that the spreading of wave packets could be significant in
affecting the analysis of experiments involving the measurement of time of
decay. In particular, we discuss a hitherto unexplored application of the Bohm
model in properly taking into account the nontrivial effect of wave packet
spreading in the CP violation experiment.


title:
A General Argument Against the Universal Validity of the Superposition
  Principle

abstract:
  We reconsider a well known problem of quantum theory, i.e. the so called
measurement (or macro-objectification) problem, and we rederive the fact that
it gives rise to serious problems of interpretation. The novelty of our
approach derives from the fact that the relevant conclusion is obtained in a
completely general way, in particular, without resorting to any of the
assumptions of ideality which are usually done for the measurement process. The
generality and unescapability of our assumptions (we take into account possible
malfunctionings of the apparatus, its unavoidable entanglement with the
environmment, its high but not absolute reliability, its fundamentally
uncontrollable features) allow to draw the conclusion that the very possibility
of performing measurements on a microsystem combined with the assumed general
validity of the linear nature of quantum evolution leads to a fundamental
contradiction.


title: What does an observed quantum system reveal to its observer ?

abstract:
  The evolution of a quantum system under observation becomes retarded or even
impeded. We review this ``quantum Zeno effect'' in the light of the criticism
that has been raised upon a previous attempt to demonstrate it, of later
reexaminations of both the projection postulate and the significance of the
observations, and of the results of a recent experiment on an individual cold
atom. Here, the micro-state of the quantum system gets unveiled with the
observation, and the effect of measurement is no longer mixed up with dephasing
the object's wave function by the reactive effect of the detection. A procedure
is outlined that promises to provide, by observation, an upper limit for the
delay of even an exponential decay.


title: Decomposition of Hilbert space in sets of coherent states

abstract:
  Within the generalized definition of coherent states as group orbits we study
the orbit spaces and the orbit manifolds in the projective spaces constructed
from linear representations. Invariant functions are suggested for arbitrary
groups. The group SU(2) is studied in particular and the orbit spaces of its
j=1/2 and j=1 representations completely determined. The orbits of SU(2) in
CP^N can be either 2 or 3 dimensional, the first of them being either
isomorphic to S^2 or to RP^2 and the latter being isomorphic to quotient spaces
of RP^3. We end with a look from the same perspective to the quantum mechanical
space of states in particle mechanics.


title: A puzzle in quantum dynamics

abstract:
  The textbook treatment in that the wave function of a dynamical system is
expanded in an eigenfunction series is investigated. With help of an elementary
example and some mathematical theorems, it is revealed that in terms of solving
the time-dependent Schr\"odinger equation the treatment involves in divergence
trouble . The root reason behind the trouble is finally analyzed.


title: Decoherence, pointer engineering and quantum state protection

abstract:
  We present a proposal for protecting states against decoherence, based on the
engineering of pointer states. We apply this procedure to the vibrational
motion of a trapped ion, and show how to protect qubits, squeezed states,
approximate phase eigenstates and superpositions of coherent states.


title:
Multiparty key distribution and secret sharing based on entanglement
  swapping

abstract:
  A general proof of the security against eavesdropping of a previously
introduced protocol for two-party quantum key distribution based on
entanglement swapping [Phys. Rev. A {\bf 61}, 052312 (2000)] is provided. In
addition, the protocol is extended to permit multiparty quantum key
distribution and secret sharing of classical information.


title: Testing Bell's Inequality with Ballistic Electrons in Semiconductors

abstract:
  We propose an experiment to test Bell's inequality violation in
condensed-matter physics. We show how to generate, manipulate and detect
entangled states using ballistic electrons in Coulomb-coupled semiconductor
quantum wires. Due to its simplicity (only five gates are required to prepare
entangled states and to test Bell's inequality), the proposed
semiconductor-based scheme can be implemented with currently available
technology. Moreover, its basic ingredients may play a role towards large-scale
quantum-information processing in solid-state devices.


title: Practical Quantum Cryptography: A Comprehensive Analysis (Part One)

abstract:
  We perform a comprehensive analysis of practical quantum cryptography (QC)
systems implemented in actual physical environments via either free-space or
fiber-optic cable quantum channels for ground-ground, ground-satellite,
air-satellite and satellite-satellite links. (1) We obtain universal
expressions for the effective secrecy capacity and rate for QC systems taking
into account three important attacks on individual quantum bits, including
explicit closed-form expressions for the requisite amount of privacy
amplification. Our analysis also includes the explicit calculation in detail of
the total cost in bits of continuous authentication, thereby obtaining new
results for actual ciphers of finite length. (2) We perform for the first time
a detailed, explicit analysis of all systems losses due to propagation, errors,
noise, etc. as appropriate to both optical fiber cable- and satellite
communications-based implementations of QC. (3) We calculate for the first time
all system load costs associated to classical communication and computational
constraints that are ancillary to, but essential for carrying out, the pure QC
protocol itself. (4) We introduce an extended family of generalizations of the
Bennett-Brassard (BB84) QC protocol that equally provide unconditional secrecy
but allow for the possibility of optimizing throughput rates against specific
cryptanalytic attacks. (5) We obtain universal predictions for maximal rates
that can be achieved with practical system designs under realistic
environmental conditions. (6) We propose a specific QC system design that
includes the use of a novel method of high-speed photon detection that may be
able to achieve very high throughput rates for actual implementations in
realistic environments.


title: New schemes for manipulating quantum states using a Kerr cell

abstract:
  In this proceeding we describe various proposals of application of an high
coefficient Kerr cell to quantum states manipulation, ranging from fast
modulation of quantum interference, GHZ states generation, Schroedinger cats
creation, translucent eavesdropping, etc.


title:
Quantum-Classical Correspondence of Dynamical Observables, Quantization
  and the Time of Arrival Correspondence Problem

abstract:
  We raise the problem of constructing quantum observables that have classical
counterparts without quantization. Specifically we seek to define and motivate
a solution to the quantum-classical correspondence problem independent from
quantization and discuss the general insufficiency of prescriptive
quantization, particularly the Weyl quantization. We demonstrate our points by
constructing time of arrival operators without quantization and from these
recover their classical counterparts.


title:
One- and two-dimensional N-qubit systems in capacitively coupled quantum
  dots

abstract:
  Coulomb blockade effects in capacitively coupled quantum dots can be utilized
for constructing an N-qubit system with antiferromagnetic Ising interactions.
Starting from the tunneling Hamiltonian, we theoretically show that the
Hamiltonian for a weakly coupled quantum-dot array is reduced to that for
nuclear magnetic resonance (NMR) spectroscopy. Quantum operations are carried
out by applying only electrical pulse sequences. Thus various error-correction
methods developed in NMR spectroscopy and NMR quantum computers are applicable
without using magnetic fields. A possible measurement scheme in an N-qubit
system is quantitatively discussed.


title:
Sympathetic ground state cooling and coherent manipulation with
  two-ion-crystals

abstract:
  We have cooled a two-ion-crystal to the ground state of its collective modes
of motion. Laser cooling, more specific resolved sideband cooling is performed
sympathetically by illuminating only one of the two $^{40}$Ca$^+$ ions in the
crystal. The heating rates of the motional modes of the crystal in our linear
trap have been measured, and we found them considerably smaller than those
previously reported by Q. Turchette {\em et. al.} Phys. Rev. A 61, 063418
(2000) in the case of trapped $^9$Be$^+$ ions. After the ground state is
prepared, coherent quantum state manipulation of the atomic population can be
performed. Within the coherence time, up to 12 Rabi oscillations are observed,
showing that many coherent manipulations can be achieved. Coherent excitation
of each ion individually and ground state cooling are important tools for the
realization of quantum information processing in ion traps.


title: Bounds on quantum ordered searching

abstract:
  We prove that any exact quantum algorithm searching an ordered list of N
elements requires more than \frac{1}{\pi}(\ln(N)-1) queries to the list. This
improves upon the previously best known lower bound of {1/12}\log_2(N) - O(1).
  Our proof is based on a weighted all-pairs inner product argument, and it
generalizes to bounded-error quantum algorithms.
  The currently best known upper bound for exact searching is roughly 0.526
\log_2(N).
  We give an exact quantum algorithm that uses \log_3(N) + O(1) queries, which
is roughly 0.631 \log_2(N). The main principles in our algorithm are an quantum
parallel use of the classical binary search algorithm and a method that allows
basis states in superpositions to communicate.


title: Uncertainty for spin systems

abstract:
  A modified definition of quantum mechanical uncertainty D for spin systems,
which is invariant under the action of SU(2), is suggested. Its range is shown
to be h^2j<D<h^2j(j+1) within any irreducible representation j of SU(2) and its
mean value in Hilbert space computed using the Fubini-Study metric is
determined to be mean(D)=h^2j(j+1/2). The most used sets of coherent states in
spin systems coincide with the set of minimum D uncertainty states.


title:
Experimental demonstration of ground state laser cooling with
  electromagnetically induced transparency

abstract:
  Ground state laser cooling of a single trapped ion is achieved using a
technique which tailors the absorption profile for the cooling laser by
exploiting electromagnetically induced transparency in the Zeeman structure of
a dipole transition. This new method is robust, easy to implement and proves
particularly useful for cooling several motional degrees of freedom
simultaneously, which is of great practical importance for the implementation
of quantum logic schemes with trapped ions.


title: Quantum information processing in semiconductor nanostructures

abstract:
  A major question for condensed matter physics is whether a solid-state
quantum computer can ever be built. Here we discuss two different schemes for
quantum information processing using semiconductor nanostructures. First, we
show how optically driven coupled quantum dots can be used to prepare maximally
entangled Bell and Greenberger-Horne-Zeilinger states by varying the strength
and duration of selective light pulses. The setup allows us to perform an
all-optical generation of the quantum teleportation of an excitonic state in an
array of coupled quantum dots.
  Second, we give a proposal for reliable implementation of quantum logic gates
and long decoherence times in a quantum dots system based on nuclear magnetic
resonance (NMR), where the nuclear resonance is controlled by the ground state
transitions of few-electron QDs in an external magnetic field. The dynamical
evolution of these systems in the presence of environmentally-induced
decoherence effects is also discussed.


title:
Two-particle model with noncommuting operators of coordinates and
  momenta

abstract:
  A nonrelativistic equation for the system of two interacting particles within
the framework of a model with noncommuting operators of coordinates and momenta
of different particles is proposed, and a self-consistent system of equations
for the wave function of every quantum state is deduced. Solutions for the
lowest states of a hydrogenlike atom are found, and the comparison with
analogous solutions of the Klein-Gordon equation for the relativistic spinless
problem is performed. In the case where the size of a two-particle system and
the Compton wavelengths of particles forming it are of the same order, the
essential differences with solutions of the Schr\"{o}dinger nonrelativistic
equation are revealed.


title:
Nonequilibrium-current-induced corrections to the
  one-particle-correlation function in a wire

abstract:
  Electron gas in a wire connected to two terminals with potential drop is
studied with the Schwinger-Keldysh formalism. Recent studies, where the current
is enforced to flow with a Lagrange-multiplier term, demonstrated that the
current enhances the one-particle-correlation function. We report that in our
model, such enhancement is not guaranteed to occur, but conditional both on the
potential drop and the positions where we observe the correlation function.
That is, under a certain condition, spatially modulated pattern is formed in
the wire owing to the nonequilibrium current.


title: Equations, States, and Lattices of Infinite-Dimensional Hilbert Spaces

abstract:
  We provide several new results on quantum state space, on lattice of
subspaces of an infinite dimensional Hilbert space, and on infinite dimensional
Hilbert space equations as well as on connections between them. In particular
we obtain an n-variable generalized orthoarguesian equation which holds in any
infinite dimensional Hilbert space. Then we strengthen Godowski's result by
showing that in an ortholattice on which strong states are defined Godowski's
equations as well as the orthomodularity hold. We also prove that all 6- and
4-variable orthoarguesian equations presented in the literature can be reduced
to new 4- and 3-variable ones, respectively and that Mayet's examples follow
from Godowski's equations. To make a breakthrough in testing these massive
equations we designed several novel algorithms for generating Greechie diagrams
with an arbitrary number of blocks and atoms (currently testing with up to 50)
and for automated checking of equations on them. A way of obtaining complex
infinite dimensional Hilbert space from the Hilbert lattice equipped with
several additional conditions and without invoking the notion of state is
presented. Possible repercussions of the results to quantum computing problems
are discussed.


title: Algorithms for Greechie Diagrams

abstract:
  We give a new algorithm for generating Greechie diagrams with arbitrary
chosen number of atoms or blocks (with 2,3,4,... atoms) and provide a computer
program for generating the diagrams. The results show that the previous
algorithm does not produce every diagram and that it is at least 100,000 times
slower. We also provide an algorithm and programs for checking of Greechie
diagram passage by equations defining varieties of orthomodular lattices and
give examples from Hilbert lattices. At the end we discuss some additional
characteristics of Greechie diagrams.

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


title:
A two-slit experiment which distinguishes between standard and Bohmian
  quantum mechanics

abstract:
  In this investigation, we have suggested a special two-slit experiment which
can distinguish between the standard and the Bohmian quantum mechanics. At the
first step, we have shown that observable individual predictions obtained from
these two theories are inconsistent for a special case. But, at the ensemble
level, they are consistent as was expected. Then, as another special case and
using selective detection, it is shown that an observable disagreement between
the two theories can exist at the ensemble level of particles. This can
encourage new efforts for finding other inconsistencies between the two
theories, theoretically and experimentally.


title: Entangled Rings

abstract:
  Consider a ring of N qubits in a translationally invariant quantum state. We
ask to what extent each pair of nearest neighbors can be entangled. Under
certain assumptions about the form of the state, we find a formula for the
maximum possible nearest-neighbor entanglement. We then compare this maximum
with the entanglement achieved by the ground state of an antiferromagnetic ring
consisting of an even number of spin-1/2 particles. We find that, though the
antiferromagnetic ground state does not maximize the nearest-neighbor
entanglement relative to all other states, it does so relative to other states
having zero z-component of spin.


title: Comment on "Quantum key distribution without alternative measurements"

abstract:
  In a recent paper [A. Cabello, Phys. Rev. A 61, 052312 (2000)], a quantum key
distribution protocol based on entanglement swapping was proposed. However, in
this comment, it is shown that this protocol is insecure if Eve use a special
strategy to attack.


title:
Universal quantum computation by holonomic and nonlocal gates with
  imperfections

abstract:
  We present a nonlocal construction of universal gates by means of holonomic
(geometric) quantum teleportation. The effect of the errors from imperfect
control of the classical parameters, the looping variation of which builds up
holonomic gates, is investigated. Additionally, the influence of quantum
decoherence on holonomic teleportation used as a computational primitive is
studied. Advantages of the holonomic implementation with respect to control
errors and dissipation are presented.


title: From Single to Multiple-Photon Decoherence in an Atom Interferometer

abstract:
  We measure the decoherence of a spatially separated atomic superposition due
to spontaneous photon scattering. We observe a qualitative change in
decoherence versus separation as the number of scattered photons increases, and
verify quantitatively the decoherence rate constant in the many-photon limit.
Our results illustrate an evolution of decoherence consistent with general
models developed for a broad class of decoherence phenomenon.


title: Performance of a deterministic source of entangled photonic qubits

abstract:
  We study the possible limitations and sources of decoherence in the scheme
for the deterministic generation of polarization-entangled photons, recently
proposed by Gheri et al. [K. M. Gheri et al., Phys. Rev. A 58, R2627 (1998)],
based on an appropriately driven single atom trapped within an optical cavity.
We consider in particular the effects of laser intensity fluctuations, photon
losses, and atomic motion.


title:
On the connection between the radial momentum operator and the
  Hamiltonian in n dimensions

abstract:
  The radial momentum operator in quantum mechanics is usually obtained through
canonical quantization of the (symmetrical form of the) classical radial
momentum. We show that the well known connection between the Hamiltonian of a
free particle and the radial momentum operator $\hat{H}=\hat{P}_{r}^2/2m+
$\hat{L}^2$}/2mr^{2}$ is true only in one or three dimensions. In general, an
extra term of the form $\hbar^{2}(n-1)(n-3)/ 2m \cdot 4r^{2}$ has to be added
to the Hamiltonian.


title: Entanglement of a Double Dot with a Quantum Point Contact

abstract:
  Entanglement between particle and detector is known to be inherent in the
measurement process. Gurvitz recently analyzed the coupling of an electron in a
double dot (DD) to a quantum point contact (QPC) detector. In this paper we
examine the dynamics of entanglement that result between the DD and QPC. The
rate of entanglement is optimized as a function of coupling when the electron
is initially in one of the dots. It decreases asymptotically towards zero with
increased coupling. The opposite behavior is observed when the DD is initially
in a superposition: the rate of entanglement increases unboundedly as the
coupling is increased. The possibility that there are conditions for which
measurement occurs versus entanglement is considered.


title: Optimal dense coding with mixed state entanglement

abstract:
  I investigate dense coding with a general mixed state on the Hilbert space
$C^{d}\otimes C^{d}$ shared between a sender and receiver. The following result
is proved. When the sender prepares the signal states by mutually orthogonal
unitary transformations with equal {\it a priori} probabilities, the capacity
of dense coding is maximized. It is also proved that the optimal capacity of
dense coding $\chi ^{*}$ satisfies $E_{R}(\rho)\leq \chi ^{*}\leq E_{R}(\rho
)+\log_{2}d$, where $E_{R}(\rho)$ is the relative entropy of entanglement of
the shared entangled state.


title: Quantum propagators in a random metric

abstract:
  We consider second order differential operators with coefficients which are
Gaussian random fields. When the covariance becomes singular at short distances
then the propagators of the Schr\"odinger equation as well as of the wave
equation behave in an anomalous way. In particular, the Feynman propagator for
the wave equation is less singular than the one with deterministic
coefficients. We suggest some applications to quantum gravity.


title: Playing a quantum game with a corrupted source

abstract:
  The quantum advantage arising in a simplified multi-player quantum game, is
found to be a disadvantage when the game's qubit-source is corrupted by a noisy
"demon". Above a critical value of the corruption-rate, or noise-level, the
coherent quantum effects impede the players to such an extent that the optimal
choice of game changes from quantum to classical.


title:
Addendum to ``Quantum key distribution without alternative
  measurements''

abstract:
  Recently, Zhang, Li, and Guo have proposed a particular eavesdropping attack
[Phys. Rev. A {\bf 63}, 036301 (2001), quant-ph/0009042] which shows that my
quantum key distribution protocol based on entanglement swapping [Phys. Rev. A
{\bf 61}, 052312 (2000), quant-ph/9911025] is insecure. However, security
against this attack can be attained with a simple modification. In addition, a
simpler version of the protocol using four qubits is introduced.


title: Concepts of a quantum information theory of many letters

abstract:
  A theoretical framework is presented allowing the treatment of quantum
messages with components of variable length. To this aim a many-letter space,
similiar to the Fock space, is constructed, generalizing the standard quantum
information theory of block messages of fixed length. In the many-letter space
a length operator can be defined measuring the length of a quantum message,
whose eigenspaces are the block Hilbert spaces used in the standard theory.


title: Coherently Controlled Nanoscale Molecular Deposition

abstract:
  Quantum interference effects are shown to provide a means of controlling and
enhancing the focusing a collimated neutral molecular beam onto a surface. The
nature of the aperiodic pattern formed can be altered by varying laser field
characteristics and the system geometry.


title: Space-bounded computation: quantum is better than classical

abstract:
  This paper has been withdrawn, as all conjectures (and one claim) have been
proven incorrect. Some of what remains may eventually reappear in a different
context.


title:
Optical tests of quantum nonlocality: from EPR-Bell tests towards
  experiments with moving observers

abstract:
  Past, present and future experimental tests of quantum nonlocality are
discussed. Consequences of assuming that the state-vector collapse is a real
physical phenomenon in space-time are developed. These lead to experiments
feasible with today's technology.


title: Consistent Histories and the Bohm Approach

abstract:
  In a recent paper Griffiths claims that the consistent histories
interpretation of quantum mechanics gives rise to results that contradict those
obtained from the Bohm interpretation. This is in spite of the fact that both
claim to provide a realist interpretation of the formalism without the need to
add any new mathematical content and both always produce exactly the same
probability predictions of the outcome of experiments. In constrasting the
differences Griffiths argues that the consistent histories interpretation
provides a more physically reasonable account of quantum phenomena. We examine
this claim and show that the consistent histories approach is not without its
difficulties.


title:
Local-field corrections to the decay rate of excited molecules in
  absorbing cavities: the Onsager model

abstract:
  The decay rate and the classical radiation power of an excited molecule
(atom) located in the center of a dispersive and absorbing dielectric sphere
taken as a simple model of a cavity are calculated adopting the Onsager model
for the local field. The local-field correction factor to the external
(radiation and absorption) power loss of the molecule is found to be
$|3\epsilon(\omega)/[3\epsilon(\omega)+1]|^2$, with $\epsilon(\omega)$ being
the dielectric function of the sphere. However, local-field corrections to the
total decay rate (power loss) of the molecule are found to be much more
complex, including those to the decay rate in the infinite cavity medium, as
derived very recently by Scheel et al. [Rev. A 60, 4094 (1999)], and similiar
corrections to the cavity-induced decay rate. The results obtained can be cast
into model-independent forms. This suggests the general results for the
local-field corrections to the decay rate and to the external power loss of a
molecule in an absorbing cavity valid for molecule positions away from the
cavity walls.


title: Bell's Theorem and Random Variables

abstract:
  Bell's theorem states that quantum correlation function of two spins can not
be represented as an expectation value of two classical random variables. Spin
is described in Bell's model by a single scalar random variable. We discuss
another classical model of spin in which spin is described by a triple of
classical random variables. It is shown that in this model the quantum
correlation function can be represented as the expectation value of classical
random variables. Implications of this result to the problem of local causality
of quantum mechanics and relations with problems of moments are briefly
mentioned.


title: Experimental NMR Realization of A Generalized Quantum Search Algorithm

abstract:
  A generalized quantum search algorithm, where phase inversions for the marked
state and the prepared state are replaced by $\pi/2$ phase rotations, is
realized in a 2-qubit NMR heteronuclear system. The quantum algorithm searches
a marked state with a smaller step compared to standard Grover algorithm. Phase
matching requirement in quantum searching is demonstrated by comparing it with
another generalized algorithm where the two phase rotations are $\pi/2$ and
$3\pi/2$ respectively. Pulse sequences which include non 90 degree pulses are
given.


title: Natural Thermal and Magnetic Entanglement in 1D Heisenberg Model

abstract:
  We investigate the entanglement between any two spins in a one dimensional
Heisenberg chain as a function of temperature and the external magnetic field.
We find that the entanglement in an antiferromagnetic chain can be increased by
increasing the temperature or the external field. Increasing the field can also
create entanglement between otherwise disentangled spins. This entanglement can
be confirmed by testing Bell's inequalities involving any two spins in the
solid.


title:
Experiments towards Falsification of Noncontextual Hidden Variable
  Theories

abstract:
  We present two experiments testing the hypothesis of noncontextual hidden
variables (NCHV's). The first one is based on observation of two-photon
pseudo-Greenberger-Horne-Zeilinger correlations, with two of the originally
three particles mimicked by the polarization degree of freedom and the spatial
degree of freedom of a single photon. The second one, a single-photon
experiment, utilizes the same trick to emulate two particle correlations, and
is an "event ready" test of a Bell-like inequality, derived from the
noncontextuality assumption. Modulo fair sampling, the data falsify NCHV's.


title: From quantum nonlocality to mind-brain interaction

abstract:
  Orthodox Copenhagen quantum theory renounces the quest to understand the
reality in which we are imbedded, and settles for practical rules that describe
connections between our observations. However, an examination of certain
nonlocal features of quantum theory suggests that the perceived need for this
renunciation was due to the uncritical importation from classical physics of a
crippling metaphysical prejudice, and that rejection of that prejudice opens
the way to a dynamical theory of the interaction between mind and brain that
has significant explanatory power.


title: Entanglement of Formation of an Arbitrary State of Two Rebits

abstract:
  We consider entanglement for quantum states defined in vector spaces over the
real numbers. Such real entanglement is different from entanglement in standard
quantum mechanics over the complex numbers. The differences provide insight
into the nature of entanglement in standard quantum theory. 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. We give a contrasting formula for the entanglement of
formation of an arbitrary state of two ``rebits,'' a rebit being a system whose
Hilbert space is a 2-dimensional real vector space.


title:
Quantum phase retrieval of a Rydberg wave packet using a half-cycle
  pulse

abstract:
  A terahertz half-cycle pulse was used to retrieve information stored as
quantum phase in an $N$-state Rydberg atom data register. The register was
prepared as a wave packet with one state phase-reversed from the others (the
"marked bit"). A half-cycle pulse then drove a significant portion of the
electron probability into the flipped state via multimode interference.


title:
The Topological AC and HMW Effects, and the Dual Current in 2+1
  Dimensions

abstract:
  We study the Aharonov-Casher (AC) effect and the related He-McKellar-Wilkens
(HMW) effect in 2+1 dimensions. In this restricted space these effects are the
result of the interaction of the electromagnetic field tensor with the dual of
a current. Transferring the dual operation from the current to the field tensor
shows that this interaction may be reinterpreted as due to the interaction of
an effective vector potential and a current, and the AC and HMW effects follow
immediately. A general proof of this for particles with an arbitrary spin is
provided.
  The restriction to 2+1 dimensions, with this interpretation, provides a
unified way of treating the AC and HMW effects for an arbitrary spin. Perhaps
more interestingly the treatment shows that a spin-0 particle can show AC and
HMW effects, although it has no magnetic or electric dipole moment in the usual
sense.


title: Classical wave-optics analogy of quantum information processing

abstract:
  An analogous model system for quantum information processing is discussed,
based on classical wave optics. The model system is applied to three examples
that involve three qubits: ({\em i}) three-particle Greenberger-Horne-Zeilinger
entanglement, ({\em ii}) quantum teleportation, and ({\em iii}) a simple
quantum error correction network. It is found that the model system can
successfully simulate most features of entanglement, but fails to simulate
quantum nonlocality. Investigations of how far the classical simulation can be
pushed show that {\em quantum nonlocality} is the essential ingredient of a
quantum computer, even more so than entanglement. The well known problem of
exponential resources required for a classical simulation of a quantum
computer, is also linked to the nonlocal nature of entanglement, rather than to
the nonfactorizability of the state vector.


title: Experimental test of local realism using non-maximally entangled states

abstract:
  In this paper we describe a test of Bell inequalities using a non- maximally
entangled state, which represents an important step in the direction of
eliminating the detection loophole. The experiment is based on the creation of
a polarisation entangled state via the superposition, by use of an appropriate
optics, of the spontaneous fluorescence emitted by two non-linear crystals
driven by the same pumping laser.


title: Quantum Zeno-like effect and spectra of particles in cascade transition

abstract:
  Shr\"odinger equation for two-step spontaneous cascade transition in a
three-level quantum system is solved by means of Markovian approximation for
non-Markovian integro-differential evolution equations for amplitudes of
states. It is shown that both decay constant and radiation shift of initial
level are affected by instability of intermediate level of the cascade. These
phenomena are interpreted as the different manifestations of quantum Zeno-like
effect. The spectra of particles emitted during the cascade transition are
calculated in the general case and, in particular, for an unusual situation
when the initial state is lower than the intermediate one. It is shown that the
spectra of particles do not have a peak-like shape in the latter case.


title: How big is a quantum computer?

abstract:
  Accounting for resources is the central issue in computational efficiency. We
point out physical constraints implicit in information readout that have been
overlooked in classical computing. The basic particle-counting mode of read-out
sets a lower bound on the resources needed to implement a quantum computer. As
a consequence, computers based on classical waves are as efficient as those
based on single quantum particles.


title:
Extended Version of "The Philosophy of the Trajectory Representation of
  Quantum Mechanics"

abstract:
  The philosophy of the trajectory representation is contrasted with the
Copenhagen and Bohmian philosophies.


title: Quantum anharmonic oscillator and quasi-exactly solvable Bose systems

abstract:
  We extend the notion of quasi-exactly solvable (QES) models from potential
ones and differential equations to Bose systems. We obtain conditions under
which algebraization of the part of the spectrum occurs. In some particular
cases simple exact expressions for several energy levels of an anharmonic Bose
oscillator are obtained explicitly. The corresponding results do not exploit
perturbation theory and include strong coupling regime. A generic Hamiltonian
under discussion cannot, in contrast to QES potential models, be expressed as a
polynomial in generators of $sl_{2}$ algebra. The suggested approach is
extendable to many-particle Bose systems with interaction.

categories: quant-ph hep-ph hep-th math-ph math.MP nlin.SI physics.comp-ph


title: On the Implementation of Constraints through Projection Operators

abstract:
  Quantum constraints of the type Q \psi = 0 can be straightforwardly
implemented in cases where Q is a self-adjoint operator for which zero is an
eigenvalue. In that case, the physical Hilbert space is obtained by projecting
onto the kernel of Q, i.e. H_phys = ker(Q) = ker(Q*). It is, however,
nontrivial to identify and project onto H_phys when zero is not in the point
spectrum but instead is in the continuous spectrum of Q, because in this case
the kernel of Q is empty.
  Here, we observe that the topology of the underlying Hilbert space can be
harmlessly modified in the direction perpendicular to the constraint surface in
such a way that Q becomes non-self-adjoint. This procedure then allows us to
conveniently obtain H_phys as the proper Hilbert subspace H_phys = ker(Q*), on
which one can project as usual. In the simplest case, the necessary change of
topology amounts to passing from an L^2 Hilbert space to a Sobolev space.


title: Lossless quantum coding in many-letter spaces

abstract:
  Based on the concept of many-letter theory, an observable is defined
measuring the raw quantum information content of single messages. A general
characterization of quantum codes using the Kraus representation is given.
Compression codes are defined by their property of decreasing the expected raw
information content of a given message ensemble. Lossless quantum codes, in
contrast to lossy codes, provide the retrieval of the original data with
perfect fidelity. A general lossless coding scheme is given that translates
between two quantum alphabets. It is shown that this scheme is never
compressive. Furthermore, a lossless quantum coding scheme, analog to the
classical Huffman scheme but different from the Braunstein scheme, is
implemented, which provides optimal compression. Motivated by the concept of
lossless quantum compression, an observable is defined that measures the core
quantum information content of a particular message with respect to a given a
priori message ensemble. The average of this observable yields the von Neumann
entropy.


title: A feasible "Kochen-Specker" experiment with single particles

abstract:
  We present a simple experimental scheme which can be used to demonstrate an
all-or-nothing type contradiction between non-contextual hidden variables and
quantum mechanics. The scheme, which is inspired by recent ideas by Cabello and
Garcia-Alcaine, shows that even for a single particle, path and spin
information cannot be predetermined in a non-contextual way.


title: Equally-distant partially-entangled alphabet states for quantum channels

abstract:
  Each Bell state has the property that by performing just local operations on
one qubit, the complete Bell basis can be generated. That is, states generated
by local operations are totally distinguishable. This remarkable property is
due to maximal quantum entanglement between the two particles. We present a set
of local unitary transformations that generate out of partially entangled
two-qubit state a set of four maximally distinguishable states that are
mutually equally distant. We discuss quantum dense coding based on these
alphabet states.


title:
Quantum information distributors: Quantum network for symmetric and
  asymmetric cloning in arbitrary dimension and continuous limit

abstract:
  We show that for any Hilbert-space dimension, the optimal universal quantum
cloner can be constructed from essentially the same quantum circuit, i.e., we
find a universal design for universal cloners. In the case of infinite
dimensions (which includes continuous variable quantum systems) the universal
cloner reduces to an essentially classical device. More generally, we construct
a universal quantum circuit for distributing qudits in any dimension which acts
covariantly under generalized displacements and momentum kicks. The behavior of
this covariant distributor is controlled by its initial state. We show that
suitable choices for this initial state yield both universal cloners and
optimized cloners for limited alphabets of states whose states are related by
generalized phase-space displacements.


title:
On the Number of Elements Needed in a POVM Attaining the Accessible
  Information

abstract:
  We investigate a symmetric set of three quantum states in three dimensions
having interesting properties, which we call the lifted trine states. We show
that for the ensemble consisting of the three lifted trine states taken with
equal probabilities, the POVM measurement realizing the accessible information
must contain six projectors, giving a counterexample to a conjecture of
Levitin.


title: Molecular-Coherent-States and Molecular-Fundamental-States

abstract:
  New families of Molecular-Coherent-States are constructed by the Perelomov
group-method. Each family is generated by a Molecular-Fundamental-State that
depends on an arbitrary sequence of complex numbers cj. Two of these families
were already obtained by D.Janssen and by J. A. Morales, E. Deumens and Y.
Ohrn. The properties of these families are investigated and we show that most
of them are independent on the cj.


title: Quantum teleportation criteria for continuous variables

abstract:
  We discuss the criteria presently used for evaluating the efficiency of
quantum teleportation schemes for continuous variables. It is argued that the
fidelity criterion used so far has some severe drawbacks, and that a fidelity
value larger than 2/3 is actually required for successful quantum
teleportation. This value has never been reached experimentally so far.


title: Quantum cloning optimal for joint measurements

abstract:
  We show that universally covariant cloning is not optimal for achieving joint
measurements of noncommuting observables with minimum added noise. For such a
purpose a cloning transformation that is covariant with respect to a restricted
transformation group is needed.


title: Homodyne characterization of active optical media

abstract:
  An effective maximum likelihood method is suggested to characterize the
absorption/amplification properties of active optical media through homodyne
detection.


title:
Spontaneous breaking of axial symmetry for Schroedinger's equation in
  the presence of a magnetic field

abstract:
  For appropriate parameters, the ground state for the Schroedinger and Ampere
coupled equations in a cylindric domain does not have axial symmetry.

categories: quant-ph cond-mat.mes-hall nlin.PS physics.plasm-ph


title: Understanding Spin: the field theory of magnetic interactions

abstract:
  Spin is commonly thought to reflect the true quantum nature of microphysics.
We show that spin is related to intrinsic and field-like properties of single
particles. These properties change continuously in external magnetic fields.
Interactions of massive particles with homogeneous and inhomogeneous fields
result in two discrete particle states, symmetric to the original one. We
analyze the difficulties in quantum mechanics to give a precise spacetime
account of the experiments and find that they arise from unsuitable analogies
for spin. In particular from the analogy of an angular momentum. Several
experiments are suggested to check the model against the standard model in
quantum mechanics.


title: Emergence of Fermi-Dirac Thermalization in the Quantum Computer Core

abstract:
  We model an isolated quantum computer as a two-dimensional lattice of qubits
(spin halves) with fluctuations in individual qubit energies and residual
short-range inter-qubit couplings. In the limit when fluctuations and couplings
are small compared to the one-qubit energy spacing, the spectrum has a band
structure and we study the quantum computer core (central band) with the
highest density of states. Above a critical inter-qubit coupling strength,
quantum chaos sets in, leading to quantum ergodicity of eigenstates in an
isolated quantum computer. The onset of chaos results in the interaction
induced dynamical thermalization and the occupation numbers well described by
the Fermi-Dirac distribution. This thermalization destroys the noninteracting
qubit structure and sets serious requirements for the quantum computer
operability.


title:
Non-Interacting Fermions in a One-Dimensional Harmonic Atom Trap: Exact
  One-Particle Properties at Zero Temperature

abstract:
  One-particle properties of non-interacting Fermions in a one-dimensional
harmonic trap and at zero temperature are studied. Exact expressions and
asymptotic results for large Fermion number N are given for the particle
density distribution n_0(z,N). For large N and near the classical boundary at
the Fermi energy the density displays increasing fluctuations. A simple scaling
of these tails of the density distribution with respect to N is established.
The Fourier transform of the density distribution is calculated exactly. It
displays a small but characteristic hump near 2 k_F with k_F being a properly
defined Fermi wave number. This is due to Friedel oscillations which are
identified and discussed. These quantum effects are missing in the
semi-classical approximation. Momentum distributions are also evaluated and
discussed. As an example of a time-dependent one-particle problem we calculate
exactly the evolution of the particle density when the trap is suddenly
switched off and find a simple scaling behaviour in agreement with recent
general results.


title: A Family of Grover's Quantum Searching Algorithms

abstract:
  We introduce the concepts of Grover operators and Grover kernels to
systematically analyse Grover's searching algorithms. Then, we investigate a
one-parameter family of quantum searching algorithms of Grover's type and we
show that the standard Grover's algorithm is a distinguished member of this
family. We show that all the algorithms of this class solve the searching
problem with an efficiency of order $O(\sqrt{N})$, with a coefficient which is
class-dependent. The analysis of this dependence is a test of the stability and
robustness of the algorithms. We show the stability of this constructions under
perturbations of the initial conditions and extend them upon a very general
class of Grover operators.


abstract:
  The derivation of Bell inequalities for beables is well-known to require a
"no-conspiracy" assumption. This assumption is widely accepted, the alternative
being correlations between instrument settings and hidden beables. Two further
assumptions are identified here: (1) a "no-contextuality" assumption, similar
to the prohibition of contextuality that is required to derive the
Kochen-Specker theorem, which is closely related to the "no-conspiracy"
assumption; (2) a "no-correlation" assumption, which prohibits correlations
between hidden beables. The three assumptions together are less acceptable than
the "no-conspiracy" assumption alone.


title:
Classical simulation of quantum entanglement without local hidden
  variables

abstract:
  Recent work has extended Bell's theorem by quantifying the amount of
communication required to simulate entangled quantum systems with classical
information. The general scenario is that a bipartite measurement is given from
a set of possibilities and the goal is to find a classical scheme that
reproduces exactly the correlations that arise when an actual quantum system is
measured. Previous results have shown that, using local hidden variables, a
finite amount of communication suffices to simulate the correlations for a Bell
state. We extend this in a number of ways. First, we show that, when the
communication is merely required to be finite {\em on average}, Bell states can
be simulated {\em without} any local hidden variables. More generally, we show
that arbitrary positive operator valued measurements on systems of $n$ Bell
states can be simulated with $O(n 2^n)$ bits of communication on average
(again, without local hidden variables). On the other hand, when the
communication is required to be {\em absolutely bounded}, we show that a finite
number of bits of local hidden variables is insufficent to simulate a Bell
state. This latter result is based on an analysis of the non-deterministic
communication complexity of the NOT-EQUAL function, which is constant in the
quantum model and logarithmic in the classical model.


title: Cell Microtubules as Cavities: Quantum Coherence and Energy Transfer?

abstract:
  A model is presented for dissipationless energy transfer in cell microtubules
due to quantum coherent states. The model is based on conjectured (hydrated)
ferroelectric properties of microtubular arrangements. Ferroelectricity is
essential in providing the necessary isolation against thermal losses in thin
interior regions, full of ordered water, near the tubulin dimer walls of the
microtubule. These play the role of cavity regions, which are similar to
electromagnetic cavities of quantum optics. As a result, the formation of
(macroscopic) quantum coherent states of electric dipoles on the tubulin dimers
may occur. Some experiments, inspired by quantum optics, are suggested for the
falsification of this scenario.


title:
Preserving entanglement under decoherence and sandwiching all separable
  states

abstract:
  Every entangled state can be perturbed, for instance by decoherence, and stay
entangled. For a large class of pure entangled states, we show how large the
perturbation can be. Our class includes all pure bipartite and all maximally
entangled states. For an entangled state, E, the constucted neighborhood of
entangled states is the region outside two parallel hyperplanes, which sandwich
the set of all separable states. The states for which these neighborhoods are
largest are the maximally entangled ones. As the number of particles, or the
dimensions of the Hilbert spaces for two of the particles increases, the
distance between two of the hyperplanes which sandwich the separable states
goes to zero. It is easy to decide if a state Q is in the neighborhood of
entangled states we construct for an entangled state E. One merely has to check
if the trace of EQ is greater than a constant which depends upon E and which we
determine.


title: Quantum lower bound for sorting

abstract:
  We prove that \Omega(n log(n)) comparisons are necessary for any quantum
algorithm that sorts n numbers with high success probability and uses only
comparisons. If no error is allowed, at least 0.110nlog_2(n) - 0.067n + O(1)
comparisons must be made. The previous known lower bound is \Omega(n).


title: Spin Distributions for Bipartite Quantum Systems

abstract:
  We carryout a comparative study of spin distributions defined over the sphere
for bipartite quantum spin assemblies. We analyse Einstein-Podolsky-Rosen-Bohm
(EPRB) spin correlations in a spin-s singlet state using these distributions.
We observe that in the classical limit EPRB spin distributions turn out to be
delta functions, thus reflecting the perfect anticorrelation property of two
spin vectors associated with a spin-s singlet state.


title: Iterative algorithm for reconstruction of entangled states

abstract:
  An iterative algorithm for the reconstruction of an unknown quantum state
from the results of incompatible measurements is proposed. It consists of
Expectation-Maximization step followed by a unitary transformation of the
eigenbasis of the density matrix. The procedure has been applied to the
reconstruction of the entangled pair of photons.


title: A Complexity Measure for Continuous Time Quantum Algorithms

abstract:
  We consider unitary dynamical evolutions on n qubits caused by time dependent
pair-interaction Hamiltonians and show that the running time of a parallelized
two-qubit gate network simulating the evolution is given by the time integral
over the chromatic index of the interaction graph. This defines a complexity
measure of continuous and discrete quantum algorithms which are in exact
one-to-one correspondence. Furthermore we prove a lower bound on the growth of
large-scale entanglement depending on the chromatic index.


title: Optical qubit using linear elements

abstract:
  A conditional scheme to prepare optical superposition of the vacuum and
one-photon states using linear elements (beam splitters and phase-shifters) and
avalanche photodetectors is suggested.


title: Engineering cavity-field states by projection synthesis

abstract:
  We propose a reliable scheme for engineering a general cavity-field state.
This is different from recently presented strategies,where the cavity is
supposed to be initially empty and the field is built up photon by photon
through resonant atom-field interactions. Here, a coherent state is previously
injected into the cavity. So, the Wigner distribution function of the desired
state is constructed from that of the initially coherent state. Such an
engineering process is achieved through an adaptation of the recently proposed
technique of projection synthesis to cavity QED phenomena.


title: Comprehensive experimental test of quantum erasure

abstract:
  In an interferometer, path information and interference visibility are
incompatible quantities. Complete determination of the path will exclude any
possibility of interference, rendering the visibility zero. However, if the
composite object and probe state is pure, it is, under certain conditions,
possible to trade the path information for improved (conditioned) visibility.
Such a procedure is called quantum erasure. We have performed such experiments
with polarization entangled photon pairs. Using a partial polarizer we could
vary the degree of entanglement between object and probe. We could also vary
the interferometer splitting ratio and thereby vary the a priori path
predictability. We have tested quantum erasure under a number of different
experimental conditions and found good agreement between experiments and
theory.


title:
Neel state of antiferromagnet as a result of a local measurement in the
  distributed quantum system

abstract:
  Single-site measurement in a distributed macroscopic antiferromagnet is
considered; we show that it can create antiferromagnetic sublattices at
macroscopic scale. We demonstrate that the result of measurement depends on the
symmetry of the ground state: for the easy-axis case the Neel state is formed,
while for the easy-plane case unusual ``fan'' sublattices appear with unbroken
rotational symmetry, and a decoherence wave is generated. For the latter case,
a macroscopically large number of measurements is needed to pin down the
orientation of the sublattices, in spite of the high degeneracy of the ground
state. We note that the type of the final state and the appearance of the
decoherence wave are governed by the degree of entanglement of spins in the
system.


title: Charge based quantum computer without charge transfer

abstract:
  A novel implementation of a charge based quantum computer is proposed. There
is no charge transfer during calculation, therefore, uncontrollable
entanglement between qubits due to long-range Coulomb forces is suppressed.
High-speed computation with 1ps per an operation looks as feasible.


title: Quantaloids Describing Causation and Propagation of Physical Properties

abstract:
  A general principle of `causal duality' for physical systems, lying at the
base of representation theorems for both compound and evolving systems, is
proved; formally it is encoded in a quantaloidal setting. Other particular
examples of quantaloids and quantaloidal morphisms appear naturally within this
setting; as in the case of causal duality, they originate from primitive
physical reasonings on the lattices of properties of physical systems.
Furthermore, an essentially dynamical operational foundation for studying
physical systems is outlined; complementary as it is to the existing static
operational foundation, it leads to the natural axiomatization of `causal
duality' in operational quantum logic.

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


title: Information Tradeoff Relations for Finite-Strength Quantum Measurements

abstract:
  In this paper we give a new way to quantify the folklore notion that quantum
measurements bring a disturbance to the system being measured. We consider two
observers who initially assign identical mixed-state density operators to a
two-state quantum system. The question we address is to what extent one
observer can, by measurement, increase the purity of his density operator
without affecting the purity of the other observer's. If there were no
restrictions on the first observer's measurements, then he could carry this out
trivially by measuring the initial density operator's eigenbasis. If, however,
the allowed measurements are those of finite strength---i.e., those
measurements strictly within the interior of the convex set of all
measurements---then the issue becomes significantly more complex. We find that
for a large class of such measurements the first observer's purity increases
the most precisely when there is some loss of purity for the second observer.
More generally the tradeoff between the two purities, when it exists, forms a
monotonic relation. This tradeoff has potential application to quantum state
control and feedback.


title: Poincar\'e covariance of relativistic quantum position

abstract:
  A great number of problems of relativistic position in quantum mechanics are
due to the use of coordinates which are not inherent objects of spacetime,
cause unnecessary complications and can lead to misconceptions. We apply a
coordinate-free approach to rule out such problems. Thus it will be clear, for
example, that the Lorentz covariance of position, required usually on the
analogy of Lorentz covariance of spacetime coordinates, is not well posed and
we show that in a right setting the Newton--Wigner position is Poincar\'e
covariant, in contradiction with the usual assertions.


title:
Reply to "Comment on: A Quantum Approach to Static Games of Complete
  Information"

abstract: This is a reply to the paper by S.C.Benjamin, quant-ph/0008127.


title: Maximum-likelihood reconstruction of CP maps

abstract:
  We present a method for the determination of the completely positive (CP) map
describing a physical device based on random preparation of the input states,
random measurements at the output, and maximum-likelihood principle. In the
numerical implementation the constraint of completely positivity can be imposed
by exploiting the isomorphism between linear transformations from Hilbert
spaces $\cal H$ to $\cal K$ and linear operators in ${\cal K}\otimes {\cal H}$.
The effectiveness of the method is shown on the basis of some examples of
reconstruction of CP maps related to quantum communication channels for qubits.


title: Experiments towards quantum information with trapped Calcium ions

abstract:
  Ground state cooling and coherent manipulation of ions in an rf-(Paul) trap
is the prerequisite for quantum information experiments with trapped ions. With
resolved sideband cooling on the optical S1/2 - D5/2 quadrupole transition we
have cooled one and two 40Ca+ ions to the ground state of vibration with up to
99.9% probability. With a novel cooling scheme utilizing electromagnetically
induced transparency on the S1/2 - P1/2 manifold we have achieved simultaneous
ground state cooling of two motional sidebands 1.7 MHz apart. Starting from the
motional ground state we have demonstrated coherent quantum state manipulation
on the S1/2 - D5/2 quadrupole transition at 729 nm. Up to 30 Rabi oscillations
within 1.4 ms have been observed in the motional ground state and in the n=1
Fock state. In the linear quadrupole rf-trap with 700 kHz trap frequency along
the symmetry axis (2 MHz in radial direction) the minimum ion spacing is more
than 5 micron for up to 4 ions. We are able to cool two ions to the ground
state in the trap and individually address the ions with laser pulses through a
special optical addressing channel.


title: Coherent Phenomena in Photonic Crystals

abstract:
  We study the spontaneous emission, the absorption and dispersion properties
of a ${\bf \Lambda}$-type atom where one transition interacts near resonantly
with a double-band photonic crystal. Assuming an isotropic dispersion relation
near the band edges, we show that two distinct coherent phenomena can occur.
First, the spontaneous emission spectrum of the adjacent free space transition
obtains `dark lines' (zeroes in the spectrum). Second, the atom can become
transparent to a probe laser field coupling to the adjacent free space
transition.


title: Three-qubit pure-state canonical forms

abstract:
  In this paper we analyze the canonical forms into which any pure three-qubit
state can be cast. The minimal forms, i.e. the ones with the minimal number of
product states built from local bases, are also presented and lead to a
complete classification of pure three-qubit states. This classification is
related to the values of the polynomial invariants under local unitary
transformations by a one-to-one correspondence.


title:
Fundamental solution method applied to time evolution of two energy
  level systems: exact and adiabatic limit results

abstract:
  A method of fundamental solutions has been used to investigate transitions in
two energy level systems with no level crossing in a real time. Compact
formulas for transition probabilities have been found in their exact form as
well as in their adiabatic limit. No interference effects resulting from many
level complex crossings as announced by Joye, Mileti and Pfister (Phys. Rev.
{\bf A44} 4280 (1991)) have been detected in either case. It is argued that
these results of this work are incorrect. However, some effects of Berry's
phases are confirmed.


title: Schmidt number witnesses and bound entanglement

abstract:
  The Schmidt number of a mixed state characterizes the minimum Schmidt rank of
the pure states needed to construct it. We investigate the Schmidt number of an
arbitrary mixed state by constructing a Schmidt number witness that detects it.
We present a canonical form of such witnesses and provide constructive methods
for their optimization. Finally, we present strong evidence that all bound
entangled states with positive partial transpose in two qutrit systems have
Schmidt number 2.


title: Implementation of a quantum phase gate by the optical Kerr effect

abstract:
  We show that the optical Kerr effect can be used to construct a quantum phase
gate. It is well known from quantum nondemolition techniques that, as two
photon field modes pass through a Kerr medium, the phase of each mode will be
shifted, and the size of the phase shift will depend on the number of photons
in both modes. We discuss the Hamiltonian responsible for this effect and show
how this can produce an effective photon-photon interaction which corresponds
to the quantum phase gate operating on two qubits each of which is represented
by the elliptical polarization of one photon field. We discuss decoherence and
losses and suggest some methods for dealing with them.


title:
Model for the arrival-time distribution in fluorescence time-of-flight
  experiments

abstract:
  An operational arrival-time distribution is defined as the distribution of
detection times of the first photons emitted by two level atoms in resonance
with a perpendicular laser beam in a time of flight experiment. For ultracold
Cesium atoms the simulations are in excellent agreement with the theoretical
ideal time-of-arrival distribution of Kijowski.


title: On The Biphoton Wavelength

abstract:
  We report on an experiment showing that the wavelength of a biphoton is
clearly dependent on the measurement scheme and on the way it is defined. It is
shown that it can take any value, depending on the control of the
interferometer phase differences. It is possible to identify the interference
of the single and two-photon wavepackets as particular cases of the most
general interference process. The variable wavelength has no implication on the
energy of the individual photons neither on the total energy of the biphoton.


title:
Anonymous-key quantum cryptography and unconditionally secure quantum
  bit commitment

abstract:
  A new cryptographic tool, anonymous quantum key technique, is introduced that
leads to unconditionally secure key distribution and encryption schemes that
can be readily implemented experimentally in a realistic environment. If
quantum memory is available, the technique would have many features of
public-key cryptography; an identification protocol that does not require a
shared secret key is provided as an illustration. The possibility is also
indicated for obtaining unconditionally secure quantum bit commitment protocols
with this technique.


title:
New method for obtaining complex roots in the semiclassical
  coherent-state propagator formula

abstract:
  A semiclassical formula for the coherent-state propagator requires the
determination of specific classical paths inhabiting a complex phase-space
through a Hamiltonian flux. Such trajectories are constrained to special
boundary conditions which render their determination difficult by common
methods. In this paper we present a new method based on Runge-Kutta integrator
for a quick, easy and accurate determination of these trajectories. Using
nonlinear one dimensional systems we show that the semiclassical formula is
highly accurate as compared to its exact counterpart . Further we clarify how
the phase of the semiclassical approximation is correctly retrieved under time
evolution.


title: Quantum Magic Bullets via Entanglement

abstract:
  Two particles that are entangled with respect to continuous variables such as
position and momentum exhibit a variety of nonclassical features. First,
measurement of one particle projects the other particle into the state that is
the complex conjugate of the state of the first particle, i.e., measurement of
one particle projects the other particle into the time-reversed state. Second,
continuous-variable entanglement can be used to implement a quantum "magic
bullet": when one particle manages to pass through a scattering potential, then
no matter how low the probability of this event, the second particle will also
pass through a related scattering potential with probability one. This
phenomenon is investigated in terms of the original EPR state, and experimental
realizations are suggested in terms of entangled photon states.


title: Note on Extended Coherent Operators and Some Basic Properties

abstract:
  This is a continuation of the paper (quant-ph/0009012).
  In this letter we extend coherent operators and study some basic properties
(the disentangling formula, resolution of unity, commutation relation, etc). We
also propose a perspective of our work.


title:
Optimal states and almost optimal adaptive measurements for quantum
  interferometry

abstract:
  We derive the optimal N-photon two-mode input state for obtaining an estimate
\phi of the phase difference between two arms of an interferometer. For an
optimal measurement [B. C. Sanders and G. J. Milburn, Phys. Rev. Lett. 75, 2944
(1995)], it yields a variance (\Delta \phi)^2 \simeq \pi^2/N^2, compared to
O(N^{-1}) or O(N^{-1/2}) for states considered by previous authors. Such a
measurement cannot be realized by counting photons in the interferometer
outputs. However, we introduce an adaptive measurement scheme that can be thus
realized, and show that it yields a variance in \phi very close to that from an
optimal measurement.


title: Bound entangled Gaussian states

abstract:
  We discuss the entanglement properties of bipartite states with Gaussian
Wigner functions. Separability and the positivity of the partial transpose are
characterized in terms of the covariance matrix of the state, and it is shown
that for systems composed of a single oscillator for Alice and an arbitrary
number for Bob, positivity of the partial transpose implies separability.
However, this implications fails with two oscillators on each side, as we show
by a five parameter family of explicit counterexamples.


title:
Quantum Clock Synchronisation based on entangled photon pairs
  transmission

abstract:
  We discuss the possibility of synchronising two atomic clocks exchanging
entangled photon pairs through a quantum channel. A proposal for implementing
practically such a scheme is discussed.


title: Quantum Erasure by Transverse Indistinguishability

abstract:
  We show that the first experiment with double-slits and twin photons detected
in coincidence can be understood as a quantum eraser. The ``which path''
information is erased by transverse indistinguishability obtained by means of
mode filtering in the twin conjugated beam. A delayed choice quantum eraser
based on the same scheme is proposed.


title:
Matter-wave entanglement and teleportation by molecular dissociation and
  collisions

abstract:
  We propose dissociation of cold diatomic molecules as a source of atom pairs
with highly correlated (entangled) positions and momenta, approximating the
original quantum state introduced by Einstein, Podolsky and Rosen (EPR) [Phys.
Rev. 47, 777 (1935)]. Wavepacket teleportation is shown to be achievable by its
collision with one of the EPR correlated atoms and manipulation of the other
atom in the pair.


title:
Quantum computation in a one-dimensional crystal lattice with NMR force
  microscopy

abstract:
  A proposal for a scalable, solid-state implementation of a quantum computer
is presented. Qubits are fluorine nuclear spins in a solid crystal of
fluorapatite [Ca_5 F(PO_4)_3] with resonant frequencies separated by a large
field gradient. Quantum logic is accomplished using nuclear-nuclear dipolar
couplings with decoupling and selective recoupling RF pulse sequences. Magnetic
resonance force microscopy is used for readout. As many as 300 qubits can be
implemented in the laboratory extremes of T=10 mK and B_0=20 T with the
existing sensitivity of force microscopy.


title: Measurement of quantum devices

abstract:
  Maximum-likelihood estimation is applied to identification of an unknown
quantum mechanical process represented by a ``black box''. In contrast to
linear reconstruction schemes the proposed approach always yields physically
sensible results. Its feasibility is demonstrated using the Monte Carlo
simulations for the two-level system (single qubit).


title: The Representation of Numbers by States in Quantum Mechanics

abstract:
  The representation of numbers by tensor product states of composite quantum
systems is examined. Consideration is limited to k-ary representations of
length L and arithmetic modulo k^{L}. An abstract representation on an L fold
tensor product Hilbert space H^{arith} of number states and operators for the
basic arithmetic operations is described. Unitary maps onto a physical
parameter based tensor product space H^{phy} are defined and the relations
between these two spaces and the dependence of algorithm dynamics on the
unitary maps is discussed. The important condition of efficient implementation
by physically realizable Hamiltonians of the basic arithmetic operations is
also discussed.


title: Quantum coherence and control in one- and two-photon optical systems

abstract:
  We investigate coherence in one- and two-photon optical systems, both
theoretically and experimentally. In the first case, we develop the density
operator representing a single photon state subjected to a non-dissipative
coupling between observed (polarization) and unobserved (frequency) degrees of
freedom. We show that an implementation of ``bang-bang'' quantum control
protects photon polarization information from certain types of decoherence. In
the second case, we investigate the existence of a "decoherence-free" subspace
of the Hilbert space of two-photon polarization states under the action of a
similar coupling. The density operator representation is developed analytically
and solutions are obtained numerically.
  NOTE: This manuscript is taken from the author's undergraduate thesis (A.B.
Dartmouth College, June 2000, advised by Dr. Walter E. Lawrence), under the
supervision of Dr. Paul G. Kwiat.


title: Quantum Computation Relative to Oracles

abstract:
  This paper has been withdrawn by Christino Tamon and Tomoyuki Yamakami
because of errors of the main theorems. An erratum appeared in the Proceedings
of the UMC 2000 Conference published by Springer.


title: Phase-space picture of resonance creation and avoided crossings

abstract:
  Complex coordinate scaling (CCS) is used to calculate resonance eigenvalues
and eigenstates for a system consisting of an inverted Gaussian potential and a
monochromatic driving field. Floquet eigenvalues and Husimi distributions of
resonance eigenfunctions are calculated using two different versions of CCS.
The number of resonance states in this system increases as the strength of the
driving field is increased, indicating that this system might have increased
stability against ionization when the field strength is very high. We find that
the newly created resonance states are scarred on unstable periodic orbits of
the classical motion. The behavior of these periodic orbits as the field
strength is increased may explain why there are more resonance states at high
field strengths than at low field strengths. Close examination of an avoided
crossing between resonance states shows that this type of avoided crossing does
not delocalize the resonance states, although it may lead to interesting
effects at certain field strengths.


title:
Characterising a universal cloning machine by maximum-likelihood
  estimation

abstract:
  We apply a general method for the estimation of completely positive maps to
the 1-to-2 universal covariant cloning machine. The method is based on the
maximum-likelihood principle, and makes use of random input states, along with
random projective measurements on the output clones. The downhill simplex
algorithm is applied for the maximisation of the likelihood functional.


title: Exponential Gain in Quantum Computing of Quantum Chaos and Localization

abstract:
  We present a quantum algorithm which simulates the quantum kicked rotator
model exponentially faster than classical algorithms. This shows that important
physical problems of quantum chaos, localization and Anderson transition can be
modelled efficiently on a quantum computer. We also show that a similar
algorithm simulates efficiently classical chaos in certain area-preserving
maps.


title:
Control of squeezed light pulse spectrum in the Kerr medium with an
  inertial nonlinearity

abstract:
  The consistent quantum theory of self-phase modulation (SPM) and cross-phase
modulation (XPM) for ultrashort light pulses (USP) in medium with electronic
Kerr-nonlinearity are developed. The approach makes use of momentum operator of
electrical field which takes account of the inertial behaviour of the
nonlinearity. The spectrum of quantum fluctuations of squeezed-quadrature
component as a function of response time of nonlinearity and values of
nonlinear phase shifts due to the SPM and XPM effects, is investigated.


title: Phase Mapping of Remote Clocks Using Quantum Entanglement

abstract:
  Recently, we have shown how the phase of an electromagnetic field can be
determined by measuring the population of either of the two states of a
two-level atomic system excited by this field, via the so-called Bloch-Siegert
oscillation resulting from the interference between the co- and
counter-rotating excitations. Here, we show how a degenerate entanglement,
created without transmitting any timing signal, can be used to teleport this
phase information. This phase-teleportation process may be applied to achieve
absolute phase-mapping of remote clocks.


title:
".. I didn't reflect much on what I was doing.." How Planck discovered
  his radiation formula

abstract:
  On December 14. 1900, Max Planck communicated his derivation of his radiation
formula, which he later called ``an act of desperation''. This date is widely
recognized as birthday of quantum theory. For Planck it meant the end of his
carefully planned and ambitious research project, in which he wanted to
establish the second law of thermodynamics as strictly deterministic law for
systems of matter and electromagnetic radiation in interaction. He knew he
could not succeed within classical mechanics, but had the somewhat strange hope
that the inclusion of Maxwell's electrodynamics would change the situation.
Later he always disagreed with Einstein's light-quantum hypothesis, because it
implied a renunciation from Maxwell's theory, which in Germany gained full
recognition and acceptance as late as the 1890's, mainly through the
theoretical and experimental work of Heinrich Hertz.