title: Confined Quantum Time of Arrival for Vanishing Potential

abstract:
  We give full account of our recent report in [E.A. Galapon, R. Caballar, R.
Bahague {\it Phys. Rev. Let.} {\bf 93} 180406 (2004)] where it is shown that
formulating the free quantum time of arrival problem in a segment of the real
line suggests rephrasing the quantum time of arrival problem to finding a
complete set of states that evolve to unitarily arrive at a given point at a
definite time. For a spatially confined particle, here it is shown explicitly
that the problem admits a solution in the form of an eigenvalue problem of a
class of compact and self-adjoint time of arrival operators derived by a
quantization of the classical time of arrival. The eigenfunctions of these
operators are numerically demonstrated to unitarilly arrive at the origin at
their respective eigenvalues.


title:
Quantization of Light Energy Directly from Classical Electromagnetic
  Theory in Vacuum

abstract:
  It is currently believed that light quantum or the quantization of light
energy is beyond classical physics and the picture of wave-particle duality,
which was criticized by Einstein but attracted a number of experimental
researches, is necessary for the description of light. We show in this paper,
however, that the quantization of light energy in vacuum, which is the same as
that in quantum electrodynamics, can be derived directly from the classical
electromagnetic theory through the consideration of statistics based on
classical physics. Therefore, the quantization of energy is an intrinsic
property of light as a classical electromagnetic wave and has no need of being
related to particles.


title:
Can the Quantum Measurement Problem be resolved within the framework of
  Schroedinger Dynamics?

abstract:
  We formulate the dynamics of the generic quantum system S_{c} comprising a
microsystem S and a macroscopic measuring instrument I, whose pointer positions
are represented by orthogonal subspaces of the Hilbert space of its pure
states. These subspaces are simultaneous eigenspaces of a set of coarse grained
intercommuting macroscopic observables and, most crucially, their
dimensionalities are astronomically large, increasing exponentially with the
number, N, of particles comprising I. We formulate conditions under which the
conservative dynamics of S_{c} yields both a reduction of the wave packet
describing the state of S and a one-to-one correspondence, following a
measurement, between the pointer position of I and the resultant eigenstate of
S; and we show that these conditions are fulfilled, up to utterly negligible
corrections that decrease exponentially with N, by the finite version of the
Coleman-Hepp model.


title: Stochastic resonance effects in quantum channels

abstract:
  We provide some examples of quantum channels where the addition of noise is
able to enhance the information transmission rate. This may happen for both
quantum and classical uses and realizes stochastic resonance effects.


title:
Extremal quantum correlations for N parties with two dichotomic
  observables per site

abstract:
  Consider a scenario where $N$ separated quantum systems are measured, each
with one among two possible dichotomic observables. Assume that the $N$ events
corresponding to the choice and performance of the measurement in each site are
space-like separated. In the present paper, the correlations among the
measurement outcomes that arise in this scenario are analyzed. It is shown that
all extreme points of this convex set are attainable by measuring $N$-qubit
pure-states with projective observables. This result allows the possibility of
using known algorithms in order decide whether some correlations are achievable
within quantum mechanics or not. It is also proven that if an $N$-partite state
$\rho$ violates a given Bell inequality, then, $\rho$ can be transformed by
stochastic local operations into an $N$-qubit state that violates the same Bell
inequality by an equal or larger amount.


title: Entanglement driven self-organization via a quantum seesaw mechanism

abstract:
  Atom-field entanglement is shown to play a crucial role for the onset of
spatial self-organization of ultracold atoms in an optical lattice within a
high-Q cavity. Like particles on a seesaw, the atoms feel a different potential
depending on their spatial distribution. The system possesses two stable
configurations, where all atoms occupy either only even or only odd lattice
sites. While for a classical cavity field description a distribution balanced
between even and odd sites is a stationary equilibrium state at zero
temperature, the possibility of atom-field entanglement in a quantum field
description yields an instant simultaneous decay of the homogeneous atomic
cloud into an entangled superposition of the two stable atomic patterns
correlated with different cavity fields. This effect could be generic for a
wide class of quantum phase transitions, whenever the quantum state can act
back on the control parameter.


title: Relationship of Quantum Entanglement to Density Functional Theory

abstract:
  The maximum von Neumann entropy principle subject to given constraints of
mean values of some physical observables determines the density matrix.
Similarly the stationary action principle in the case of time-dependent
(dissipative) situations under similar constraints yields the density matrix.
The free energy and measures of entanglement are expressed in terms of such a
density matrix and thus define respective functionals of the mean values. In
the light of several model calculations, it is found that the density matrix
contains information about both quantum entanglement and phase transitions even
though there may not be any direct relationship implied by one on the other.


title: Decoherence modes of entangled qubits within neutron interferometry

abstract:
  We study two different decoherence modes for entangled qubits by considering
a Liouville - von Neumann master equation. Mode A is determined by projection
operators onto the eigenstates of the Hamiltonian and mode B by projectors onto
rotated states. We present solutions for general and for Bell diagonal states
and calculate for the later the mixedness and the amount of entanglement given
by the concurrence.
  We propose a realization of the decoherence modes within neutron
interferometry by applying fluctuating magnetic fields. An experimental test of
the Kraus operator decomposition describing the evolution of the system for
each mode is presented.


title: Linear Optics Quantum Computation: an Overview

abstract:
  We give an overview of linear optics quantum computing, focusing on the
results from the original KLM paper. First we give a brief summary of the
advances made with optics for quantum computation prior to KLM. We next discuss
the KLM linear optics scheme, giving detailed examples. Finally we go through
quantum error correction for the LOQC theory, showing how to obtain the
threshold when dealing with Z-measurement errors.


title: Deriving Landauer's erasure principle from statistical mechanics

abstract:
  We present a concise derivation of Landauer's erasure principle from the
postulates of statistical mechanics, along with a small number of additional
but uncontroversial axioms.


title:
A class of entanglement monotones for general pure multipartite states
  based on complex projective variety

abstract:
  We construct a measure of entanglement for general pure multipartite states
based on Segre variety. We also construct a class of entanglement monotones
based on the Pl\"{u}cker coordinate equations of the Grassmann variety.
Moreover, we discuss and compare these measures of entanglement.


title:
Observation of the Preservation of the Two-Photon Coherence in
  Plasmon-assisted Transmission

abstract:
  We experimentally study two-photon coherence in plasmon-assisted transmission
with a two-photon Mach-Zehnder (MZ) interferometer. Two collinear photons of
identical or orthogonal polarization are simultaneously incident on one
optically thick metal film, perforated with a periodic array of subwavelength
holes. The de Broglie wavelength of plasmon-assisted transmitted photons is
measured, which shows that two photons are re-eradiated by the plasmons and the
quantum coherence of biphoton is preserved in the conversion process of
transforming biphoton to plasmons and then back to biphoton.


title: Image method solutions for free-particle wave packets

abstract:
  Using analogs of familiar image methods in electrostatics and optics, we show
how to construct closed form wave packet solutions of the two-dimensional
free-particle Schrodinger equation in geometries restricted by two infinite
wall barriers separated by an angle Theta = pi/N. As an example, we evaluate
probability densities and expectation values for a zero-momentum wave packet
solution initially localized in a pi/3 = 60 degree wedge. We review the
time-development of zero-momentum wave packets placed near a single infinite
wall barrier in an Appendix.


title:
A Lower Bound for the Sturm-Liouville Eigenvalue Problem on a Quantum
  Computer

abstract:
  We study the complexity of approximating the smallest eigenvalue of a
univariate Sturm-Liouville problem on a quantum computer. This general problem
includes the special case of solving a one-dimensional Schroedinger equation
with a given potential for the ground state energy.
  The Sturm-Liouville problem depends on a function q, which, in the case of
the Schroedinger equation, can be identified with the potential function V.
Recently Papageorgiou and Wozniakowski proved that quantum computers achieve an
exponential reduction in the number of queries over the number needed in the
classical worst-case and randomized settings for smooth functions q. Their
method uses the (discretized) unitary propagator and arbitrary powers of it as
a query ("power queries"). They showed that the Sturm-Liouville equation can be
solved with O(log(1/e)) power queries, while the number of queries in the
worst-case and randomized settings on a classical computer is polynomial in
1/e. This proves that a quantum computer with power queries achieves an
exponential reduction in the number of queries compared to a classical
computer.
  In this paper we show that the number of queries in Papageorgiou's and
Wozniakowski's algorithm is asymptotically optimal. In particular we prove a
matching lower bound of log(1/e) power queries, therefore showing that log(1/e)
power queries are sufficient and necessary. Our proof is based on a frequency
analysis technique, which examines the probability distribution of the final
state of a quantum algorithm and the dependence of its Fourier transform on the
input.


title: Efficient Construction of Photonic Quantum Computational Clusters

abstract:
  We demonstrate a method of creating photonic two-dimensional cluster states
that is considerably more efficient than previously proposed approaches. Our
method uses only local unitaries and type-I fusion operations. The increased
efficiency of our method compared to previously proposed constructions is
obtained by identifying and exploiting local equivalence properties inherent in
cluster states.


title: Self-Testing of Quantum Circuits

abstract:
  We prove that a quantum circuit together with measurement apparatuses and EPR
sources can be fully verified without any reference to some other trusted set
of quantum devices. Our main assumption is that the physical system we are
working with consists of several identifiable sub-systems, on which we can
apply some given gates locally.
  To achieve our goal we define the notions of simulation and equivalence. The
concept of simulation refers to producing the correct probabilities when
measuring physical systems. To enable the efficient testing of the composition
of quantum operations, we introduce the notion of equivalence. Unlike
simulation, which refers to measured quantities (i.e., probabilities of
outcomes), equivalence relates mathematical objects like states, subspaces or
gates.
  Using these two concepts, we prove that if a system satisfies some simulation
conditions, then it is equivalent to the one it is purposed to implement. In
addition, with our formalism, we can show that these statements are robust, and
the degree of robustness can be made explicit (unlike the robustness results of
[DMMS00]). In particular, we also prove the robustness of the EPR Test [MY98].
Finally, we design a test for any quantum circuit whose complexity is linear in
the number of gates and qubits, and polynomial in the required precision.


title:
Evolution of the superposition of displaced number states with the
  two-atom multiphoton Jaynes-Cummings model: interference and entanglement

abstract:
  In this paper we study the evolution of the two two-level atoms interacting
with a single-mode quantized radiation field, namely, two-atom multiphoton
Jaynes-Cummings model when the radiation field and atoms are initially prepared
in the superpostion of displaced number states and excited atomic states,
respectively. For this system we investigate the atomic inversion, Wigner
function, phase distribution and entanglement.


title: Deriving Spin within a discrete-time theory

abstract:
  We prove that the classical theory with a discrete time (chronon) is a
particular case of a more general theory in which spinning particles are
associated with generalized Lagrangians containing time-derivatives of any
order (a theory that has been called "Non-Newtonian Mechanics"). As a
consequence, we get, for instance, a classical kinematical derivation of
Hamiltonian and spin vector for the mentioned chronon theory (e.g., in
Caldirola et al.'s formulation).


title: A Categorical Quantum Logic

abstract:
  We define a strongly normalising proof-net calculus corresponding to the
logic of strongly compact closed categories with biproducts. The calculus is a
full and faithful representation of the free strongly compact closed category
with biproducts on a given category with an involution. This syntax can be used
to represent and reason about quantum processes.


title:
Time evolution of the relativistic excited state in the unified
  formulation of quantum and kinetics dynamics

abstract:
  Description of time evolution of the relativistic unstable electromagnetic
system consisting of Fermi-Dirac particle interacting with electromagnetic
field, in the framework of the Liouville space extension of quantum mechanics
is done. The work was carried out on the basis of Prigogine's unified
formulation of quantum and kinetic dynamics. The eigenvalues problem for the
relativistic Hamiltonian of the electromagnetic system was solved. The obtained
results can be used as the ground for the further studies of the observed
physical processes such as bremsstrahlung, relaxation of excited states of
atoms and atomic nuclei, particles decay.


title: Spintronic devices as quantum networks

abstract:
  We explore spintronics from a quantum information (QI) perspective. We show
that QI specific methods can be an effective tool in designing new devices.
Using the formalism of quantum gates acting on spin and mode degrees of
freedom, we provide a solution to a reverse engineering problem, namely how to
design a device performing a given transformation between input and output.
Among these, we describe an orientable Stern-Gerlach device and a new scheme to
entangle two spins by transferring the entanglement from orbital to spin
degrees of freedom. Finally, we propose a simple scheme to produce
hyper-entangle electrons, i.e., particles entangled in both spin and mode
degrees of freedom.


title:
Quantum computation using weak nonlinearities: robustness against
  decoherence

abstract:
  We investigate decoherence effects in the recently suggested quantum
computation scheme using weak nonlinearities, strong probe coherent fields,
detection and feedforward methods. It is shown that in the
weak-nonlinearity-based quantum gates, decoherence in nonlinear media it can be
made arbitrarily small simply by using arbitrarily strong probe fields, if
photon number resolving detection is used. On the contrary, we find that
homodyne detection with feedforward is not appropriate for this scheme because
in this case decoherence rapidly increases as the probe field gets larger.


title:
Reference potential approach to the inverse Schr\"{o}dinger problem:
  explicit demonstration of Levinson theorem and a solution scheme for Krein
  equation

abstract:
  A recently proposed reference potential approach to the inverse
Schr\"{o}dinger problem is further developed. As previously, theoretical
developments are demonstrated on example of diatomic xenon molecule in its
ground electronic state. An exactly solvable reference potential for this
quantum system is used, which enables to solve the related energy eigenvalue
problem exactly. Moreover, the full energy dependence of the phase shift can
also be calculated analytically, and as a particular result, full agreement
with Levinson theorem has been achieved and explicitly demonstrated. In
principle, this important spectral information can be reused to calculate an
improved potential for the system, and such possibilities are discussed in the
paper. Aiming at this goal, one may calculate an auxiliary potential with no
bound states, whose spectral density for positive energies is exactly the same
as that of the reference potential. To this end, one may solve Krein equation,
which in the present context is simpler than using Gelfand-Levitan method.
General solution of Krein equation can be expressed as a Neumann series.
Convergence of this series of multi-dimensional integrals at distances not
close to the origin is hard to achieve without a simple asymptotic formula for
calculating the kernel of Krein equation. As proven in this paper, such an
asymptotic formula exists, and its parameters can be easily ascertained.


title: On the Generators of Quantum Stochastic Master Equation

abstract:
  A characterisation of the stochastic bounded generators of quantum
irreversible Master equations is given. This suggests the general form of
quantum stochastic evolution with respect to the Poisson (jumps), Wiener
(diffusion) or general Quantum Noise. The corresponding irreversible Heisenberg
evolution in terms of stochastic completely positive (CP) maps is found and the
general form of the stochastic completely dissipative (CD) operator equation is
discovered.


title: The General Quantum Interference Principle and the Duality Computer

abstract:
  In this article, we propose a general principle of quantum interference for
quantum system, and based on this we propose a new type of computing machine,
the duality computer, that may outperform in principle both classical computer
and the quantum computer.
  According to the general principle of quantum interference, the very essence
of quantum interference is the interference of the sub-waves of the quantum
system itself. A quantum system considered here can be any quantum system: a
single microscopic particle, a composite quantum system such as an atom or a
molecule, or a loose collection of a few quantum objects such as two
independent photons.
  In the duality computer, the wave of the duality computer is split into
several sub-waves and they pass through different routes, where different
computing gate operations are performed. These sub-waves are then re-combined
to interfere to give the computational results. The quantum computer, however,
has only used the particle nature of quantum object. In a duality computer, it
may be possible to find a marked item from an unsorted database using only a
single query, and all NP-complete problems may have polynomial algorithms. Two
proof-of-the-principle designs of the duality computer are presented: the giant
molecule scheme and the nonlinear quantum optics scheme. We also proposed
thought experiment to check the related fundamental issues, the measurement
efficiency of a partial wave function


title:
Normal mode splitting and mechanical effects of an optical lattice in a
  ring cavity

abstract:
  A novel regime of atom-cavity physics is explored, arising when large atom
samples dispersively interact with high-finesse optical cavities. A stable far
detuned optical lattice of several million rubidium atoms is formed inside an
optical ring resonator by coupling equal amounts of laser light to each
propagation direction of a longitudinal cavity mode. An adjacent longitudinal
mode, detunedby about 3 GHz, is used to perform probe transmission spectroscopy
of the system. The atom-cavity coupling for the lattice beams and the probe is
dispersive and dissipation results only from the finite photon-storage time.
The observation of two well-resolved normal modes demonstrates the regime of
strong cooperative coupling. The details of the normal mode spectrum reveal
mechanical effects associated with the retroaction of the probe upon the
optical lattice.


title: Anonymous Transmission of Quantum Information

abstract:
  We propose a protocol for anonymous distribution of quantum information which
can be used in two modifications. In the first modification the receiver of the
message is publicly known, but the sender remains unknown (even to receiver).
In the second modification the sender is known, but the receiver is unknown
(even to sender). Our protocol achieves this goal with unconditional security
using classical anonymous message transfer proposed by Chaum as a subprotocol.


title: Afshar's Experiment does not show a Violation of Complementarity

abstract:
  A recent experiment performed by S. Afshar [first reported by M. Chown, New
Scientist {\bf 183}, 30 (2004)] is analyzed. It was claimed that this
experiment could be interpreted as a demonstration of a violation of the
principle of complementarity in quantum mechanics. Instead, it is shown here
that it can be understood in terms of classical wave optics and the standard
interpretation of quantum mechanics. Its performance is quantified and it is
concluded that the experiment is suboptimal in the sense that it does not fully
exhaust the limits imposed by quantum mechanics.


title:
Multipartite entanglement in three-mode Gaussian states of continuous
  variable systems: Quantification, sharing structure and decoherence

abstract:
  We present a complete analysis of multipartite entanglement of three-mode
Gaussian states of continuous variable systems. We derive standard forms which
characterize the covariance matrix of pure and mixed three-mode Gaussian states
up to local unitary operations, showing that the local entropies of pure
Gaussian states are bound to fulfill a relationship which is stricter than the
general Araki-Lieb inequality. Quantum correlations will be quantified by a
proper convex roof extension of the squared logarithmic negativity (the
contangle), satisfying a monogamy relation for multimode Gaussian states, whose
proof will be reviewed and elucidated. The residual contangle, emerging from
the monogamy inequality, is an entanglement monotone under Gaussian local
operations and classical communication and defines a measure of genuine
tripartite entanglement. We analytically determine the residual contangle for
arbitrary pure three-mode Gaussian states and study the distribution of quantum
correlations for such states. This will lead us to show that pure, symmetric
states allow for a promiscuous entanglement sharing, having both maximum
tripartite residual entanglement and maximum couplewise entanglement between
any pair of modes. We thus name these states GHZ/$W$ states of continuous
variable systems because they are simultaneous continuous-variable counterparts
of both the GHZ and the $W$ states of three qubits. We finally consider the
action of decoherence on tripartite entangled Gaussian states, studying the
decay of the residual contangle. The GHZ/$W$ states are shown to be maximally
robust under both losses and thermal noise.

categories: quant-ph cond-mat.stat-mech math-ph math.MP physics.optics


title: Quantum information and computation

abstract:
  This article deals with theoretical developments in the subject of quantum
information and quantum computation, and includes an overview of classical
information and some relevant quantum mechanics. The discussion covers topics
in quantum communication, quantum cryptography, and quantum computation, and
concludes by considering whether a perspective in terms of quantum information
sheds new light on the conceptual problems of quantum mechanics.


title: Study on Dynamics of N Level System of Atom by Laser Fields

abstract:
  This paper is an extension of Fujii et al (quant--ph/0307066) and in this one
we again treat a model of atom with n energy levels interacting with n(n-1)/2
external laser fields, which is a natural extension of usual two level system.
Then the rotating wave approximation (RWA) is assumed from the beginning.
  To solve the Schr{\" o}dinger equation we set the {\bf consistency condition}
in our terminology and reduce it to a matrix equation with symmetric matrix $Q$
consisting of coupling constants.
  However, to calculate $\exp(-itQ)$ {\bfexplicitly} is not easy. In the case
of three and four level systems we determine it in a complete manner, so our
model in these levels becomes realistic.
  In last, we make a comment on Cavity QED quantum computation based on three
energy levels of atoms as a forthcoming target.


title: A Possible Generalization of Quantum Mechanics

abstract:
  A "minimal" generalization of Quantum Mechanics is proposed, where the
Lagrangian or the action functional is a mapping from the (classical) states of
a system to the Lie algebra of a general compact Lie group, and the wave
function takes values in the corresponding group algebra. This formalism admits
a probability interpretation and a suitable dynamics, but has no obvious
classical correspondence. Allowing the Lagrangian or the action functional to
take values in a general Lie algebra instead of only the real number field
(actually the u(1) algebra) enlarges the extent of possible physical laws that
can describe the real world. The generalized quantum dynamics of a point
particle in a background gauge field is given as an example, which realizes the
gauge invariance by a Wilson line structure and shows that some
Schrodinger-like equation can be deduced within this formalism. Some possible
developments of this formalism are also discussed.


title: Long-Distance Quantum Communication with Neutral Atoms

abstract:
  The architecture proposed by Duan, Lukin, Cirac, and Zoller (DLCZ) for
long-distance quantum communication with atomic ensembles is analyzed. Its
fidelity and throughput in entanglement distribution, entanglement swapping,
and quantum teleportation is derived within a framework that accounts for
multiple excitations in the ensembles as well as loss and asymmetries in the
channel. The DLCZ performance metrics that are obtained are compared to the
corresponding results for the trapped-atom quantum communication architecture
that has been proposed by a team from the Massachusetts Institute of Technology
and Northwestern University (MIT/NU). Both systems are found to be capable of
high-fidelity entanglement distribution. However, the DLCZ scheme only provides
conditional teleportation and repeater operation, whereas the MIT/NU
architecture affords full Bell-state measurements on its trapped atoms.
Moreover, it is shown that achieving unity conditional fidelity in DLCZ
teleportation and repeater operation requires ideal photon-number resolving
detectors. The maximum conditional fidelities for DLCZ teleportation and
repeater operation that can be realized with non-resolving detectors are 1/2
and 2/3, respectively.


title: Quantum motion of a neutron in a wave-guide in the gravitational field

abstract:
  We study theoretically the quantum motion of a neutron in a horizontal
wave-guide in the gravitational field of the Earth. The wave-guide in question
is equipped with a mirror below and a rough absorber above. We show that such a
system acts as a quantum filter, i.e. it effectively absorbs quantum states
with sufficiently high transversal energy but transmits low-energy states. The
states transmitted are mainly determined by the potential well formed by the
gravitational field of the Earth and the mirror. The formalism developed for
quantum motion in an absorbing wave-guide is applied to the description of the
recent experiment on the observation of the quantum states of neutrons in the
Earth's gravitational field.


title: Cluster state quantum computation for many-level systems

abstract:
  The cluster state model for quantum computation [Phys. Rev. Lett. 86, 5188]
outlines a scheme that allows one to use measurement on a large set of
entangled quantum systems in what is known as a cluster state to undertake
quantum computations. The model itself and many works dedicated to it involve
using entangled qubits. In this paper we consider the issue of using entangled
qudits instead. We present a complete framework for cluster state quantum
computation using qudits, which not only contains the features of the original
qubit model but also contains the new idea of adaptive computation: via a
change in the classical computation that helps to correct the errors that are
inherent in the model, the implemented quantum computation can be changed. This
feature arises through the extra degrees of freedom that appear when using
qudits. Finally, for prime dimensions, we give a very explicit description of
the model, making use of mutually unbiased bases.


title: Decoherence according to Environment and Self Induced Decoherences

abstract:
  A generalized decoherence formalism that can be used both in open (using
Environment Induced Decoherence-EID) and closed (using Self Induced
Decoherence-SID) quantum systems is sketched


title: Towards bringing Quantum Mechanics and General Relativity together

abstract:
  Two questions are suggested as having priority when trying to bring together
Quantum Mechanics and General Relativity. Both questions have a scope which
goes well beyond Physics, and in particular Quantum Mechanics and General
Relativity.


title:
Broadband Spectrally Correlated Light - Properties, Sources and
  Applications (Ph.D Thesis)

abstract:
  The coherence properties of broadband down converted light are investigated
theoretically and experimentally in both the classical and quantum mechanical
frameworks. Although broadband down converted light is one-photon incoherent
noise, it possesses unique two-photon coherence. Thus, for performing
two-photon processes, down-converted light is equivalent to coherent ultrashort
pulses in some aspects and to coherent CW laser radiation in others. This
equivalence is theoretically established and experimentally demonstrated in the
classical, high-power regime. Two applications that take advantage of
multi-photon coherence are then described in detail; one for optical spread
spectrum communication and the other for sub-diffraction limit optical
lithography. A key part of this research is the design and implementation of an
efficient source that generates high-power broadband down conversion in a
cavity. A broadband oscillation in the cavity is ensured by a mechanism very
similar to passive mode-locking of ultrashort pulse laser sources, which we
term as pair-wise mode locking, thus extending the equivalence to ultrashort
pulses to the light generating sources also. Finally, the quantum mechanical
properties of broadband down-conversion are explored experimentally, by
performing a two-photon process (sum frequency generation) at the low power
level of entangled photon pairs. The non-classical nature of the light is
expressed by a linear intensity dependence of the non-linear process. Temporal
shaping with femtosecond resolution of the entangled photon pairs is
demonstrated using this non-linear interaction.


title: Present status of controversies regarding the thermal Casimir force

abstract:
  It is well known that, beginning in 2000, the behavior of the thermal
correction to the Casimir force between real metals has been hotly debated. As
was shown by several research groups, the Lifshitz theory, which provides the
theoretical foundation for the calculation of both the van der Waals and
Casimir forces, leads to different results depending on the model of metal
conductivity used. To resolve these controversies, the theoretical
considerations based on the principles of thermodynamics and new experimental
tests were invoked. We analyze the present status of the problem (in
particular, the advantages and disadvantages of the approaches based on the
surface impedance and on the Drude model dielectric function) using rigorous
analytical calculations of the entropy of a fluctuating field. We also discuss
the results of a new precise experiment on the determination of the Casimir
pressure between two parallel plates by means of a micromechanical torsional
oscillator.


title:
Effective Hamiltonians in quantum physics: resonances and geometric
  phase

abstract:
  Effective Hamiltonians are often used in quantum physics, both in time
dependent and time independent contexts. Analogies are drawn between the two
usages, the discussion framed particularly for the geometric phase of a
time-dependent Hamiltonian and for resonances as stationary states of a
time-independent Hamiltonian.


title: A New Wave Equation For a Continuous Nondemolition Measurement

abstract:
  A stochastic model for nondemolition continuous measurement in a quantum
system is given. It is shown that the posterior dynamics, including a
continuous collapse of the wave function, is described by a nonlinear
stochastic wave equation. For a particle in an electromagnetic field it reduces
the Schroedinger equation with extra imaginary stochastic potentials.


title: A Quantum Particle Undergoing Continuous Observation

abstract:
  A stochastic model for the continuous nondemolition ohservation of the
position of a quantum particle in a potential field and a boson reservoir is
given. lt is shown that any Gaussian wave function evolving according to the
posterior wave equation with a quadratic potential collapses to a Gaussian wave
packet given by the stationary solution of this equation.


title: Nondemolition observation of a free quantum particle

abstract:
  A stochastic model of a continuous nondemolition observation of a free
quantum Brownian motion is presented. The nonlinear stochastic wave equation
describing the posterior dynamics of the observed quantum system is solved in a
Gaussian case for a free particle of mass m. It is shown that the dispersion of
the wave packet does not increase to infinity like for the free unobserved
particle but tends to the finite limit.


title:
Entanglement of Assistance is not a bipartite measure nor a tripartite
  monotone

abstract:
  The entanglement of assistance quantifies the entanglement that can be
generated between two parties, Alice and Bob, given assistance from a third
party, Charlie, when the three share a tripartite state and where the
assistance consists of Charlie initially performing a measurement on his share
and communicating the result to Alice and Bob through a one-way classical
channel. We argue that if this quantity is to be considered an operational
measure of entanglement, then it must be understood to be a tripartite rather
than a bipartite measure. We compare it with a distinct tripartite measure that
quantifies the entanglement that can be generated between Alice and Bob when
they are allowed to make use of a two-way classical channel with Charlie. We
show that the latter quantity, which we call the entanglement of collaboration,
can be greater than the entanglement of assistance. This demonstrates that the
entanglement of assistance (considered as a tripartite measure of
entanglement), and its multipartite generalizations such as the localizable
entanglement, are not entanglement monotones, thereby undermining their
operational significance.


title: A Simple Five-Dimensional Wave Equation for a Dirac Particle

abstract:
  A first-order relativistic wave equation is constructed in five dimensions.
Its solutions are eight-component spinors, which are interpreted as
single-particle fermion wave functions in four-dimensional spacetime. Use of a
``cylinder condition'' (the removal of explicit dependence on the fifth
coordinate) reduces each eight-component solution to a pair of degenerate
four-component spinors obeying the Dirac equation. This five-dimensional method
is used to obtain solutions for a free particle and for a particle moving in
the Coulomb potential. It is shown that, under the cylinder condition, the
results are the same as those from the Dirac equation. Without the cylinder
condition, on the other hand, the equation predicts some interesting new
phenomena. It implies the existence of a scalar potential, and for zero-mass
particles it leads to a four-dimensional fermionic equation analogous to
Maxwell's equation with sources.


title:
Homodyne detection and optical parametric amplification: a classical
  approach applied to proposed "loophole-free" Bell tests

abstract:
  Recent proposed ``loophole-free'' Bell tests are discussed in the light of
classical models for the relevant features of optical parametric amplification
and homodyne detection. The Bell tests themselves are uncontroversial: there
are no obvious loopholes that might cause bias and hence, if the world does,
after all, obey local realism, no violation of a Bell inequality will be
observed. Interest centres around the question of whether or not the proposed
criterion for ``non-classical'' light is valid. If it is not, then the
experiments will fail in their initial concept, since both quantum theorists
and local realists will agree that we are seeing a purely classical effect. The
Bell test, though, is not the only criterion by which the quantum-mechanical
and local realist models can be judged. It is suggested that the
quantum-mechanical models given in the proposals will also fail in their
detailed predictions. If the experiments are extended by including a range of
parameter values and by analysing, in addition to the proposed digitised
voltage differences, the raw voltages, the models can be compared in their
overall performance and plausibility.


title: Unambiguous discrimination among quantum operations

abstract:
  We address the problem of unambiguous discrimination among a given set of
quantum operations. The necessary and sufficient condition for them to be
unambiguously distinguishable is derived in the cases of single use and
multiple uses respectively. For the latter case we explicitly construct the
input states and corresponding measurements that accomplish the task. It is
found that the introduction of entanglement can improve the discrimination.


title:
Exploring Quantum Phase Transitions with a Novel Sublattice Entanglement
  Scenario

abstract:
  We introduce a new measure called reduced entropy of sublattice to quantify
entanglement in spin, electron and boson systems. By analyzing this quantity,
we reveal an intriguing connection between quantum entanglement and quantum
phase transitions in various strongly correlated systems: the local extremes of
reduced entropy and its first derivative as functions of the coupling constant
coincide respectively with the first and second order transition points. Exact
numerical studies merely for small lattices reproduce several well-known
results, demonstrating that our scenario is quite promising for exploring
quantum phase transitions.


title: Heisenberg limited measurements with superconducting circuits

abstract:
  We describe an assembly of N superconducting qubits contained in a
single-mode cavity. In the dispersive regime, the correlation between the
cavity field and each qubit results in an effective interaction between qubits
that can be used to dynamically generate maximally entangled states. With only
collective manipulations, we show how to create maximally entangled quantum
states and how to use these states to reach the Heisenberg limit in the
determination of the qubit bias control parameter (gate charge for charge
qubits, external magnetic flux for rf-SQUIDs).


title:
Persistent single-photon production by tunable on-chip micromaser with a
  superconducting quantum circuit

abstract:
  We propose a tunable on-chip micromaser using a superconducting quantum
circuit (SQC). By taking advantage of externally controllable state
transitions, a state population inversion can be achieved and preserved for the
two working levels of the SQC and, when needed, the SQC can generate a single
photon. We can regularly repeat these processes in each cycle when the
previously generated photon in the cavity is decaying, so that a periodic
sequence of single photons can be produced persistently. This provides a
controllable way for implementing a persistent single-photon source on a
microelectronic chip.


title:
The limits of the rotating wave approximation in the electromagnetic
  field propagation in a cavity

abstract:
  We consider three two-level atoms inside a one-dimensional cavity,
interacting with the electromagnetic field in the rotating wave approximation
(RWA), commonly used in the atom-radiation interaction. One of the three atoms
is initially excited, and the other two are in their ground state. We
numerically calculate the propagation of the field spontaneously emitted by the
excited atom and scattered by the second atom, as well as the excitation
probability of the second and third atom. The results obtained are analyzed
from the point of view of relativistic causality in the atom-field interaction.
We show that, when the RWA is used, relativistic causality is obtained only if
the integrations over the field frequencies are extended to $-\infty$; on the
contrary, noncausal tails remain even if the number of field modes is
increased. This clearly shows the limit of the RWA in dealing with subtle
problems such as relativistic causality in the atom-field interaction.


title:
The Problem of Quantum Measurement and Entangled States: Interactions
  Among States and Formation of Detector Images

abstract:
  We first review and critically examine some basic concepts and ambiguities
related to quantum mechanics and quantum measurement to understand the success
and shortcomings of current theories. We also touch on ideas regarding
expression of variables within a complex system. Then we discuss a model for
quantum measurement proposed by us, in which the quantum system is allowed to
interact with its image created within the detector, followed by a first
passage random walk in the Hilbert space. Definitions and ideas from the first
part are used in the context of the model. In the end, we discuss the puzzling
question of entanglement. We propose how borrowing concepts from our model for
quantum measurement may enable us to formulate a hidden variable scenario that
does not violate Bell's inequality.


title: Quantum teleportation between nanomechanical modes

abstract:
  We study a quantum teleportation scheme between two nanomechanical modes
without local interaction. The nanomechanical modes are linearly coupled to and
connected by the continuous variable modes of a superconducting circuit
consisting of a transmission line and Josephson junctions. We calculate the
fidelity of transferring Gaussian states at finite temperature and non-unit
detector efficiency. For coherent state, a fidelity above the classical limit
of 1/2 can be achieved for a large range of parameters.


title:
Quantum state transfer from light to molecules via coherent two-color
  photo-association in an atomic Bose-Einstein condensate

abstract:
  By using a quantized input light, we theoretically revisit the coherent
two-color photo-association process in an atomic Bose-Einstein condensate.
Under the single-mode approximations, we show two interesting regimes of the
light transmission and the molecular generation. The quantum state transfer
from light to molecules is exhibited, without or with the depletion of trapped
atoms.


title:
Statistical Separability and the Consistency between Quantum Theory,
  Relativity and the Causality

abstract:
  We show that the non-locality together with the statistical character makes
the world statistically separable. The super-luminal signal transmission is
impossible. The quantum theory is therefore consistent with the relativity and
the causality.


title:
Quantum measurements of spatial conjugate variables: Displacement and
  tilt of a Gaussian beam

abstract:
  We consider the problem of measurement of optical transverse profile
parameters and their conjugate variable. Using multi-mode analysis, we
introduce the concept of detection noise-modes. For Gaussian beams,
displacement and tilt are a pair of transverse profile conjugate variables. We
experimentally demonstrate their optimal encoding and detection with a spatial
homodyning scheme. Using higher order spatial mode squeezing, we show the
sub-shot noise measurements for the displacement and tilt of a Gaussian beam.


title:
Optical storage of high density information beyond the diffraction limit
  : a quantum study

abstract:
  We propose an optical read-out scheme allowing a demonstration of principle
of information extraction below the diffraction limit. This technique, which
could lead to improvement in data read-out density onto optical discs, is
independent from the wavelength and numerical aperture of the reading
apparatus, and involves a multi-pixel array detector. Furthermore, we show how
to use non classical light in order to perform bit discrimination beyond the
quantum noise limit.


title: Asymptotic violation of Bell inequalities and distillability

abstract:
  A multipartite quantum state violates a Bell inequality asymptotically if,
after jointly processing by general local operations an arbitrarily large
number of copies of it, the result violates the inequality. In the bipartite
case we show that asymptotic violation of the CHSH-inequality is equivalent to
distillability. Hence, bound entangled states do not violate it. In the
multipartite case we consider the complete set of full-correlation Bell
inequalities with two dichotomic observables per site, also called
WWZB-inequalities. We show that asymptotic violation of any of these
inequalities by a multipartite state implies that pure-state entanglement can
be distilled from it, although the corresponding distillation protocol may
require that some of the parties join into several groups. We also obtain the
extreme points of the set of distributions generated by measuring $N$ quantum
systems with two dichotomic observables per site. It is shown that when
considering the violation of any Bell inequality after preprocessing, either
deterministic LOCC or stochastic local operations (without communication) is
enough.


title: A concise guide to complex Hadamard matrices

abstract:
  Complex Hadamard matrices, consisting of unimodular entries with arbitrary
phases, play an important role in the theory of quantum information. We review
basic properties of complex Hadamard matrices and present a catalogue of
inequivalent cases known for dimension N=2,...,16. In particular, we explicitly
write down some families of complex Hadamard matrices for N=12,14 and 16, which
we could not find in the existing literature.


title: Valence bond solid formalism for d-level one-way quantum computation

abstract:
  The d-level or qudit one-way quantum computer (d1WQC) is described using the
valence bond solid formalism and the generalised Pauli group. This formalism
provides a transparent means of deriving measurement patterns for the
implementation of quantum gates in the computational model. We introduce a new
universal set of qudit gates and use it to give a constructive proof of the
universality of d1WQC. We characterise the set of gates that can be performed
in one parallel time step in this model.


title:
More on the Asymmetric Infinite Square Well: Energy Eigenstates with
  Zero Curvature

abstract:
  We extend the standard treatment of the asymmetric infinite square well to
include solutions that have zero curvature over part of the well. This type of
solution, both within the specific context of the asymmetric infinite square
well and within the broader context of bound states of arbitrary
piecewise-constant potential energy functions, is not often discussed as part
of quantum mechanics texts at any level. We begin by outlining the general
mathematical condition in one-dimensional time-independent quantum mechanics
for a bound-state wave function to have zero curvature over an extended region
of space and still be a valid wave function. We then briefly review the
standard asymmetric infinite square well solutions, focusing on zero-curvature
solutions as represented by energy eigenstates in position and momentum space.


title:
Pairwise entanglement and readout of atomic-ensemble and optical
  wave-packet modes in traveling-wave Raman interactions

abstract:
  We analyze quantum entanglement of Stokes light and atomic electronic
polarization excited during single-pass, linear-regime, stimulated Raman
scattering in terms of optical wave-packet modes and atomic-ensemble spatial
modes. The output of this process is confirmed to be decomposable into multiple
discrete, bosonic mode pairs, each pair undergoing independent evolution into a
two-mode squeezed state. For this we extend the Bloch-Messiah reduction
theorem, previously known for discrete linear systems (S. L. Braunstein, Phys.
Rev. A, vol. 71, 055801 (2005)). We present typical mode functions in the case
of one-dimensional scattering in an atomic vapor. We find that in the absence
of dispersion, one mode pair dominates the process, leading to a simple
interpretation of entanglement in this continuous-variable system. However,
many mode pairs are excited in the presence of dispersion-induced temporal
walkoff of the Stokes, as witnessed by the photon-count statistics. We also
consider the readout of the stored atomic polarization using the anti-Stokes
scattering process. We prove that the readout process can also be decomposed
into multiple mode pairs, each pair undergoing independent evolution analogous
to a beam-splitter transformation. We show that this process can have unit
efficiency under realistic experimental conditions. The shape of the output
light wave packet can be predicted. In case of unit readout efficiency it
contains only excitations originating from a specified atomic excitation mode.


title:
Nonlinear evolution as a possible explanation for quantum mechanical
  statevector reduction

abstract:
  A non-local toy-model is proposed for the purpose of modelling the ``wave
function collapse'' of a two-state quantum system. The collapse is driven by a
nonlinear evolution equation with an extreme sensitivity to absolute phase. It
is hypothesized that the phase, or a part of it, is displaying chaotic
behaviour. This chaotic behaviour can then be responsible for the indeterminacy
we are experiencing for a single quantum system. Through this randomness, we no
longer need the statistical ``ensemble'' behaviour to describe a single quantum
system. A brief introduction to the ``measurement problem'' is also given.


title: How to Make the Quantum Adiabatic Algorithm Fail

abstract:
  The quantum adiabatic algorithm is a Hamiltonian based quantum algorithm
designed to find the minimum of a classical cost function whose domain has size
N. We show that poor choices for the Hamiltonian can guarantee that the
algorithm will not find the minimum if the run time grows more slowly than
square root of N. These poor choices are nonlocal and wash out any structure in
the cost function to be minimized and the best that can be hoped for is Grover
speedup. These failures tell us what not to do when designing quantum adiabatic
algorithms.


title: Time Extended Measurement of the Position of a Particle

abstract:
  The von Neumann interaction between a particle and an apparatus has been
considered in the measurement of the position of a particle when the
interaction lasts for a finite amount of time. When the measurement has finite
duration, both the motion of the pointer and the particle influence the result
of the measurement. Provided that the particle is in an eigenstate of its
position at the start of the measurement, the pointer will indicate the
arithmetic average between the initial and final position of the particle.
Furthermore, the probability that the pointer will indicate a given average
value is equal to the transition probability for the undisturbed particle to
experience the change in position. If the initial state of the pointer is a
narrow wavepacket, then for any initial state of the particle, the measurement
yields, approximately, the undisturbed probability distribution for the
position of the particle at the end of the measurement.


title:
Rigorous approach to the comparison between experiment and theory in
  Casimir force measurements

abstract:
  In most experiments on the Casimir force the comparison between measurement
data and theory was done using the concept of the root-mean-square deviation, a
procedure that has been criticized in literature. Here we propose a special
statistical analysis which should be performed separately for the experimental
data and for the results of the theoretical computations. In so doing, the
random, systematic, and total experimental errors are found as functions of
separation, taking into account the distribution laws for each error at 95%
confidence. Independently, all theoretical errors are combined to obtain the
total theoretical error at the same confidence. Finally, the confidence
interval for the differences between theoretical and experimental values is
obtained as a function of separation. This rigorous approach is applied to two
recent experiments on the Casimir effect.


title:
Nonlocality I: Nonlocality, singularity, and elastic scattering in
  quantum fields

abstract:
  Using path integrals we express the quantum nonlocality of AB-effect type in
the form of singularity. The gauge-fixing term in path integrals induce the AB
effect in ordinary scattering processes. This means that all scattering
processes are accompanied by nonlocal effect. The formulae are then extended to
theory of fields that additionally include a scalar potential. It turns out
that the degree of freedom of nonlocality in quantum fields is just the degree
of the ghosts. Furthermore, renormalization method can be related to this type
of nonlocal effect.


title:
Long-distance distribution of time-bin entanglement generated in a
  cooled fiber

abstract:
  This paper reports the first demonstration of the generation and distribution
of entangled photon pairs in the 1.5-um band using spontaneous four-wave mixing
in a cooled fiber. Noise photons induced by spontaneous Raman scattering were
suppressed by cooling a dispersion shifted fiber with liquid nitrogen, which
resulted in a significant improvement in the visibility of two-photon
interference. By using this scheme, time-bin entangled qubits were successfully
distributed over 60 km of optical fiber with a visibility of 76%, which was
obtained without removing accidental coincidences.


title: Nonlinear entanglement witnesses

abstract:
  Entanglement detection typically relies on linear inequalities for mean
values of certain observables (entanglement witnesses), where violation
indicates entanglement. We provide a general method to improve any of these
inequalities for bipartite systems via nonlinear expressions. The
nonlinearities are of different orders and can be directly measured in
experiments, often without any extra effort.


title:
Quantum manipulation of two-color stationary light: Quantum wavelength
  conversion

abstract:
  We present a quantum manipulation of a traveling light pulse using double
atomic coherence for two-color stationary light and quantum frequency
conversion. The quantum frequency conversion rate of the traveling light
achieved by the two-color stationary light phenomenon is near unity. We
theoretically discuss the two-color stationary light for the frequency
conversion process in terms of pulse area, energy transfer and propagation
directions. The resulting process may apply the coherent interactions of a weak
field to nonlinear quantum optics such as quantum nondemolition measurement.


title:
Asymptotic expansion of Gaussian integrals of analytic functionals on
  infinite-dimensional spaces and quantum averages

abstract:
  We study asymptotic expansions of Gaussian integrals of analytic functionals
on infinite-dimensional spaces (Hilbert and nuclear Frechet). We obtain an
asymptotic equality coupling the Gaussian integral and the trace of the
composition of scaling of the covariation operator of a Gaussian measure and
the second (Frechet) derivative of a functional. In this way we couple
classical average (given by an infinite-dimensional Gaussian integral) and
quantum average (given by the von Neumann trace formula). We can interpret this
mathematical construction as a procedure of ``dequantization'' of quantum
mechanics. We represent quantum mechanics as an asymptotic projection of
classical statistical mechanics with infinite-dimensional phase-space. This
space can be represented as the space of classical fields, so quantum mechanics
is represented as a projection of ``Prequantum Classical Statistical Field
Theory''.


title: Physical accessibility of non-completely positive maps

abstract:
  Maps that are not completely positive (CP) are often useful to describe the
dynamics of open systems. An apparent violation of complete positivity can
occur because there are prior correlations of the principal system with the
environment, or if the applied transformation is correlated with the state of
the system. We provide a physically motivated definition of accessible non-CP
maps and derive two necessary conditions for a map to be accessible. We also
show that entanglement between the system and the environment is not necessary
to generate a non-CP dynamics. We describe two simple approximations that may
be sufficient for some problems in process tomography, and then outline what
these methods may be able to tell us in other situations where non-CP dynamics
naturally arise.


title:
Can relativity be considered complete ? From Newtonian nonlocality to
  quantum nonlocality and beyond

abstract:
  We review the long history of nonlocality in physics with special emphasis on
the conceptual breakthroughs over the last few years. For the first time it is
possible to study "nonlocality without signaling" {\it from the outside}, that
is without all the quantum physics Hilbert space artillery. We emphasize that
physics has always given a nonlocal description of Nature, except during a
short 10 years gap. We note that the very concept of "nonlocality without
signaling" is totally foreign to the spirit of relativity, the only strictly
local theory.


title: Deterministic and Unambiguous Dense Coding

abstract:
  Optimal dense coding using a partially-entangled pure state of Schmidt rank
$\bar D$ and a noiseless quantum channel of dimension $D$ is studied both in
the deterministic case where at most $L_d$ messages can be transmitted with
perfect fidelity, and in the unambiguous case where when the protocol succeeds
(probability $\tau_x$) Bob knows for sure that Alice sent message $x$, and when
it fails (probability $1-\tau_x$) he knows it has failed. Alice is allowed any
single-shot (one use) encoding procedure, and Bob any single-shot measurement.
For $\bar D\leq D$ a bound is obtained for $L_d$ in terms of the largest
Schmidt coefficient of the entangled state, and is compared with published
results by Mozes et al. For $\bar D > D$ it is shown that $L_d$ is strictly
less than $D^2$ unless $\bar D$ is an integer multiple of $D$, in which case
uniform (maximal) entanglement is not needed to achieve the optimal protocol.
The unambiguous case is studied for $\bar D \leq D$, assuming $\tau_x>0$ for a
set of $\bar D D$ messages, and a bound is obtained for the average
$\lgl1/\tau\rgl$. A bound on the average $\lgl\tau\rgl$ requires an additional
assumption of encoding by isometries (unitaries when $\bar D=D$) that are
orthogonal for different messages. Both bounds are saturated when $\tau_x$ is a
constant independent of $x$, by a protocol based on one-shot entanglement
concentration. For $\bar D > D$ it is shown that (at least) $D^2$ messages can
be sent unambiguously. Whether unitary (isometric) encoding suffices for
optimal protocols remains a major unanswered question, both for our work and
for previous studies of dense coding using partially-entangled states,
including noisy (mixed) states.


title: Error correcting codes for adiabatic quantum computation

abstract:
  Recently, there has been growing interest in using adiabatic quantum
computation as an architecture for experimentally realizable quantum computers.
One of the reasons for this is the idea that the energy gap should provide some
inherent resistance to noise. It is now known that universal quantum
computation can be achieved adiabatically using 2-local Hamiltonians. The
energy gap in these Hamiltonians scales as an inverse polynomial in the problem
size. Here we present stabilizer codes which can be used to produce a constant
energy gap against 1-local and 2-local noise. The corresponding fault-tolerant
universal Hamiltonians are 4-local and 6-local respectively, which is the
optimal result achievable within this framework.


title: Kaonic Qubits

abstract:
  Quantum mechanics can also be tested in high energy physics; in particular,
the neutral kaon system is very well suited. We show that these massive
particles can be considered as qubits --kaonic qubits-- in the very same way as
spin-1/2 particles or polarized photons. But they also have other important
properties, namely they are instable particles and they violate the CP symmetry
(C...charge conjugation, P...parity). We consider a Bell inequality and,
surprisingly, the premises of local realistic theories require strict CP
conservation, in contradiction to experiment. Furthermore we investigate Bohr's
complementary relation in order to describe the physics of the time evolution
of kaons. Finally, we discuss quantum marking and eraser experiments with
kaons, which prove in a new way the very concept of a quantum eraser.


title: Optical Quantum Cloning - a Review

abstract:
  After a brief introduction to the quantum no-cloning theorem and its link
with the linearity and causality of quantum mechanics, the concept of quantum
cloning machines is sketched, following, whenever possible, the chronology of
the main results. The important classes of quantum cloning machines are
reviewed, in particular state-independent and state-dependent cloning machines.
The 1-to-2 cloning problem is then studied from a formal point of view, using
the isomorphism between completely positive maps and operators, which leads to
the so-called double-Bell ansatz. This also yields an efficient numerical
approach to quantum cloning, based on semidefinite programming methods. The
derivation of the optimal N-to-M universal cloning machine in d dimensions is
then detailed, as well as the notion of asymmetric cloning machines. In the
second part of this review, the optical implementation of cloning machines is
considered. It is shown that the universal cloning of photons can be achieved
by parametric amplification of light or by symmetrization via the
Hong-Ou-Mandel effect. The various experimental demonstrations of quantum
cloning machines are reviewed. The cloning of orthogonally polarized photons is
also considered, as well as the asymmetric and phase-covariant cloning of
photons. Finally, the extension of quantum cloning to continuous variables is
analyzed. The optimal cloning of coherent states of light by phase-insensitive
amplification is explained, as well as the experimental realization of
continuous-variable quantum cloning with linear optics, measurement, and
feed-forward operations.


title: Entanglement purification for high dimensional multipartite systems

abstract:
  We propose an entanglement purification protocol for high-dimensional
multipartite systems. In the protocol we can select a subensemble in a pure
generalized Greenberger-Horne-Zeilinger (GHZ) state. This post-selection can be
made by detecting the noise which contaminated the initial pure ensemble when
the systems past through a noisy environment. For the detection of noise we
investigate correlation properties of GHZ states and analyze their possible
errors due to a noisy environment. We show that the presented protocol is more
efficient than a simple generalization of the purification protocol for a
bipartite state in high dimensions.


title:
Implementation of quantum logic operations and creation of entanglement
  in a silicon-based quantum computer with constant interaction

abstract:
  We describe how to implement quantum logic operations in a silicon-based
quantum computer with phosphorus atoms serving as qubits. The information is
stored in the states of nuclear spins and the conditional logic operations are
implemented through the electron spins using nuclear-electron hyperfine and
electron-electron exchange interactions. The electrons in our computer should
stay coherent only during implementation of one Control-Not gate. The exchange
interaction is constant and selective excitations are provided by a magnetic
field gradient. The quantum logic operations are implemented by rectangular
radio-frequency pulses. This architecture is scalable and does not require
manufacturing nanoscale electronic gates. As shown in this paper parameters of
a quantum protocol can be derived analytically even for a computer with a large
number of qubits using our perturbation approach. We present the protocol for
initialization of the nuclear spins and the protocol for creation of
entanglement. All analytical results are tested numerically using a two-qubit
system.


title: Dynamics of a pulsed continuous variable quantum memory

abstract:
  We study the transfer dynamics of non-classical fluctuations of light to the
ground-state collective spin components of an atomic ensemble during a pulsed
quantum memory sequence, and evaluate the relevant physical quantities to be
measured in order to characterize such a quantum memory. We show in particular
that the fluctuations stored into the atoms are emitted in temporal modes which
are always different than those of the readout pulse, but which can
nevertheless be retrieved efficiently using a suitable temporal mode-matching
technique. We give a simple toy model - a cavity with variable transmission -
which accounts for the behavior of the atomic quantum memory.


title:
A generalized structure of Bell inequalities for bipartite arbitrary
  dimensional systems

abstract:
  We propose a generalized structure of Bell inequalities for arbitrary
d-dimensional bipartite systems, which includes the existing two types of Bell
inequalities introduced by Collins-Gisin-Linden-Massar-Popescu [Phys. Rev.
Lett. 88, 040404 (2002)] and Son-Lee-Kim [Phys. Rev. Lett. 96, 060406 (2006)].
We analyze Bell inequalities in terms of correlation functions and joint
probabilities, and show that the coefficients of correlation functions and
those of joint probabilities are in Fourier transform relations. We finally
show that the coefficients in the generalized structure determine the
characteristics of quantum violation and tightness.


title:
Separable Measurement Estimation of Density Matrices and its Fidelity
  Gap with Collective Protocols

abstract:
  We show that there exists a gap between the performance of separable and
collective measurements in qubit mixed-state estimation that persists in the
large sample limit. We characterize such gap in terms of the corresponding
bounds on the mean fidelity. We present an adaptive protocol that attains the
separable-measurement bound. This (optimal separable) protocol uses von Neumann
measurements and can be easily implemented with current technology.


title: Buonomano against Bell: Nonergodicity or nonlocality?

abstract:
  The aim of this note is to attract attention of the quantum foundational
community to the fact that in Bell's arguments one can not distinguish two
hypotheses: a) quantum mechanics is {\it nonlocal}, b) quantum mechanics is
{\it nonergodic.} Therefore experimental violations of Bell's inequality can be
as well interpreted as supporting the hypothesis that stochastic processes
induced by quantum measurements are nonergodic. The latter hypothesis was
discussed actively by Buonomano since 1980th. However, in contrast to Bell's
hypothesis on nonlocality it did not attract so much attention. The only
experiment testing the hypothesis on nonergodicity was performed in neutron
interferometry (by Summhammer, in 1989). This experiment can be considered as
rejecting this hypothesis. However, it cannot be considered as a decisive
experiment. New experiments are badly needed. We point out that a nonergodic
model can be realistic, i.e., the distribution of hidden (local!) variables is
well defined. We also discuss coupling of violation of the Bell inequality with
violation of the condition of weak mixing for ergodic dynamical systems.


title: An AB effect without closing a loop

abstract:
  We discuss the consequences of the Aharonov-Bohm effect in setups involving
several charged particles, wherein none of the charged particles encloses a
closed loop around the magnetic flux. We show that in such setups, the AB phase
is encoded either in the relative phase of a bi-partite or multi-partite
entangled photons states, or alternatively, gives rise to an overall AB phase
that can be measured relative to another reference system. These setups involve
processes of annihilation or creation of electron/hole pairs. We discuss the
relevance of such effects in "vacuum Birefringence" in QED, and comment on
their connection to other known effects.


title:
Entanglement criteria via the uncertainty relations in su(2) and su(1,1)
  algebra: detection of non-Gaussian entangled states

abstract:
  We derive a class of inequalities, from the uncertainty relations of the
SU(1,1) and the SU(2) algebra in conjunction with partial transposition, that
must be satisfied by any separable two-mode states. These inequalities are
presented in terms of the su(2) operators J_x, J_y, and the total photon number
N_a+N_b. They include as special cases the inequality derived by Hillery and
Zubairy [Phys. Rev. Lett. 96, 050503 (2006)], and the one by Agarwal and Biswas
[New J. Phys. 7, 211 (2005)]. In particular, optimization over the whole
inequalities leads to the criterion obtained by Agarwal and Biswas. We show
that this optimal criterion can detect entanglement for a broad class of
non-Gaussian entangled states, i.e., the su(2) minimum-uncertainty states.
Experimental schemes to test the optimal criterion are also discussed,
especially the one using linear optical devices and photodetectors.


title: Detecting entanglement with a thermometer

abstract:
  We present a general argument showing that the temperature as well as other
thermodynamical state variables can qualify as entanglement witnesses for
spatial entanglement. This holds for a variety of systems and we exemplify our
ideas using a simple free non-interacting Bosonic gas. We find that
entanglement can exist at arbitrarily high temperatures, provided that we can
probe smaller and smaller regions of space. We then discuss the relationship
between the occurrence of Bose-Einstein condensation and our conditions for the
presence of entanglement and compare the respective critical temperatures. We
close with a short discussion of the idea of seeing entanglement as a
macroscopic property in thermodynamical systems and its possible relation to
phase transitions in general.


title:
Nonlocality II: Nonlocality as the dynamical origin of the non-markovian
  process in quantum isolated system

abstract:
  In the previous paper, it has been proved that elastic scattering processes
of two quantum particles are always accompanied with nonlocal processes.
Furthermore, it is found that setting an additional Hamiltonian after the
originally scattering one can help to describe the two type of processes in a
united frame. Here we discuss the contribution of this additional Hamiltonian
to irreversible process in isolated quantum systems. The use of the Hamiltonian
can induce the non-Markovian Langevin equation, showing a complex memory
effect, and thus revealing the irreversible essence of isolated system without
appealing to reservoir or approximate methods (e.g. coarse grain) as usually
done.


title:
A finite element analysis of a silicon based double quantum dot
  structure

abstract:
  We present the results of a finite-element solution of the Laplace equation
for the silicon-based trench-isolated double quantum-dot and the
capacitively-coupled single-electron transistor device architecture. This
system is a candidate for charge and spin-based quantum computation in the
solid state, as demonstrated by recent coherent-charge oscillation experiments.
Our key findings demonstrate control of the electric potential and electric
field in the vicinity of the double quantum-dot by the electric potential
applied to the in-plane gates. This constitutes a useful theoretical analysis
of the silicon-based architecture for quantum information processing
applications.


title: Quantum-state input-output relations for absorbing cavities

abstract:
  The quantized electromagnetic field inside and outside an absorbing high-$Q$
cavity is studied, with special emphasis on the absorption losses in the
coupling mirror and their influence on the outgoing field. Generalized operator
input-output relations are derived, which are used to calculate the Wigner
function of the outgoing field. To illustrate the theory, the preparation of
the outgoing field in a Schr\"{o}dinger cat-like state is discussed.


title: New multiplicativity results for qubit maps

abstract:
  Let $\Phi$ be a trace-preserving, positivity-preserving (but not necessarily
completely positive) linear map on the algebra of complex $2 \times 2$
matrices, and let $\Omega$ be any finite-dimensional completely positive map.
For $p=2$ and $p \geq 4$, we prove that the maximal $p$-norm of the product map
$\Phi \ot \Omega$ is the product of the maximal $p$-norms of $\Phi$ and
$\Omega$. Restricting $\Phi$ to the class of completely positive maps, this
settles the multiplicativity question for all qubit channels in the range of
values $p \geq 4$.


title: Squeezing and entangling nuclear spins in helium 3

abstract:
  We present a realistic model for transferring the squeezing or the
entanglement of optical field modes to the collective ground state nuclear spin
of $^3$He using metastability exchange collisions. We discuss in detail the
requirements for obtaining good quantum state transfer efficiency and study the
possibility to readout the nuclear spin state optically.


title: On the Dynamical Solution of Quantum Measurement Problem

abstract:
  The development of quantum measurement theory, initiated by von Neumann, only
indicated a possibility for resolution of the interpretational crisis of
quantum mechanics. We do this by divorcing the algebra of the dynamical
generators and the algebra of the actual observables, or beables. It is shown
that within this approach quantum causality can be rehabilitated in the form of
a superselection rule for compatibility of the past beables with the potential
future. This rule, together with the self-compatibility of the measurements
insuring the consistency of the histories, is called the nondemolition, or
causality principle in modern quantum theory. The application of this rule in
the form of the dynamical commutation relations leads in particular to the
derivation of the von Neumann projection postulate. This gives a quantum
stochastic solution, in the form of the dynamical filtering equations, of the
notorious measurement problem which was tackled unsuccessfully by many famous
physicists starting with Schroedinger and Bohr.


title: Nondemolition Principle of Quantum Measurement Theory

abstract:
  We give an explicit axiomatic formulation of the quantum measurement theory
which is free of the projection postulate. It is based on the generalized
nondemolition principle applicable also to the unsharp, continuous-spectrum and
continuous-in-time observations. The "collapsed state-vector" after the
"objectification" is simply treated as a random vector of the a posteriori
state given by the quantum filtering, i.e., the conditioning of the a priori
induced state on the corresponding reduced algebra. The nonlinear
phenomenological equation of "continuous spontaneous localization" has been
derived from the Schroedinger equation as a case of the quantum filtering
equation for the diffusive nondemolition measurement. The quantum theory of
measurement and filtering suggests also another type of the stochastic equation
for the dynamical theory of continuous reduction, corresponding to the counting
nondemolition measurement, which is more relevant for the quantum experiments.


title: Measurements continuous in time and a posteriori states in quantum

abstract:
  Measurements continuous in time were consistently introduced in quantum
mechanics and applications worked out, mainly in quantum optics. In this
context a quantum filtering theory has been developed giving the reduced state
after the measurement when a certain trajectory of the measured observables is
registered (the a posteriori states). In this paper a new derivation of
filtering equations is presented, in the cases of counting processes and of
measurement processes of diffusive type. It is also shown that the equation for
the a posteriori dynamics in the diffusive case can be obtained, by a suitable
limit, from that one in the counting case. Moreover, the paper is intended to
clarify the meaning of the various concepts involved and to discuss the
connections among them. As an illustration of the theory, simple models are
worked out.


title: Weakened linearity for quantum fields

abstract:
  There are still no interacting models of the Wightman axioms, suggesting that
the axioms are too tightly drawn. Here a weakening of linearity for quantum
fields is proposed, with the algebra still linear but with the quantum fields
no longer required to be tempered distributions, allowing explicit interacting
quantum field models. Interacting quantum fields should be understood to be
nonlinear quantum fields in this sense, because a set of effective field
theories encodes a dependence on the energy scale of measurement -- which is a
nontrivial property of the test functions -- so that correlation functions are
implicitly nonlinear functions of test functions in the conventional formalism.
In Local Quantum Physics terms, the algebraic models constructed here do not
satisfy the additivity property. Finite nonlinear deformations of quantized
electromagnetism are constructed as examples.


title: Nonlocality III: General Nonlocality in Quantum Fields

abstract:
  The waves of fermions display nonlocality in low energy limit of quantum
fields. In this \QTR{it}{ab initio} paper we propose a complex-geometry model
that reveals the affection of nonlocality on the interaction between material
particles of spin-1/2. To make nonlocal properties appropriately involved in a
quantum theory, the special unitary group SU(n) and spinor representation
$D^{(1/2,1/2)}$ of Lorentz group are generalized by making complex
spaces--which are spanned by wave functions of quantum particles--curved. The
curved spaces are described by the geometry used in General Relativity by
replacing the real space with complex space and additionally imposing the
analytic condition on the space. The field equations for fermions and for
bosons are respectively associated with geodesic motion equations and with
local curvature of the considered space. The equation for fermions can restore
all the terms of quadratic form of Dirac equation. According to the field
equation it is found that, for the U(1) field [generalized Quantum
Electrodynamics (QED)], when the electromagnetic fields $\vec E$ and $\vec B$
satisfy $\vec E^2-\vec B^2\neq 0$, the bosons will gain masses. In this model,
a physical region is empirically defined, which can be characterized by a
determinant occurring in boson field equation. Applying the field equation to
U(3) field [generalized Quantum Chromodynamics (QCD)], the quark-confining
property can be understood by carrying out the boundary of physical region.


title:
A Stochastic Hamiltonian Approach for Quantum Jumps, Spontaneous
  Localizations, and Continuous Trajectories

abstract:
  We give an explicit stochastic Hamiltonian model of discontinuous unitary
evolution for quantum spontaneous jumps like in a system of atoms in quantum
optics, or in a system of quantum particles that interacts singularly with
"bubbles" which admit a continual counting observation. This model allows to
watch a quantum trajectory in a photodetector or in a cloud chamber by
spontaneous localisations of the momentums of the scattered photons or bubbles.
Thus, the continuous reduction and spontaneous localization theory is obtained
from a Hamiltonian singular interaction as a result of quantum filtering, i.e.,
a sequential time continuous conditioning of an input quantum process by the
output measurement data. We show that in the case of indistinguishable
particles or atoms the a posteriori dynamics is mixing, giving rise to an
irreversible Boltzmann-type reduction equation. The latter coincides with the
nonstochastic Schroedinger equation only in the mean field approximation,
whereas the central limit yelds Gaussian mixing fluctuations described by a
quantum state reduction equation of diffusive type.


title: Quantum state tomography of molecular rotation

abstract:
  We show how the rotational quantum state of a linear or symmetric top rotor
can be reconstructed from finite time observations of the polar angular
distribution under certain conditions. The presented tomographic method can
reconstruct the complete rotational quantum state in many non-adiabatic
alignment experiments. Our analysis applies for measurement data available with
existing measurement techniques.


title:
The role of initial state reconstruction in short and long time
  deviations from exponential decay

abstract:
  We consider the role of the reconstruction of the initial state in the
deviation from exponential decay at short and long times. The long time decay
can be attributed to a wave that was, in a classical-like, probabilistic sense,
fully outside the initial state or the inner region at intermediate times,
i.e., to a completely reconstructed state, whereas the decay during the
exponential regime is due instead to a non-reconstructed wave. At short times
quantum interference between regenerated and non-regenerated paths is
responsible for the deviation from the exponential decay. We may thus conclude
that state reconstruction is a ``consistent history'' for long time deviations
but not for short ones.


title: Locality of quantum entanglement

abstract:
  This article presents a local realistic interpretation of quantum
entanglement. The entanglement is explained as innate interference between the
non-empty state associated with the peaked piece of one particle and the empty
states associated with the non-peaked pieces of the others of entangled
particles, which inseparably join together. The correlation of the results of
measurements on the ensemble of composite entangled systems is related to this
kind of interference. Consequently, there is no nonlocal influence between
entangled particles in measurements. Particularly, this explanation thus rules
out the possibility of quantum teleportation which is nowadays considered as
one of cornerstones of quantum information processing. Besides, likewise,
communication and computation schemes based on alleged spooky action at a
distance are unlikely to be promising.


title:
On the Dynamical Interpretation for the Quantum-Measurement Projection
  Postulate

abstract:
  An apparatus model with discrete momentum space suitable for the exact
solution of the problem is considered. The special Hamiltonian of its
interaction with the object system under consideration is chosen. In this
simple case it is easy to illustrate how difficulties in constructing the
dynamical interpretation of selective collapse could be overcomed without any
limiting procedure. For this purpose one can apply either averaging with
respect to a non-quantum parameter or reducing the algebra of the joint system
operators (i. e. passing to the quantum system subalgebra). The latter
procedure effectively implies averaging with respect to apparatus quantum
variables not belonging to the system.


title: Measurable entanglement

abstract:
  Amount of entanglement carried by a quantum bipartite state is usually
evaluated in terms of concurrence (see Ref. 1). We give a physical
interpretation of concurrence that reveals a way of its direct measurement and
discuss possible generalizations.


title: Bohm-Aharonov type effects in dissipative atomic systems

abstract:
  A state in quantum mechanics is defined as a positive operator of norm 1. For
finite systems, this may be thought of as a positive matrix of trace 1. This
constraint of positivity imposes severe restrictions on the allowed evolution
of such a state. From the mathematical viewpoint, we describe the two forms of
standard dynamical equations - global (Kraus) and local (Lindblad) - and show
how each of these gives rise to a semi-group description of the evolution. We
then look at specific examples from atomic systems, involving 3-level systems
for simplicity, and show how these mathematical constraints give rise to
non-intuitive physical phenomena, reminiscent of Bohm-Aharonov effects.
  In particular, we show that for a multi-level atomic system it is generally
impossible to isolate the levels, and this leads to observable effects on the
population relaxation and decoherence.


title: Multiparticle entanglement and ranks of density matrices

abstract:
  Based on the ranks of reduced density matrices, we derive necessary
conditions for the separability of multiparticle arbitrary-dimensional mixed
states, which are equivalent to sufficient conditions for entanglement. In a
similar way we obtain necessary conditions for the separability of a given
mixed state with respect to partitions of all particles of the system into
subsets. The special case of pure states is discussed separately.


title:
Capacities of noiseless quantum channels for massive indistinguishable
  particles: Bosons vs. fermions

abstract:
  We consider information transmission through a noiseless quantum channel,
where the information is encoded into massive indistinguishable particles:
bosons or fermions. We study the situation in which the particles are
noninteracting. The encoding input states obey a set of physically motivated
constraints on the mean values of the energy and particle number. In such a
case, the determination of both classical and quantum capacity reduces to a
constrained maximization of entropy. In the case of noninteracting bosons,
signatures of Bose Einstein condensation can be observed in the behavior of the
capacity. A major motivation for these considerations is to compare the
information carrying capacities of channels that carry bosons with those that
carry fermions. We show analytically that fermions generally provide higher
channel capacity, i.e., they are better suited for transferring bits as well as
qubits, in comparison to bosons. This holds for a large range of power law
potentials, and for moderate to high temperatures. Numerical simulations seem
to indicate that the result holds for all temperatures. Also, we consider the
low temperature behavior for the three-dimensional box and harmonic trap, and
again we show that the fermionic capacity is higher than the bosonic one for
sufficiently low temperatures.


title: On the logical structure of Bell theorems without inequalities

abstract:
  Bell theorems show how to experimentally falsify local realism. Conclusive
falsification is highly desirable as it would provide support for the most
profoundly counterintuitive feature of quantum theory - nonlocality. Despite
the preponderance of evidence for quantum mechanics, practical limits on
detector efficiency and the difficulty of coordinating space-like separated
measurements have provided loopholes for a classical worldview; these loopholes
have never been simultaneously closed. A number of new experiments have
recently been proposed to close both loopholes at once. We show some of these
novel designs fail in the most basic way, by not ruling out local hidden
variable models, and we provide an explicit classical model to demonstrate
this. They share a common flaw, which reveals a basic misunderstanding of how
nonlocality proofs work. Given the time and resources now being devoted to such
experiments, theoretical clarity is essential. Our explanation is presented in
terms of simple logic and should serve to correct misconceptions and avoid
future mistakes. We also show a nonlocality proof involving four participants
which has interesting theoretical properties.


title: Tachyons and EPR correlations

abstract:
  No causal paradoxes will occur if a preferred reference frame for tachyons
propagation is assumed, and results of Bell's inequality experiments may be
well explained without using any telepathyc effect. We can read G. Faraci's and
others' results, Lettere al Nuovo Cimento, 15, 607-611 (1974), as a first
quantitive indication on the tachyons preferred reference frame velocity with
respect to the Earth, as well as on the tachyons velocity in their preferred
reference frame. In order to experimentally prove this assumption's validity,
Aspect-like experiments should be slightly modified.


title:
"Quantum-states-as-information" meets Wigner's friend: A comment on
  Hagar and Hemmo

abstract:
  This is a comment on the paper by Hagar and Hemmo (quant-ph/0512095) in which
they suggest that information-theoretic approaches to quantum theory are
incomplete.


title:
Study of localization in the quantum sawtooth map emulated on a quantum
  information processor

abstract:
  Quantum computers will be unique tools for understanding complex quantum
systems. We report an experimental implementation of a sensitive, quantum
coherence-dependent localization phenomenon on a quantum information processor
(QIP). The localization effect was studied by emulating the dynamics of the
quantum sawtooth map in the perturbative regime on a three-qubit QIP. Our
results show that the width of the probability distribution in momentum space
remained essentially unchanged with successive iterations of the sawtooth map,
a result that is consistent with localization. The height of the peak relative
to the baseline of the probability distribution did change, a result that is
consistent with our QIP being an ensemble of quantum systems with a
distribution of errors over the ensemble. We further show that the previously
measured distributions of control errors correctly account for the observed
changes in the probability distribution.


title: The Nondemolition Measurement of Quantum Time

abstract:
  The problem of time operator in quantum mechanics is revisited. The unsharp
measurement model for quantum time based on the dynamical system-clock
interaction, is studied. Our analysis shows that the problem of the quantum
time operator with continuous spectrum cannot be separated from the measurement
problem for quantum time.


title:
Quantum Stochastics, Dirac Boundary Value Problem, and the Ultra
  Relativistic Limit

abstract:
  We prove that a single-jump quantum stochastic unitary evolution is
equivalent to a Dirac boundary value problem on the half line in an extra
dimension. This amounts to the equivalence of the quantum measurement
boundary-value problem in infinite number particles space to the stochastic
calculus in Fock space. It is shown that this exactly solvable model can be
obtained from a Schroedinger boundary value problem for a positive relativistic
Hamiltonian in the half-line as the inductive ultra relativistic limit,
correspondent to the input flow of Dirac particles with asymptotically infinite
momenta. Thus the stochastic limit can be interpreted in terms of quantum
stochastic scheme for time-continuous non-demolition observation. The question
of microscopic time reversibility is also studied for this paper.


title: Random Delayed-Choice Quantum Eraser via Two-Photon Imaging

abstract:
  We report on a delayed-choice quantum eraser experiment based on a two-photon
imaging scheme using entangled photon pairs. After the detection of a photon
which passed through a double-slit, a random delayed choice is made to erase or
not erase the which-path information by the measurement of its distant
entangled twin; the particle-like and wave-like behavior of the photon are then
recorded simultaneously and respectively by only one set of joint detection
devices. The present eraser takes advantage of two-photon imaging. The complete
which-path information of a photon is transferred to its distant entangled twin
through a "ghost" image. The choice is made on the Fourier transform plane of
the ghost image between reading "complete information" or "partial information"
of the double-path.


title:
Quantum Noise, Bits and Jumps: Uncertainties, Decoherence, Trajectories
  and Filtering

abstract:
  It is shown that many dissipative phenomena of "old" quantum mechanics which
appeared 100 years ago in the form of the statistics of quantum thermal noise
and quantum spontaneous jumps, have never been explained by the "new"
conservative quantum mechanics discovered 75 years ago by Heisenberg and
Schroedinger. This led to numerous quantum paradoxes which are reconsidered in
this paper. The development of quantum measurement theory, initiated by von
Neumann, indicated a possibility for resolution of this interpretational crisis
by divorcing the algebra of the dynamical generators from the algebra of the
actual observables. It is shown that within this approach quantum causality can
be rehabilitated in the form of a superselection rule for compatibility of past
observables with the potential future. This rule, together with the
self-compatibility of measurements insuring the consistency of histories, is
called the nondemolition principle. The application of this causality condition
in the form of the dynamical commutation relations leads to the derivation of
the generalized von Neumann reductions, usharp, instantaneous, spontaneous, and
even continuous in time. This gives a quantum probabilistic solution, in the
form of the dynamical filtering equations, of the notorious measurement problem
which was tackled unsuccessfully by many famous physicists starting with
Schroedinger and Bohr. The simplest Markovian quantum stochastic model for the
continuous in time measurements involves a boundary-value problem in second
quantization for input "offer" waves in one extra dimension, and a reduction of
the algebra of "actual" observables to an Abelian subalgebra for the output
waves.


title: Quantum Computation, Complexity, and Many-Body Physics

abstract:
  Recently developed quantum algorithms suggest that quantum computers can
solve certain problems and perform certain tasks more efficiently than
conventional computers. Among other reasons, this is due to the possibility of
creating non-classical correlations, or quantum entanglement, which is a
phenomena hard or impossible to reproduce by classical-information methods.
  In this thesis I first investigate the simulation of quantum systems on a
quantum computer constructed of two-level quantum elements or qubits. For this
purpose, I present algebra mappings that allow one to obtain physical
properties and compute correlation functions of fermionic, anyonic, and bosonic
systems with such a computer. The results obtained show that the complexity of
preparing a quantum state which contains the desired information for the
computation is crucial.
  Second, I present a wide class of quantum computations, which could involve
entangled states, that can be simulated with the same efficiency on both types
of computers. The notion of generalized quantum entanglement then naturally
emerges. This generalization of entanglement is based on the idea that
entanglement is an observer-dependent concept, that is, relative to a set of
preferred observables.


title: Decoherence assisting a measurement-driven quantum evolution process

abstract:
  We study the problem of driving an unknown initial mixed quantum state onto a
known pure state without using unitary transformations. This can be achieved,
in an efficient manner, with the help of sequential measurements on at least
two unbiased bases. However here we found that, when the system is affected by
a decoherence mechanism, only one observable is required in order to achieve
the same goal. In this way the decoherence can assist the process. We show
that, depending on the sort of decoherence, the process can converge faster or
slower than the method implemented by means of two complementary observables.


title:
A position dependent atom-atom entanglement in real-time Cavity QED
  system

abstract:
  We study a special two-atom entanglement case in assumed Cavity QED
experiment in which only one atom effectively exchanges a single photon with a
cavity mode. We compute diatom entanglement under position-dependent atomic
resonant dipole-dipole interaction (RDDI) for large interatomic separation
limit. We show that the RDDI, even which is much smaller than the maximal
atomic Rabi frequency, can induce distinct diatom entanglement. The peak
entanglement (PE) reaches a maximum when RDDI strength can compare with the
Rabi frequency of an atom.


title:
Observation of Four-Photon de Broglie Wavelength by State Projection
  Measurement

abstract:
  A measurement process is constructed to project an arbitrary two-mode
$N$-photon state to a maximally entangled $N$-photon state (the {\it
NOON}-state). The result of this projection measurement shows a typical
interference fringe with an $N$-photon de Broglie wavelength. For an
experimental demonstration, this measurement process is applied to a
four-photon superposition state from two perpendicularly oriented type-I
parametric down-conversion processes. Generalization to arbitrary $N$-photon
states projection measurement can be easily made and may have wide applications
in quantum information. As an example, we formulate it for precision phase
measurement.