title: Optimal fingerprinting strategies with one-sided error

abstract:
  Fingerprinting enables two parties to infer whether the messages they hold
are the same or different when the cost of communication is high: each message
is associated with a smaller fingerprint and comparisons between messages are
made in terms of their fingerprints alone. In the simultaneous message passing
model, it is known that fingerprints composed of quantum information can be
made exponentially smaller than those composed of classical information. For
small message lengths, we present constructions of optimal classical
fingerprinting strategies with one-sided error, in both the one-way and
simultaneous message passing models, and provide bounds on the worst-case error
probability with the help of extremal set theory. The performance of these
protocols is then compared to that for quantum fingerprinting strategies
constructed from spherical codes, equiangular tight frames and mutually
unbiased bases.


title: The Entanglement of Superpositions

abstract:
  Given a bipartite quantum state (in arbitrary dimension) and a decomposition
of it as a superposition of two others, we find bounds on the entanglement of
the superposition state in terms of the entanglement of the states being
superposed. In the case that the two states being superposed are bi-orthogonal,
the answer is simple, and, for example, the entanglement of the superposition
cannot be more than one e-bit more than the average of the entanglement of the
two states being superposed. However for more general states, the situation is
very different.


title:
Generation of generalized coherent states with two coupled Bose-Einstein
  condensates

abstract:
  We present a scheme to prepare generalized coherent states in a system with
two species of Bose-Einstein condensates. First, within the two-mode
approximation, we demonstrate that a Schrodinger cat-like can be dynamically
generated and, by controlling the Josephson-like coupling strength, the number
of coherent states in the superposition can be varied. Later, we analyze
numerically the dynamics of the whole system when interspecies collisions are
inhibited. Variables such as fractional population, Mandel parameter and
variances of annihilation and number operators are used to show that the
evolved state is entangled and exhibits sub-Poisson statistics.


title: Another Look at Quantum Teleportation

abstract:
  A dialog with Asher Peres regarding the meaning of quantum teleportation is
briefly reviewed. The Braunstein-Kimble method for teleportation of light is
analyzed in the language of quantum wave functions. A pictorial example of
continuous variable teleportation is presented using computer simulation.


title:
Comment on 'Quantum Theory Looks at Time Travel' by D.Greenberger &
  K.Svozil

abstract:
  It is claimed in the above paper that, if time travel were possible, quantum
propagation would prevent classic time travel paradoxes by establishing
consistent loops; an example circuit is used to demonstrate such a loop. It is
argued here that established loops are not the framework in which the classic
paradoxes arise; rather they arise via the establishment of a concrete initial
history in which no disturbing time travel is allowed and then disturbing that
history via the launch of the time traveller. It is shown that, operated in
this two-pass fashion, if the first forward evolution of their circuit produces
a definite triggering of a backwards time travelling state, the re-evolution
thereby engendered may be organised so as to prohibit the triggering of this
state, thereby creating a classic time travel paradox.


title:
Phase-space descriptions of operators and the Wigner distribution in
  quantum mechanics I. A Dirac inspired view

abstract:
  Drawing inspiration from Dirac's work on functions of non commuting
observables, we develop a fresh approach to phase space descriptions of
operators and the Wigner distribution in quantum mechanics. The construction
presented here is marked by its economy, naturalness and more importantly, by
its potential for extensions and generalisations to situations where the
underlying configuration space is non Cartesian.


title:
Phase-space descriptions of operators and the Wigner distribution in
  quantum mechanics II. The finite dimensional case

abstract:
  A complete solution to the problem of setting up Wigner distribution for
N-level quantum systems is presented. The scheme makes use of some of the ideas
introduced by Dirac in the course of defining functions of noncommuting
observables and works uniformly for all N. Further, the construction developed
here has the virtue of being essentially input-free in that it merely requires
finding a square root of a certain N^2 x N^2 complex symmetric matrix, a task
which, as is shown, can always be accomplished analytically. As an
illustration, the case of a single qubit is considered in some detail and it is
shown that one recovers the result of Feynman and Wootters for this case
without recourse to any auxiliary constructs.


title:
Ancilla-Assisted Enhancement of Channel Estimation for Low-Noise
  Parameters

abstract:
  In order to make a unified treatment for estimation problems of a very small
noise or a very weak signal in a quantum process, we introduce the notion of a
low-noise quantum channel with one noise parameter. It is known in several
examples that prior entanglement together with nonlocal output measurement
improves the performance of the channel estimation. In this paper, we study
this ``ancilla-assisted enhancement'' for estimation of the noise parameter in
a general low-noise channel. For channels on two level systems we prove that
the enhancement factor, the ratio of the Fisher information of the
ancilla-assisted estimation to that of the original one, is always upper
bounded by 3/2. Some conditions for the attainability are also given with
illustrative examples.


title: Lorentz-covariant reduced spin density matrix and EPR-Bohm correlations

abstract:
  We show that it is possible to define a Lorentz-covariant reduced spin
density matrix for massive particles. Such a matrix allows one to calculate the
mean values of observables connected with spin measurements (average
polarizations). Moreover, it contains not only information about polarization
of the particle but also information about its average kinematical state. We
also use our formalism to calculate the correlation function in the
Einstein--Podolsky--Rosen--Bohm type experiment with massive relativistic
particles.


title: Effect of noise and enhancement of nonlocality in on/off photodetection

abstract:
  Nonlocality of two-mode states of light is addressed by means of CHSH
inequality based on displaced on/off photodetection. Effects due to non-unit
quantum efficiency and nonzero dark counts are taken into account. Nonlocality
of both balanced and unbalanced superpositions of few photon-number states, as
well as that of multiphoton twin beams, is investigated. We find that
unbalanced superpositions show larger nonlocality than balanced one when noise
affects the photodetection process. De-Gaussification by means of
(inconclusive) photon subtraction is shown to enhance nonlocality of twin beams
in the low energy regime. We also show that when the measurement is described
by a POVM, rather than a set of projectors, the maximum achievable value of the
Bell parameter in the CHSH inequality is decreased, and is no longer given by
the Cirel'son bound.


title:
Reduced randomness in quantum cryptography with sequences of qubits
  encoded in the same basis

abstract:
  We consider the cloning of sequences of qubits prepared in the states used in
the BB84 or 6-state quantum cryptography protocol, and show that the
single-qubit fidelity is unaffected even if entire sequences of qubits are
prepared in the same basis. This result is of great importance for practical
quantum cryptosystems because it reduces the need for high-speed random number
generation without impairing on the security against finite-size attacks.


title: Experimental demonstration of time coding quantum key distribution

abstract:
  Time coding quantum key distribution with coherent faint pulses is
experimentally demonstrated. A measured 3.3 % quantum bit error rate and a
relative contrast loss of 8.4 % allow a 0.49 bit/pulse advantage to Bob.


title:
On the Complexity of Searching Maximum of a Function on a Quantum
  Computer

abstract:
  We deal with a problem of finding maximum of a function from the Holder class
on a quantum computer. We show matching lower and upper bounds on the
complexity of this problem. We prove upper bounds by constructing an algorithm
that uses the algorithm for finding maximum of a discrete sequence. To prove
lower bounds we use results for finding logical OR of sequence of bits. We show
that quantum computation yields a quadratic speed-up over deterministic and
randomized algorithms.


title: Differential atom interferometry beyond the standard quantum limit

abstract:
  We analyze methods to go beyond the standard quantum limit for a class of
atomic interferometers, where the quantity of interest is the difference of
phase shifts obtained by two independent atomic ensembles. An example is given
by an atomic Sagnac interferometer, where for two ensembles propagating in
opposite directions in the interferometer this phase difference encodes the
angular velocity of the experimental setup. We discuss methods of squeezing
separately or jointly observables of the two atomic ensembles, and compare in
detail advantages and drawbacks of such schemes. In particular we show that the
method of joint squeezing may improve the variance by up to a factor of 2. We
take into account fluctuations of the number of atoms in both the preparation
and the measurement stage, and obtain bounds on the difference of the numbers
of atoms in the two ensembles, as well as on the detection efficiency, which
have to be fulfilled in order to surpass the standard quantum limit. Under
realistic conditions, the performance of both schemes can be improved
significantly by reading out the phase difference via a quantum non-demolition
(QND) measurement. Finally, we discuss a scheme using macroscopically entangled
ensembles.


title:
On Multiparticle Entanglement via Resonant Interaction between Light and
  atomic Ensembles

abstract:
  Multiparticle entangled states generated via interaction between narrow-band
light and an ensemble of identical two-level atoms are considered. Depending on
the initial photon statistics, correlation between atoms and photons can give
rise to entangled states of these systems. It is found that the state of any
pair of atoms interacting with weak single-mode squeezed light is inseparable
and robust against decay. Optical schemes for preparing entangled states of
atomic ensembles by projective measurement are described.


title: Trojan Horse attacks on Quantum Key Distribution systems

abstract:
  General Trojan horse attacks on quantum key distribution systems are
analyzed. We illustrate the power of such attacks with today's technology and
conclude that all system must implement active counter-measures. In particular
all systems must include an auxiliary detector that monitors any incoming
light. We show that such counter-measures can be efficient, provided enough
additional privacy amplification is applied to the data. We present a practical
way to reduce the maximal information gain that an adversary can gain using
Trojan horse attacks. This does reduce the security analysis of the 2-way {\it
Plug-&-Play} system to those of the standard 1-way systems.


title: Strategies for Real-Time Position Control of a Single Atom in Cavity QED

abstract:
  Recent realizations of single-atom trapping and tracking in cavity QED open
the door for feedback schemes which actively stabilize the motion of a single
atom in real time. We present feedback algorithms for cooling the radial
component of motion for a single atom trapped by strong coupling to
single-photon fields in an optical cavity. Performance of various algorithms is
studied through simulations of single-atom trajectories, with full dynamical
and measurement noise included. Closed loop feedback algorithms compare
favorably to open-loop "switching" analogs, demonstrating the importance of
applying actual position information in real time. The high optical information
rate in current experiments enables real-time tracking that approaches the
standard quantum limit for broadband position measurements, suggesting that
realistic active feedback schemes may reach a regime where measurement
backaction appreciably alters the motional dynamics.


title: Theory of Photon Blockade by an Optical Cavity with One Trapped Atom

abstract:
  In our recent paper [1], we reported observations of photon blockade by one
atom strongly coupled to an optical cavity. In support of these measurements,
here we provide an expanded discussion of the general phenomenology of photon
blockade as well as of the theoretical model and results that were presented in
Ref. [1]. We describe the general condition for photon blockade in terms of the
transmission coefficients for photon number states. For the atom-cavity system
of Ref. [1], we present the model Hamiltonian and examine the relationship of
the eigenvalues to the predicted intensity correlation function. We explore the
effect of different driving mechanisms on the photon statistics. We also
present additional corrections to the model to describe cavity birefringence
and ac-Stark shifts. [1] K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T.
E. Northup, and H. J. Kimble, Nature 436, 87 (2005).


title:
Efficient construction of 2-D cluster states with probabilistic quantum
  gates

abstract:
  We propose an efficient scheme for constructing arbitrary 2-D cluster states
using probabilistic entangling quantum gates.In our scheme, the 2-D cluster
state is constructed with star-like basic units generated from 1-D cluster
chains.By applying parallel operations, the process of generating 2-D (or
higher dimensional) cluster states is significantly accelerated, which provides
an efficient way to implement realistic one way quantum computers.


title:
Entanglement of two-mode Gaussian states: characterization and
  experimental production and manipulation

abstract:
  A powerful theoretical structure has emerged in recent years on the
characterization and quantification of entanglement in continuous-variable
systems. After reviewing this framework, we will illustrate it with an original
set-up based on a type-II OPO with adjustable mode coupling. Experimental
results allow a direct verification of many theoretical predictions and provide
a sharp insight into the general properties of two-mode Gaussian states and
entanglement resource manipulation.


title:
A scheme for the teleportation of multiqubit quantum information via the
  control of many agents in a network

abstract:
  We present a new scheme for teleporting multiqubit quantum information from a
sender to a distant receiver via the control of many agents in a network. We
show that the receiver can successfully restore the original state of each
qubit as long as all the agents cooperate. However, it is remarkable that for
certain type of teleported states, the receiver can not gain any amplitude
information even if one agent does not collaborate. In addition, our analysis
shows that for general input states of each message qubit, the average fidelity
for the output states, when even one agent does not take action, is the same as
that for the previous proposals.


title: Distributing a multiparticle state by entanglement swapping

abstract:
  Using entanglement swapping, we construct a scheme to distribute an arbitrary
multiparticle state to remote receivers. Only Bell states and two-qubit
collective measurements are required.


title: On the geometry of a class of N-qubit entanglement monotones

abstract:
  A family of N-qubit entanglement monotones invariant under stochastic local
operations and classical communication (SLOCC) is defined. This class of
entanglement monotones includes the well-known examples of the concurrence, the
three-tangle, and some of the four, five and N-qubit SLOCC invariants
introduced recently. The construction of these invariants is based on bipartite
partitions of the Hilbert space in the form ${\bf C}^{2^N}\simeq{\bf
C}^L\otimes{\bf C}^l$ with $L=2^{N-n}\geq l=2^n$. Such partitions can be given
a nice geometrical interpretation in terms of Grassmannians Gr(L,l) of l-planes
in ${\bf C}^L$ that can be realized as the zero locus of quadratic polinomials
in the complex projective space of suitable dimension via the Plucker
embedding. The invariants are neatly expressed in terms of the Plucker
coordinates of the Grassmannian.


title: The quantum double well anharmonic oscillator in an external field

abstract:
  The aim of this paper is twofold. First of all, we study the behaviour of the
lowest eigenvalues of the quantum anharmonic oscillator under influence of an
external field. We try to understand this behaviour using perturbation theory
and compare the results with numerical calculations. This brings us to the
second aim of selecting the best method to carry out the numerical calculations
accurately.


title:
Maximally entangled mixed states of two atoms trapped inside an optical
  cavity

abstract:
  In some off-resonant cases, the reduced density matrix of two atoms
symmetrically coupled with an optical cavity can very approximately approach to
maximally entangled mixed states or maximal Bell violation mixed states in
their evolution. The influence of phase decoherence on the generation of
maximally entangled mixed state is also discussed.
  PACS numbers: 03.67.-a, 03.65.Ud


title: Optimal estimation of SU(d) using exact and approximate 2-designs

abstract:
  We consider the problem of estimating an SU(d) quantum operation when n
copies of it are available at the same time. It is well known that, if one uses
a separable state as the input for the unitaries, the optimal mean square error
will decrease as 1/n. However it is shown here that, if a proper entangled
state is used, the optimal mean square error will decrease at a 1/n^2 rate. It
is also shown that spherical 2-designs (e.g. complete sets of mutually unbiased
bases and symmetric informationally complete positive operator valued measures)
can be used to design optimal input states. Although 2-designs are believed to
exist for every dimension, this has not yet been proven. Therefore, we give an
alternative input state based on approximate 2-designs which can be made
arbitrarily close to optimal. It is shown that measurement strategies which are
based on local operations and classical communication between the ancilla and
the rest of the system can be optimal.


title: Broadband laser cooling of trapped atoms with ultrafast pulses

abstract:
  We demonstrate broadband laser cooling of atomic ions in an rf trap using
ultrafast pulses from a modelocked laser. The temperature of a single ion is
measured by observing the size of a time-averaged image of the ion in the known
harmonic trap potential. While the lowest observed temperature was only about 1
K, this method efficiently cools very hot atoms and can sufficiently localize
trapped atoms to produce near diffraction-limited atomic images.


title:
Resource requirements of private quantum channels and consequence for
  oblivious remote state preparation

abstract:
  Shannon in celebrated works had shown that n bits of shared key is necessary
and sufficient to transmit n-bit classical information in an
information-theoretically secure way. Ambainis, Mosca, Tapp and de Wolf in
quant-ph/0003101 considered a more general setting, referred to as Private
quantum channels, in which instead of classical information, quantum states are
required to be transmitted and only one-way communication is allowed. They show
that in this case 2n bits of shared key is necessary and sufficient to transmit
an n-qubit state. We consider the most general setting in which we allow for
all possible combinations i.e. we let the input to be transmitted, the message
sent and the shared resources to be classical/quantum. We develop a general
framework by which we are able to show tight bounds on communication/shared
resources in all of these cases and this includes the results of Shannon and
Ambainis et al.
  As a consequence of our arguments we also show that in a one-way oblivious
Remote state preparation protocol for transferring an n-qubit pure state, the
entropy of the communication must be 2n and the entanglement measure of the
shared resource must be n. This generalizes on the result of Leung and Shor
which shows same bound on the length of communication in the special case when
the shared resource is maximally entangled e.g. EPR pairs and hence settles an
open question asked in their paper regarding protocols without maximally
entangled shared resource.


title: Measuring non-linear functionals of quantum harmonic oscillator states

abstract:
  Using only linear interactions and a local parity measurement we show how
entanglement can be detected between two harmonic oscillators. The scheme
generalizes to measure both linear and non-linear functionals of an arbitrary
oscillator state. This leads to many applications including purity tests,
eigenvalue estimation, entropy and distance measures - all without the need for
non-linear interactions or complete state reconstruction. Remarkably,
experimental realization of the proposed scheme is already within the reach of
current technology with linear optics.


title:
Entanglement monotones for multi-qubit states based on geometric
  invariant theory

abstract:
  We construct entanglement monotones for multi-qubit states based on
Pl\"{u}cker coordinate equations of Grassmann variety, which are central notion
in geometric invariant theory. As an illustrative example, we in details
investigate entanglement monotones of a three-qubit state.


title: Homodyne tomography and the reconstruction of quantum states of light

abstract:
  Quantum tomography is a procedure to determine the quantum state of a
physical system, or equivalently, to estimate the expectation value of any
operator. It consists in appropriately averaging the outcomes of the
measurement results of different observables, obtained on identical copies of
the same system. Alternatively, it consists in maximizing an appropriate
likelihood function defined on the same data. The procedure can be also used to
completely characterize an unknown apparatus. Here we focus on the
electromagnetic field, where the tomographic observables are obtained from
homodyne detection.


title: Two-Photon Entanglement in a Two-Mode Supersymmetric Model

abstract:
  We will study entangled two-photon states generated from a two-mode
supersymmetric model and quantify degree of entanglement in terms of the
entropy of entanglement. The influences of the nonlinearity on the degree of
entanglement is also examined, and it is shown that amount of entanglement
increase with increasing the nonlinear coupling constant.


title: Teleportation with trapped ions in a magnetic field gradient

abstract:
  By means of the Ising terms generated by Coulomb interaction between ions and
the magnetic field gradient, we carry out teleportation with insurance with
trapped ions. We show the feasibility and the favorable feature of our scheme
by comparing with the recently achieved teleportation experiments with trapped
ions.


title: Minimax discrimination of two Pauli channels

abstract:
  We consider the problem of optimally discriminating two Pauli channels in the
minimax strategy, maximizing the smallest of the probabilities of correct
identification of the channel. We find the optimal input state at the channel
and show the conditions under which using entanglement strictly enhances
distinguishability. We finally compare the minimax strategy with the Bayesian
one.


title:
Mesoscopic superposition and sub-Planck-scale structure in molecular
  wave packets

abstract:
  We demonstrate the possibility of realizing sub-Planck-scale structures in
the mesoscopic superposition of molecular wave packets involving vibrational
levels. The time evolution of the wave packet, taken here as the SU(2) coherent
state of the Morse potential describing hydrogen iodide molecules, produces
macroscopicquantum- superposition-like states, responsible for the above
phenomenon. We investigate the phase-space dynamics of the coherent state
through the Wigner function approach and identify the interference phenomena
behind the sub-Planck-scale structures. The optimal parameter ranges are
specified for observing these features.


title: Harmonic entanglement with second-order non-linearity

abstract:
  We investigate the second-order non-linear interaction as a means to generate
entanglement between fields of differing wavelengths. And show that perfect
entanglement can, in principle, be produced between the fundamental and second
harmonic fields in these processes. Neither pure second harmonic generation,
nor parametric oscillation optimally produce entanglement, such optimal
entanglement is rather produced by an intermediate process. An experimental
demonstration of these predictions should be imminently feasible.


title: Weak nonlinearities: A new route to optical quantum computation

abstract:
  Quantum information processing (QIP) offers the promise of being able to do
things that we cannot do with conventional technology. Here we present a new
route for distributed optical QIP, based on generalized quantum non-demolition
measurements, providing a unified approach for quantum communication and
computing. Interactions between photons are generated using weak
non-linearities and intense laser fields--the use of such fields provides for
robust distribution of quantum information. Our approach requires only a
practical set of resources, and it uses these very efficiently. Thus it
promises to be extremely useful for the first quantum technologies, based on
scarce resources. Furthermore, in the longer term this approach provides both
options and scalability for efficient many-qubit QIP.


title:
Spectral singularities of non-Hermitian Hamiltonians and SUSY
  transformations

abstract:
  Simple examples of non-Hermitian Hamiltonians with purely real spectra
defined in $L^2(R^+)$ having spectral singularities inside the continuous
spectrum are given. It is shown that such Hamiltonians may appear by shifting
the ndependent variable of a real potential into the complex plane. Also they
may be created as SUSY partners of Hermitian Hamiltonians. In the latter case
spectral singularities of a non-Hermitian Hamiltonian are ordinary points of
the continuous spectrum for its Hermitian SUSY partner. Conditions for
transformation functions are formulated when a complex potential with complex
eigenenergies and spectral singularities has a SUSY partner with a real
spectrum without spectral singularities. Finally we shortly discuss why
Hamiltonians with spectral singularities are `bad'.


title: Experimental violation of a cluster state Bell inequality

abstract:
  Cluster states are a new type of multiqubit entangled states with
entanglement properties exceptionally well suited for quantum computation. In
the present work, we experimentally demonstrate that correlations in a
four-qubit linear cluster state cannot be described by local realism. This
exploration is based on a recently derived Bell-type inequality [V. Scarani et
al., Phys. Rev A 71, 042325 (2005)] which is tailored, by using a combination
of three- and four-particle correlations, to be maximally violated by cluster
states but not violated at all by GHZ states. We observe a cluster state Bell
parameter of $2.59\pm 0.08$, which is more than 7 standard deviations larger
than the threshold of 2 imposed by local realism.


title:
Efficient and long-lived field-free orientation of molecules by a single
  hybrid short pulse

abstract:
  We show that a combination of a half-cycle pulse and a short nonresonant
laser pulse produces a strongly enhanced postpulse orientation. Robust
transients that display both efficient and long-lived orientation are obtained.
The mechanism is analyzed in terms of optimal oriented target states in finite
Hilbert subspaces and shows that hybrid pulses can prove useful for other
control issues.


title: Chain-rules for channel capacity

abstract:
  We show some chain-rules for the capacity of classical-quantum and quantum
channels. We use the concept of Nash-Equilibrium in game-theory, and its
existence in suitably defined games, to arrive at the chain-rules.


title: The Plane of the Present and the New Transactional Paradigm of Time

abstract:
  This is a book chapter on the nature of time, from the point of view of the
transactional interpretation of quantum mechanics.


title:
On the unique possibility to increase significantly the contrast of dark
  resonances on D1 line of $^{87}$Rb

abstract:
  We propose and study, theoretically and experimentally, a new scheme of
excitation of a coherent population trapping resonance for D1 line of alakli
atoms with nuclear spin $I=3/2$ by bichromatic linearly polarized light ({\em
lin}$||${\em lin} field) at the conditions of spectral resolution of the
excited state. The unique properties of this scheme result in a high contrast
of dark resonance for D1 line of $^{87}$Rb.


title: Entangled light pulses from single cold atoms

abstract:
  The coherent interaction between a laser-driven single trapped atom and an
optical high-finesse resonator allows to produce entangled multi-photon light
pulses on demand. The mechanism is based on the mechanical effect of light. The
degree of entanglement can be controlled through the parameters of the laser
excitation. Experimental realization of the scheme is within reach of current
technology. A variation of the technique allows for controlled generation of
entangled subsequent pulses, with the atomic motion serving as intermediate
memory of the quantum state.


title:
Quantum-state filtering applied to the discrimination of Boolean
  functions

abstract:
  Quantum state filtering is a variant of the unambiguous state discrimination
problem: the states are grouped in sets and we want to determine to which
particular set a given input state belongs.The simplest case, when the N given
states are divided into two subsets and the first set consists of one state
only while the second consists of all of the remaining states, is termed
quantum state filtering. We derived previously the optimal strategy for the
case of N non-orthogonal states, {|\psi_{1} >, ..., |\psi_{N} >}, for
distinguishing |\psi_1 > from the set {|\psi_2 >, ..., |\psi_N >} and the
corresponding optimal success and failure probabilities. In a previous paper
[PRL 90, 257901 (2003)], we sketched an appplication of the results to
probabilistic quantum algorithms. Here we fill in the gaps and give the
complete derivation of the probabilstic quantum algorithm that can optimally
distinguish between two classes of Boolean functions, that of the balanced
functions and that of the biased functions. The algorithm is probabilistic, it
fails sometimes but when it does it lets us know that it did. Our approach can
be considered as a generalization of the Deutsch-Jozsa algorithm that was
developed for the discrimination of balanced and constant Boolean functions.


title:
Quantum optics in different representations of the algebra of canonical
  commutation relations (I): Unexpected properties of Rabi oscillations --
  theory and experiment

abstract:
  We discuss the Jaynes-Cummings model in different representations of the
algebra of canonical commutation relations. The first conclusion is that all
the irreducible representations lead to equivalent physical predictions.
However, the reducible representation recently introduced as a candidate for
`QED without infinities' leads to new effects. We analyze from this perspective
the experiments on Rabi oscillations performed by the Kastler-Brossel
Laboratory group from Paris. Surprisingly, the results seem to support the
reducible representation approach. We also discuss possibilities of more
definitive tests of the new formalism.


title:
Wigner distributions for finite dimensional quantum systems: An
  algebraic approach

abstract:
  We discuss questions pertaining to the definition of `momentum', `momentum
space', `phase space', and `Wigner distributions'; for finite dimensional
quantum systems. For such systems, where traditional concepts of `momenta'
established for continuum situations offer little help, we propose a physically
reasonable and mathematically tangible definition and use it for the purpose of
setting up Wigner distributions in a purely algebraic manner. It is found that
the point of view adopted here is limited to odd dimensional systems only. The
mathematical reasons which force this situation are examined in detail.


title:
Using weak nonlinearity under decoherence for macroscopic-entanglement
  generation and quantum computation

abstract:
  Recently, there have been several suggestions that weak Kerr nonlinearity can
be used for generation of macroscopic superpositions and entanglement and for
linear optics quantum computation. However, it is not immediately clear that
this approach can overcome decoherence effects. Our numerical study in this
paper shows that nonlinearity of weak strength could be useful for macroscopic
entanglement generation and quantum gate operations in the presence of
decoherence. We suggest specific values for real experiments based on our
analysis. Our discussion shows that the generation of macroscopic entanglement
using this approach is within reach of current technology.


title: Non-destructive Orthonormal State Discrimination

abstract:
  We provide explicit quantum circuits for the non-destructive deterministic
discrimination of Bell states in the Hilbert space $C^{d^{n}}$, where $d$ is
qudit dimension. We discuss a method for generalizing this to non-destructive
measurements on any set of orthogonal states distributed among $n$ parties.
  From the practical viewpoint, we show that such non-destructive measurements
can help lower quantum communication complexity under certain conditions.


title:
Minimally-disturbing Heisenberg-Weyl symmetric measurements using
  hard-core collisions of Schr\"odinger particles

abstract:
  In a previous paper we have presented a general scheme for the implementation
of symmetric generalized measurements (POVMs) on a quantum computer. This
scheme is based on representation theory of groups and methods to decompose
matrices that intertwine two representations. We extend this scheme in such a
way that the measurement is minimally disturbing, i.e., it changes the state
vector \ket{\Psi} of the system to \sqrt{\Pi} \ket{\Psi} where \Pi is the
positive operator corresponding to the measured result.
  Using this method, we construct quantum circuits for measurements with
Heisenberg-Weyl symmetry. A continuous generalization leads to a scheme for
optimal simultaneous measurements of position and momentum of a Schr"odinger
particle moving in one dimension such that the outcomes satisfy \Delta x \Delta
p \geq \hbar.
  The particle to be measured collides with two probe particles, one for the
position and the other for the momentum measurement. The position and momentum
resolution can be tuned by the entangled joint state of the probe particles
which is also generated by a collision with hard-core potential. The parameters
of the POVM can then be controlled by the initial widths of the wave functions
of the probe particles. We point out some formal similarities and differences
to simultaneous measurements of quadrature amplitudes in quantum optics.


title: An Alternative Treatment for Yukawa-Type Potentials

abstract:
  We propose a new approximation scheme to obtain analytic expressions for the
bound state energies and eigenfunctions of Yukawa like potentials. The
predicted energies are in excellent agreement with the accurate numerical
values reported in the literature.


title:
Multipartite entanglement generation and fidelity decay in disordered
  qubit systems

abstract:
  We investigate multipartite entanglement dynamics in disordered spin-1/2
lattice models exhibiting a transition from integrability to quantum chaos.
Borrowing from the recently introduced generalized entanglement framework, we
construct measures for correlations relative to arbitrary local and bi-local
spin observables, and show how they naturally signal the crossover between
distinct dynamical regimes. In particular, we find that the generation of
global entanglement is directly ruled by the local density of states in the
short time limit, whereas the asymptotic amount of entanglement is proportional
to the degree of delocalization of the chaotic many-body state. Our results are
relevant to the stability of quantum information in disordered quantum
computing hardware.


title: Postquantum eavesdropping without superluminal signaling

abstract:
  In a recent Letter (Phys. Rev. Lett. 95 (2005) 010503) Barrett, Hardy and
Kent (BHK) considered a very interesting question which of the fundamental laws
of physics ensure security of quantum cryptographic protocols. In particular,
they presented quantum key distribution protocol and claimed its security in a
very general framework, which allows - what they call - postquantum
eavesdropping strategies i.e. which "allows for eavesdroppers who can break the
laws of quantum mechanics, as long as nothing they can do implies the
possibility of superluminal signaling". In this Comment, however, we show that
it is still possible to construct a strategy, which although consistent with
all asumptions explicitely stated in BHK paper, enables perfect eavesdropping
in their protocol.


title:
Geometric phase induced by a cyclically evolving squeezed vacuum
  reservoir

abstract:
  We propose a new way to generate an observable geometric phase by means of a
completely incoherent phenomenon. We show how to imprint a geometric phase to a
system by "adiabatically" manipulating the environment with which it interacts.
As a specific scheme we analyse a multilevel atom interacting with a broad-band
squeezed vacuum bosonic bath. As the squeezing parameters are smoothly changed
in time along a closed loop, the ground state of the system acquires a
geometric phase. We propose also a scheme to measure such geometric phase by
means of a suitable polarization detection.


title: On the conflict between local realism and classical physics

abstract:
  In contrast to the intuitively plausible assumption of local realism,
entangled particles, even when isolated, are not allowed to possess definite
properties in their own right, as quantitatively expressed by violations of
Bell's inequalities [1]. Even as entanglement is now a key feature of quantum
information and communication technology [2,3], it remains the most puzzling
feature of quantum mechanics [4] and its conceptual foundation is still widely
debated. Here we demonstrate that physical systems providing dicotomic outcomes
are not able to guarantee both the rotation properties of physical quantities
and local realism. This result opens the way to a new formulation of quantum
mechanics based on only two elementary physical principles replacing the
abstract mathematical axiomes of the present theory. According to this
formulation, the coexistence of discrete outcomes with the classical continuous
transformation properties of physical quantities under coordinate
transformation inevitably implies quantum probabilities. These results, provide
a simple physical explanation to the most debated quantum features and put into
question the existence of physical quantities displaying continuous outcomes in
agreement with approaches that attempt to integrate quantum theory with general
relativity [5-8].


title: Matrix Element Distribution as a Signature of Entanglement Generation

abstract:
  We explore connections between an operator's matrix element distribution and
its entanglement generation. Operators with matrix element distributions
similar to those of random matrices generate states of high multi-partite
entanglement. This occurs even when other statistical properties of the
operators do not conincide with random matrices. Similarly, operators with some
statistical properties of random matrices may not exhibit random matrix element
distributions and will not produce states with high levels of multi-partite
entanglement. Finally, we show that operators with similar matrix element
distributions generate similar amounts of entanglement.


title:
Informationally complete measurements on bipartite quantum systems:
  comparing local with global measurements

abstract:
  Informationally complete measurements allow the estimation of expectation
values of any operator on a quantum system, by changing only the
data-processing of the measurement outcomes. In particular, an informationally
complete measurement can be used to perform quantum tomography, namely to
estimate the density matrix of the quantum state. The data-processing is
generally nonunique, and can be optimized according to a given criterion. In
this paper we provide the solution of the optimization problem which minimizes
the variance in the estimation. We then consider informationally complete
measurements performed over bipartite quantum systems focusing attention on
universally covariant measurements, and compare their statistical efficiency
when performed either locally or globally on the two systems. Among global
measurements we consider the special case of Bell measurements, which allow to
estimate the expectation of a restricted class of operators. We compare the
variance in the three cases: local, Bell, and unrestricted global--and derive
conditions for the operators to be estimated such that one type of measurement
is more efficient than the other. In particular, we find that for factorized
operators and Bell projectors the Bell measurement always performs better than
the unrestricted global measurement, which in turn outperforms the local one.
For estimation of the matrix elements of the density operator, the relative
performances depend on the basis on which the state is represented, and on the
matrix element being diagonal or off-diagonal, however, with the global
unrestricted measurement generally performing better than the local one.


title:
Complementary Descriptions (PART I): A Set of Ideas Regarding the
  Interpretation of Quantum Mechanics

abstract:
  Niels Bohr introduced the concept of complementarity in order to give a
general account of quantum mechanics, however he stressed that the idea of
complementarity is related to the general difficulty in the formation of human
ideas, inherent in the distinction between subject and object. The
complementary descriptions approach is a framework for the interpretation of
quantum mechanics, more specifically, it focuses in the development of the idea
of complementarity and the concept of potentiality in the orthodox quantum
formulation. In PART I of this article, we analyze the ideas of Bohr and
present the principle of complementary description which takes into account
Einstein's ontological position. We argue, in PART II, that this development
allows a better understanding of some of the paradigmatic interpretational
problems in quantum mechanics, such as the measurement problem and the quantum
to classical limit. We conclude that one should further develop complementarity
in order to elaborate a consistent worldview.


title: Symmetrization, quantum images and measurement

abstract:
  We argue that symmetrization of an incoming microstate with similar states in
a sea of microstates contained in a macroscopic detector can produce an
effective image, which does not contradict the no-cloning theorem, and such a
combinatorial set can then be used with first passage random walk interactions
suggested in an earlier work to give the right quantum mechanical weight for
measured eigenvalues.


title:
Decoherence in composite quantum open systems: the effectiveness of
  unstable degrees of freedom

abstract:
  The effect induced by an environment on a composite quantum system is
studied. The model considers the composite system as comprised by a subsystem A
coupled to a subsystem B which is also coupled to an external environment. We
study all possible four combinations of subsystems A and B made up with a
harmonic oscillator and an upside down oscillator. We analyzed the decoherence
suffered by subsystem A due to an effective environment composed by subsystem B
and the external reservoir. In all the cases we found that subsystem A
decoheres even though it interacts with the environment only through its sole
coupling to B. However, the effectiveness of the diffusion depends on the
unstable nature of subsystem A and B. Therefore, the role of this degree of
freedom in the effective environment is analyzed in detail

categories: quant-ph cond-mat.other cond-mat.stat-mech hep-ph


title: Influence-free states on compound quantum systems

abstract:
  Let Alice and Bob be able to make local quantum measurements and communicate
classically. The set of mathematically consistent joint probability assignments
(``states'') for such measurements is properly larger than the set of
quantum-mechanical mixed states for the Alice-Bob system. It is canonically
isomorphic to the set of positive (not necessarily completely positive) linear
maps Phi from the bounded linear operators on Alice's space to those on Bob's,
for which Tr Phi(I)=1. We review the fact that allowing classical communication
is equivalent to enforcing ``no-instantaneous-signalling'' (``no--influence'')
in the direction opposite the communication. We establish that in the subclass
of ``decomposable'' states, i.e. convex combinations of positive states with
"PTP" ones whose partial transpose is positive, the extremal states are just
the extremal positive and extremal PTP states. We show that two such states,
shared by the same pair of parties, cannot necessarily be combined as
independent states (their tensor product) if the full set of quantum operations
is allowed locally to each party. We use a framework of ``test spaces'' and
states on these, suited for exhibiting the analogies and deviations of
empirical probabilistic theories from classical probability theory. This leads
to a deeper understanding of analogies between quantum mechanics and Bayesian
probability theory. The existence of a ``most Bayesian'' quantum rule for
updating states after measurement, and its association with the situation when
information on one system is gained by measuring another, is a case of a
general proposition holding for test spaces combined subject to the
no-signalling requirement.


title: Quantum computational gradient estimation

abstract:
  Classically, determining the gradient of a black-box function f:R^p->R
requires p+1 evaluations. Using the quantum Fourier transform, two evaluations
suffice. This is based on the approximate local periodicity of
exp(2*pi*i*f(x)). It is shown that sufficiently precise machine arithmetic
results in gradient estimates of any required accuracy.


title:
Differential phase shift quantum key distribution experiment over 105 km
  fibre

abstract:
  Since several papers appeared in 2000, the quantum key distribution (QKD)
community has been well aware that photon number splitting (PNS) attack by Eve
severely limits the secure key distribution distance in BB84 QKD systems with
Poissonian photon sources. In attempts to solve this problem,
entanglement-based QKD, single-photon based QKD, and entanglement
swapping-based QKD, have been studied in recent years. However, there are many
technological difficulties that must be overcome before these schemes can
become practical systems. Here we report a very simple QKD system, in which
secure keys were generated over >100 km fibre for the first time. We used an
alternative protocol of differential phase shift keying (DPSK) but with a
Poissonian source. We analysed the security of the DPSK protocol and showed
that it is robust even against hybrid attacks including collective PNS attack
over consecutive pulses, intercept-and-resend (I-R) attack and beamsplitting
(BS) attack, because of the non-deterministic collapse of a wavefunction in a
quantum measurement. To implement this protocol, we developed a new detector
for the 1.5 um band based on frequency up-conversion in a periodically poled
lithium niobate (PPLN) waveguide followed by a Si avalanche photodiode (APD).
The use of the new detectors increased the sifted key generation rate up to > 1
Mbit/s over 30 km fibre, which is two orders of magnitude larger than the
previous record.


title:
High brightness single mode source of correlated photon pairs using a
  photonic crystal fiber

abstract:
  We demonstrate a picosecond source of correlated photon pairs using a
micro-structured fibre with zero dispersion around 715 nm wavelength. The fibre
is pumped in the normal dispersion regime at ~708 nm and phase matching is
satisfied for widely spaced parametric wavelengths. Here we generate up to 10^7
photon pairs per second in the fibre at wavelengths of 587 nm and 897 nm. On
collecting the light in single-mode-fibre-coupled Silicon avalanche diode
photon counting detectors we detect ~3.2.10^5 coincidences per second at pump
power 0.5 mW.


title:
Implementation of a CNOT gate in two Rydberg atoms by the nonholonomic
  control technique

abstract:
  We present a demonstrative application of the nonholonomic control method to
a real physical system composed of two cold Cesium atoms. In particular, we
show how to implement a CNOT quantum gate in this system by means of a
controlled Stark field.


title: Quantum Electrodynamics near a Dielectric Half-space

abstract:
  We determine the photon propagator in the presence of a non-dispersive
dielectric half-space and use it to calculate the self-energy of an electron
near a dielectric surface.


title:
Complementary Descriptions (PART II): A Set of Ideas Regarding the
  Interpretation of Quantum Mechanics


title:
Foundations of a spacetime path formalism for relativistic quantum
  mechanics

abstract:
  Quantum field theory is the traditional solution to the problems inherent in
melding quantum mechanics with special relativity. However, it has also long
been known that an alternative first-quantized formulation can be given for
relativistic quantum mechanics, based on the parametrized paths of particles in
spacetime. Because time is treated similarly to the three space coordinates,
rather than as an evolution parameter, such a spacetime approach has proved
particularly useful in the study of quantum gravity and cosmology. This paper
shows how a spacetime path formalism can be considered to arise naturally from
the fundamental principles of the Born probability rule, superposition, and
Poincar\'e invariance. The resulting formalism can be seen as a foundation for
a number of previous parametrized approaches in the literature, relating, in
particular, "off-shell" theories to traditional on-shell quantum field theory.
It reproduces the results of perturbative quantum field theory for free and
interacting particles, but provides intriguing possibilities for a natural
program for regularization and renormalization. Further, an important
consequence of the formalism is that a clear probabilistic interpretation can
be maintained throughout, with a natural reduction to non-relativistic quantum
mechanics.


title: Quantum searching amidst uncertainty

abstract:
  Consider a database most of whose entries are marked but the precise fraction
of marked entries is not known. What is known is that the fraction of marked
entries is 1-X, where X is a random variable that is uniformly distributed in
the range (0,X_0) (X_0 is a small number). The problem is to try to select a
marked item from the database in a single query. If the algorithm selects a
marked item, it succeeds, else if it selects an unmarked item, it makes an
error. How low can we make the probability of error? The best possible
classical algorithm can lower the probability of error to O((X_0)^2). The best
known quantum algorithms for this problem could also only lower the probability
of error to O((X_0)^2). Using a recently invented quantum search technique,
this paper gives an algorithm that reduces the probability of error to
O((X_0)^3). The algorithm is asymptotically optimal.


title:
One dimensional Coulomb-like problem in deformed space with minimal
  length

abstract:
  Spectrum and eigenfunctions in the momentum representation for 1D Coulomb
potential with deformed Heisenberg algebra leading to minimal length are found
exactly. It is shown that correction due to the deformation is proportional to
square root of the deformation parameter. We obtain the same spectrum using
Bohr-Sommerfeld quantization condition.


title: Quantum Relative States

abstract:
  We study quantum state estimation problems where the reference system with
respect to which the state is measured should itself be treated quantum
mechanically. In this situation, the difference between the system and the
reference tends to fade. We investigate how the overlap between two pure
quantum states can be optimally estimated, in several scenarios, and we
re-visit homodyne detection.


title:
Exact solutions of Dirac equation on (1+1)-dimensional spacetime coupled
  to a static scalar field

abstract:
  We use a generalized scheme of supersymmetric quantum mechanics to obtain the
energy spectrum and wave function for Dirac equation in (1+1)-dimensional
spacetime coupled to a static scalar field.


title: Simulating quantum correlations as a distributed sampling problem

abstract:
  It is known that quantum correlations exhibited by a maximally entangled
qubit pair can be simulated with the help of shared randomness, supplemented
with additional resources, such as communication, post-selection or non-local
boxes. For instance, in the case of projective measurements, it is possible to
solve this problem with protocols using one bit of communication or making one
use of a non-local box. We show that this problem reduces to a distributed
sampling problem. We give a new method to obtain samples from a biased
distribution, starting with shared random variables following a uniform
distribution, and use it to build distributed sampling protocols. This approach
allows us to derive, in a simpler and unified way, many existing protocols for
projective measurements, and extend them to positive operator value
measurements. Moreover, this approach naturally leads to a local hidden
variable model for Werner states.


title: Popper's Experiment and Superluminal Communication

abstract:
  We comment on Tabesh Qureshi, "Understanding Popper's Experiment," AJP 73,
541 (June 2005), in particular on the implications of its section IV. We show,
in the situation envisaged by Popper, that analysis solely with conventional
non-relativistic quantum mechanics suffices to exclude the possibility of
superluminal communication.


title: A Pragmatic Interpretation of Quantum Logic

abstract:
  Scholars have wondered for a long time whether quantum mechanics (QM)
subtends a quantum concept of truth which originates quantum logic (QL) and is
radically different from the classical (Tarskian) concept of truth. We show in
this paper that QL can be interpreted as a pragmatic language of pragmatically
decidable assertive formulas, which formalize statements about physical systems
that are empirically justified or unjustified in the framework of QM. According
to this interpretation, QL formalizes properties of the metalinguistic concept
of empirical justification within QM rather than properties of a quantum
concept of truth. This conclusion agrees with a general integrationist
perspective, according to which nonstandard logics can be interpreted as
theories of metalinguistic concepts different from truth, avoiding competition
with classical notions and preserving the globality of logic. By the way, some
elucidations of the standard concept of quantum truth are also obtained.


title:
Quantum analysis of the nondegenerate optical parametric oscillator with
  injected signal

abstract:
  In this paper we study the nondegenerate optical parametric oscillator with
injected signal, both analytically and numerically. We develop a perturbation
approach which allows us to find approximate analytical solutions, starting
from the full equations of motion in the positive P-representation. We
demonstrate the regimes of validity of our approximations via comparison with
the full stochastic results. We and that, with reasonably low levels of
injected signal, the system allows for demonstrations of quantum entanglement
and the Einstein-Podolsky-Rosen paradox. In contrast to the normal optical
parametric oscillator operating below threshold, these features are
demonstrated with relatively intense felds.


title: Real trajectories in the semiclassical coherent state propagator

abstract:
  The semiclassical approximation to the coherent state propagator requires
complex classical trajectories in order to satisfy the associated boundary
conditions, but finding these trajectories in practice is a difficult task that
may compromise the applicability of the approximation. In this work several
approximations to the coherent state propagator are derived that make use only
of real trajectories, which are easier to handle and have a more direct
physical interpretation. It is verified in a particular example that these real
trajectories approximations may have excellent accuracy.


title:
Comments on quant-ph/0506137: Fast quantum search algorithms by qubit
  comparisons exploiting global phase interference

abstract:
  Recently, Andreas de Vries proposed a quantum algorithm that would find an
element in an unsorted database exponentially faster than Grover's algorithm.
We show that de Vries' algorithm does not work as intended and does not give
any clue about the position of the searched element.


title: On asymptotic continuity of functions of quantum states

abstract:
  A useful kind of continuity of quantum states functions in asymptotic regime
is so-called asymptotic continuity. In this paper we provide general tools for
checking if a function possesses this property. First we prove equivalence of
asymptotic continuity with so-called it robustness under admixture. This allows
us to show that relative entropy distance from a convex set including maximally
mixed state is asymptotically continuous. Subsequently, we consider it arrowing
- a way of building a new function out of a given one. The procedure originates
from constructions of intrinsic information and entanglement of formation. We
show that arrowing preserves asymptotic continuity for a class of functions
(so-called subextensive ones). The result is illustrated by means of several
examples.


title:
Control of decoherence in the generation of photon pairs from atomic
  ensembles

abstract:
  We report an investigation to establish the physical mechanisms responsible
for decoherence in the generation of photon pairs from atomic ensembles, via
the protocol of Duan et. al for long distance quantum communication [Nature
(London) 414, 413 (2001)] and present the experimental techniques necessary to
properly control the process. We develop a theory to model in detail the
decoherence process in experiments with magneto-optical traps. The
inhomogeneous broadening of the ground state by the trap magnetic field is
identified as the principal mechanism for decoherence. In conjunction with our
theoretical analysis, we report a series of measurements to characterize and
control the coherence time in our experimental setup. We use copropagating
stimulated Raman spectroscopy to access directly the ground state energy
distribution of the ensemble. These spectroscopic measurements allow us to
switch off the trap magnetic field in a controlled way, optimizing the
repetition rate for single-photon measurements. With the magnetic field off, we
then measure nonclassical correlations for pairs of photons generated by the
ensemble as a function of the storage time of the single collective atomic
excitation. We report coherence times longer than 10 microseconds,
corresponding to an increase of two orders of magnitude compared to previous
results in cold ensembles. The coherence time is now two orders of magnitude
longer than the duration of the excitation pulses. The comparison between these
experimental results and the theory shows good agreement. Finally, we employ
our theory to devise ways to improve the experiment by optical pumping to
specific initial states.


title: Generation of Hyperentangled Photons Pairs

abstract:
  We experimentally demonstrate the first quantum system entangled in every
degree of freedom (hyperentangled). Using pairs of photons produced in
spontaneous parametric downconversion, we verify entanglement by observing a
Bell-type inequality violation in each degree of freedom: polarization, spatial
mode and time-energy. We also produce and characterize maximally hyperentangled
states and novel states simultaneously exhibiting both quantum and classical
correlations. Finally, we report the tomography of a 2x2x3x3 system
(36-dimensional Hilbert space), which we believe is the first reported photonic
entangled system of this size to be so characterized.


title: Simple scheme for two-qubit Grover search in cavity QED

abstract:
  Following the proposal by F. Yamaguchi et al.[Phys. Rev. A 66, 010302 (R)
(2002)], we present an alternative way to implement the two-qubit Grover search
algorithm in cavity QED. Compared with F. Yamaguchi et al.'s proposal, with a
strong resonant classical field added, our method is insensitive to both the
cavity decay and thermal field, and doesn't require that the cavity remain in
the vacuum state throughout the procedure. Moreover, the qubit definitions are
the same for both atoms, which makes the experiment easier. The strictly
numerical simulation shows that our proposal is good enough to demonstrate a
two-qubit Grover's search with high fidelity.


title: Extremal quantum cloning machines

abstract:
  We investigate the problem of cloning a set of states that is invariant under
the action of an irreducible group representation. We then characterize the
cloners that are "extremal" in the convex set of group covariant cloning
machines, among which one can restrict the search for optimal cloners. For a
set of states that is invariant under the discrete Weyl-Heisenberg group, we
show that all extremal cloners can be unitarily realized using the so-called
"double-Bell states", whence providing a general proof of the popular ansatz
used in the literature for finding optimal cloners in a variety of settings.
Our result can also be generalized to continuous-variable optimal cloning in
infinite dimensions, where the covariance group is the customary
Weyl-Heisenberg group of displacements.


title:
Ramsauer-Townsend Diffraction Oscillations in the Two-Dimensional
  Momentum Distribution of Laser-Ionized electrons

abstract:
  We analyze the two-dimensional momentum distribution of electrons ionized by
few-cycle laser pulses in the transition regime from multiphoton absorption to
tunneling by solving the time-dependent Schr\"odinger equation and by a
classical-trajectory Monte Carlo simulation with tunneling (CTMC-T). We find a
complex two-dimensional interference pattern that resembles ATI rings at higher
energies and displays Ramsauer-Townsend diffraction oscillations in the angular
distribution near threshold. CTMC-T calculations provide a semiclassical
explanation for the dominance of selected partial waves. While the present
calculation pertains to hydrogen, we find surprising qualitative agreement with
recent experimental data for rare gases [1].


title: An explicitly solvable model of the spontaneous PT-symmetry breaking

abstract:
  We contemplate the pair of the purely imaginary delta-function potentials on
a finite interval with Dirichlet boundary conditions. The two parameter model
exhibits nicely the expected quantitative features of the unavoided level
crossing and of a "phase-transition" complexification of the energies.
Combining analytic and numerical techniques we investigate strength- and
position-dependence of its spectrum.


title: Quantum Machine and SR Approach: a Unified Model

abstract:
  The Geneva-Brussels approach to quantum mechanics (QM) and the semantic
realism (SR) nonstandard interpretation of QM exhibit some common features and
some deep conceptual differences. We discuss in this paper two elementary
models provided in the two approaches as intuitive supports to general
reasonings and as a proof of consistency of general assumptions, and show that
Aerts' quantum machine can be embodied into a macroscopic version of the
microscopic SR model, overcoming the seeming incompatibility between the two
models. This result provides some hints for the construction of a unified
perspective in which the two approaches can be properly placed.


title: Standard forms of noisy quantum operations via depolarization

abstract:
  We consider noisy, non-local unitary operations or interactions, i.e. the
corresponding evolutions are described by completely positive maps or master
equations of Lindblad form. We show that by random local operations the
completely positive maps can be depolarized to a standard form with a reduced
number of parameters describing the noise process in such a way that the
noiseless (unitary) part of the evolution is not altered. A further reduction
of the parameters, in many cases even to a single one (i.e. global white
noise), is possible by tailoring the decoherence process and increasing the
amount of noise. We generalize these results to the dynamical case where the
ideal unitary operation is given by some interaction Hamiltonian. The resulting
standard forms may be used to compute lower bounds on channel capacities, to
simplify quantum process tomography or to derive error thresholds for
entanglement purification and quantum computation.


title: Thermalization of Squeezed States

abstract:
  Starting with a thermal squeezed state defined as a conventional thermal
state based on an appropriate hamiltonian, we show how an important physical
property, the signal-to-noise ratio, is degraded, and propose a simple model of
thermalization (Kraus thermalization).


title:
Commuting Position and Momentum Operators, Exact Decoherence and
  Emergent Classicality

abstract:
  Inspired by an old idea of von Neumann, we seek a pair of commuting operators
X,P which are, in a specific sense, "close" to the canonical non-commuting
position and momentum operators, x,p. The construction of such operators is
related to the problem of finding complete sets of orthonormal phase space
localized states, a problem severely constrained by the Balian-Low theorem.
Here these constraints are avoided by restricting attention to situations in
which the density matrix is reasonably decohered (i.e., spread out in phase
space). Commuting position and momentum operators are argued to be of use in
discussions of emergent classicality from quantum mechanics. In particular,
they may be used to give a discussion of the relationship between exact and
approximate decoherence in the decoherent histories approach to quantum theory.


title:
Quantum Phase Gate Operation Based on Nonlinear Optics: Full Quantum
  Analysis

abstract:
  We present a full quantum treatment of a five-level atomic system coupled to
two quantum and two classical light fields. The two quantum fields undergo a
cross-phase modulation induced by electro-magnetically induced transparency.
The performance of this configuration as a two-qubit quantum phase gate for
travelling single-photons is examined. A trade-off between the size of the
conditional phase shift and the fidelity of the gate is found. Nonetheless, a
satisfactory gate performance is still found to be possible in the transient
regime, corresponding to a fast gate operation.


title: An overview of simply pulsed qubits

abstract:
  The behavior of simply pulsed qubits (quantum systems with two linearly
independent states) may be characterized by the energy difference $\Delta E$
between the two states of the qubit and by an external stimulating potential
$V(t)$ that causes transitions between them. Thus, the operation of such
quantum mechanical systems may be categorized in various regions that
explicitly depend on $\Delta E$ and $V(t)$. Limiting cases of degenerate,
perturbative, and adiabatic regions are discussed. A comprehensive and
illustrative map for simply pulsed qubits is presented that can be used as a
visual tool for students. Furthermore, analytic solutions may be obtained when
the interaction $V(t)$ is proportional to $\delta(t-t_k)$, namely when a fast
interaction, called a kick, is used.


title: Enhancement of interferometric precision using fast light

abstract:
  We show that anomalous dispersion characteristic of fast-light can be used to
enhance the sensitivity of optical interferometry under certain conditions. In
particular, we show that a dual-chamber Fabry-Perot interferometer with a
shared mirror-pair can be used in a way so that its sensitivity is increased by
operating near the critically anomalous dispersion condition where the group
index is much less than unity. The enhancement factor can be as high as 108 for
realistic conditions. The process of bi-frequency pumped Raman gain in a
lambda-type atomic medium can be used to achieve this effect.


title: Classical and quantum coupled oscillators: symplectic structure

abstract:
  We consider a set of N linearly coupled harmonic oscillators and show that
the diagonalization of this problem can be put in geometrical terms. The matrix
techniques developed here allowed for solutions in both the classical and
quantum regimes.


title: A Theory of Physical Quantum Computation: The Quantum Computer Condition

abstract:
  In this paper we present a new unified theoretical framework that describes
the full dynamics of quantum computation. Our formulation allows any questions
pertaining to the physical behavior of a quantum computer to be framed, and in
principle, answered. We refer to the central organizing principle developed in
this paper, on which our theoretical structure is based, as the *Quantum
Computer Condition* (QCC), a rigorous mathematical statement that connects the
irreversible dynamics of the quantum computing machine, with the reversible
operations that comprise the quantum computation intended to be carried out by
the quantum computing machine. Armed with the QCC, we derive a powerful result
that we call the *Encoding No-Go Theorem*. This theorem gives a precise
mathematical statement of the conditions under which fault-tolerant quantum
computation becomes impossible in the presence of dissipation and/or
decoherence. In connection with this theorem, we explicitly calculate a
universal critical damping value for fault-tolerant quantum computation. In
addition we show that the recently-discovered approach to quantum error
correction known as "operator quantum error-correction" (OQEC) is a special
case of our more general formulation. Our approach furnishes what we will refer
to as "operator quantum fault-tolerance" (OQFT). In particular, we show how the
QCC allows one to derive error thresholds for fault tolerance in a completely
general context. We prove the existence of solutions to a class of
time-dependent generalizations of the Lindblad equation. Using the QCC, we also
show that the seemingly different circuit, graph- (including cluster-) state,
and adiabatic paradigms for quantum computing are in fact all manifestations of
a single, universal paradigm for all physical quantum computation.


title:
Measurement of the transverse spatial quantum state of light at the
  single-photon level

abstract:
  We present an experimental method to measure the transverse spatial quantum
state of an optical field in coordinate space at the single-photon level. The
continuous-variable measurements are made with a photon-counting,
parity-inverting Sagnac interferometer based on all-reflecting optics. The
technique provides a large numerical aperture without distorting the shape of
the wave front, does not introduce astigmatism, and allows for characterization
of fully or partially coherent optical fields at the single-photon level.
Measurements of the transverse spatial Wigner functions for highly attenuated
coherent beams are presented and compared to theoretical predictions.


title:
Eavesdropping on the "Ping-Pong" Quantum Communication Protocol Freely
  in a Noise Channel

abstract:
  We introduce an attack scheme for eavesdropping the ping-pong quantum
communication protocol proposed by Bostr$\ddot{o}$m and Felbinger [Phys. Rev.
Lett. \textbf{89}, 187902 (2002)] freely in a noise channel. The vicious
eavesdropper, Eve, intercepts and measures the travel photon transmitted
between the sender and the receiver. Then she replaces the quantum signal with
a multi-photon signal in a same state, and measures the photons return with the
measuring basis with which Eve prepares the fake signal except for one photon.
This attack increase neither the quantum channel losses nor the error rate in
the sampling instances for eavesdropping check. It works for eavesdropping the
secret message transmitted with the ping-pong protocol. Finally, we propose a
way for improving the security of the ping-pong protocol.


title:
Inseparability inequalities for higher-order moments for bipartite
  systems

abstract:
  There are several examples of bipartite entangled states of continuous
variables for which the existing criteria for entanglement using the
inequalities involving the second order moments are insufficient. We derive new
inequalities involving higher order correlation, for testing entanglement in
non-Gaussian states. In this context we study an example of a non-Gaussian
state, which is a bipartite entangled state of the form $\psi(x_{\rm a},x_{\rm
b})\propto (\alpha x_{\rm a}+\beta x_{\rm b})e^{-(x_{\rm a}^2+x_{\rm b}^2)/2}$.
Our results open up an avenue to search for new inequalities to test
entanglement in non-Gaussian states.


title:
Explanation of the Gibbs paradox within the framework of quantum
  thermodynamics

abstract:
  The issue of the Gibbs paradox is that when considering mixing of two gases
within classical thermodynamics, the entropy of mixing appears to be a
discontinuous function of the difference between the gases: it is finite for
whatever small difference, but vanishes for identical gases. The resolution
offered in the literature, with help of quantum mixing entropy, was later shown
to be unsatisfactory precisely where it sought to resolve the paradox.
Macroscopic thermodynamics, classical or quantum, is unsuitable for explaining
the paradox, since it does not deal explicitly with the difference between the
gases. The proper approach employs quantum thermodynamics, which deals with
finite quantum systems coupled to a large bath and a macroscopic work source.
Within quantum thermodynamics, entropy generally looses its dominant place and
the target of the paradox is naturally shifted to the decrease of the maximally
available work before and after mixing (mixing ergotropy). In contrast to
entropy this is an unambiguous quantity. For almost identical gases the mixing
ergotropy continuously goes to zero, thus resolving the paradox. In this
approach the concept of ``difference between the gases'' gets a clear
operational meaning related to the possibilities of controlling the involved
quantum states. Difficulties which prevent resolutions of the paradox in its
entropic formulation do not arise here. The mixing ergotropy has several
counter-intuitive features. It can increase when less precise operations are
allowed. In the quantum situation (in contrast to the classical one) the mixing
ergotropy can also increase when decreasing the degree of mixing between the
gases, or when decreasing their distinguishability. These points go against a
direct association of physical irreversibility with lack of information.


title: Dense coding with multipartite quantum states

abstract:
  We consider generalisations of the dense coding protocol with an arbitrary
number of senders and either one or two receivers, sharing a multiparty quantum
state, and using a noiseless channel. For the case of a single receiver, the
capacity of such information transfer is found exactly. It is shown that the
capacity is not enhanced by allowing the senders to perform joint operations.
We provide a nontrivial upper bound on the capacity in the case of two
receivers. We also give a classification of the set of all multiparty states in
terms of their usefulness for dense coding. We provide examples for each of
these classes, and discuss some of their properties.


title: Scale symmetry in classical and quantum mechanics

abstract:
  In this paper we address again the issue of the scale anomaly in quantum
mechanical models with inverse square potential. In particular we examine the
interplay between the classical and quantum aspects of the system using in both
cases an operatorial approach.


title:
Entanglement as Measure of Electron-Electron Correlation in Quantum
  Chemistry Calculations

abstract:
  In quantum chemistry calculations, the correlation energy is defined as the
difference between the Hartree-Fock limit energy and the exact solution of the
nonrelativistic Schrodinger equation. With this definition, the electron
correlation effects are not directly observable. In this report, we show that
the entanglement can be used as an alternative measure of the electron
correlation in quantum chemistry calculations. Entanglement is directly
observable and it is one of the most striking properties of quantum mechanics.
As an example we calculate the entanglement for He atom and H2 molecule with
different basis sets.


title: On local-hidden-variable no-go theorems

abstract:
  The strongest attack against quantum mechanics came in 1935 in the form of a
paper by Einstein, Podolsky and Rosen. It was argued that the theory of quantum
mechanics could not be called a complete theory of Nature, for every element of
reality is not represented in the formalism as such. The authors then put forth
a proposition: we must search for a theory where, upon knowing everything about
the system, including possible hidden variables, one could make precise
predictions concerning elements of reality. This project was ultimatly doomed
in 1964 with the work of Bell Bell, who showed that the most general local
hidden variable theory could not reproduce correlations that arise in quantum
mechanics. There exist mainly three forms of no-go theorems for local hidden
variable theories. Although almost every physicist knows the consequences of
these no-go theorems, not every physicist is aware of the distinctions between
the three or even their exact definitions. Thus we will discuss here the three
principal forms of no-go theorems for local hidden variable theories of Nature.
We will define Bell inequalities, Bell inequalities without inequalities and
pseudo-telepathy. A discussion of the similarities and differences will follow.


title: Quantum Interferometric Sensors

abstract:
  Quantum entanglement has the potential to revolutionize the entire field of
interferometric sensing by providing many orders of magnitude improvement in
interferometer sensitivity. The quantum-entangled particle interferometer
approach is very general and applies to many types of interferometers. In
particular, without nonlocal entanglement, a generic classical interferometer
has a statistical-sampling shot-noise limited sensitivity that scales like
$1/\sqrt{N}$, where $N$ is the number of particles passing through the
interferometer per unit time. However, if carefully prepared quantum
correlations are engineered between the particles, then the interferometer
sensitivity improves by a factor of $\sqrt{N}$ to scale like 1/N, which is the
limit imposed by the Heisenberg Uncertainty Principle. For optical
interferometers operating at milliwatts of optical power, this quantum
sensitivity boost corresponds to an eight-order-of-magnitude improvement of
signal to noise. This effect can translate into a tremendous science pay-off
for space missions. For example, one application of this new effect is to fiber
optical gyroscopes for deep-space inertial guidance and tests of General
Relativity (Gravity Probe B). Another application is to ground and orbiting
optical interferometers for gravity wave detection, Laser Interferometer
Gravity Observatory (LIGO) and the European Laser Interferometer Space Antenna
(LISA), respectively. Other applications are to Satellite-to-Satellite laser
Interferometry (SSI) proposed for the next generation Gravity Recovery And
Climate Experiment (GRACE II).


title: On Entanglement with Vacuum

abstract:
  The so-called entanglement with vacuum is not a property of the Fock space,
but of some rather pathological representations of CCR/CAR algebras. In some
other Fock space representations the notion simply does not exist. We have
checked all the main Gedanken experiments where the notion of entanglement with
vacuum was used, and found that all the calculations could be performed at a
representation-independent level. In particular any such experiment can be
formulated in a Fock-space representation where the notion of entanglement with
vacuum is meaningless. So, for the moment there is no single experiment where
the notion is needed, and probably it is simply unphysical.


title: Playing games with EPR-type experiments

abstract:
  An approach towards quantum games is proposed that uses the unusual
probabilities involved in EPR-type experiments directly in two-player games.


title:
Noise Correlations and Quantum Coherence in Hard-core Bosons in
  One-dimensional Lattices

abstract:
  Noise correlations, such as those observable in the time of flight images of
a released cloud, are calculated for hard-core bosonic (HCB) atoms. We find
that the standard mapping of HCB systems onto spin-1/2 XY models fails in
application to computation of noise correlations. This is due to the
contribution of multiply occupied virtual states to noise correlations in
bosonic systems. Such states do not exist in spin models. We use these
correlations to explore quantum coherence of the ground states and re-address
the relationship between the peaks present in noise correlation and the Mott
phase. Our analysis points to distinctive new experimental signatures of the
Mott phase. The importance of these correlations is illustrated in an example
of a quasiperiodic potential that exhibits a localization transition. In this
case, in contrast to the momentum distribution, the noise correlations reveal
the presence of quasiperiodic order in the localized phase.


title: Security of quantum key distribution with discrete rotational symmetry

abstract:
  We prove the unconditional security of quantum key distribution protocols
using attenuated laser pulses with M different linear polarizations. When M=4,
the proof covers the so-called SARG04 protocol [V.~Scarani et al., Phys. Rev.\
Lett. {\bf 92}, 057901 (2004)], which uses exactly the same quantum
communication as the Bennett-Brassard 1984 protocol. For a channel with
transmission $\eta$, we show that the key rate in SARG04 scales as
$O(\eta^{3/2})$. When we increase the number of states to M=2k-1 or 2k, the key
rate scaling improves as $O(\eta^{(k+1)/k})$.


title: Theoretical Setting of Inner Reversible Quantum Measurements

abstract:
  We show that any unitary transformation performed on the quantum state of a
closed quantum system, describes an inner, reversible, generalized quantum
measurement. We also show that under some specific conditions it is possible to
perform a unitary transformation on the state of the closed quantum system by
means of a collection of generalized measurement operators. In particular,
given a complete set of orthogonal projectors, it is possible to implement a
reversible quantum measurement that preserves the probabilities. In this
context, we introduce the concept of "Truth-Observable", which is the physical
counterpart of an inner logical truth.


title: Non-Holonomic Control I

abstract:
  In this paper, we present a universal control technique, the non-holonomic
control, which allows us to impose any arbitrarily prescribed unitary evolution
to any quantum system through the alternate application of two well-chosen
perturbations.


title: Non-holonomic Control II : Non-holonomic Quantum Devices

abstract:
  In this paper, we show how the non-holonomic control technique can be
employed to build completely controlled quantum devices. Examples of such
controlled structures are provided.


title:
Non-Holonomic Control III : Coherence Protection by the Quantum Zeno
  Effect and Non-Holonomic Control

abstract:
  In this paper, we present a coherence protection method based upon a
multidimensional generalization of the Quantum Zeno Effect, as well as ideas
from the coding theory. The non-holonomic control technique is employed as a
physical tool which allows its effective implementation. The two limiting cases
of small and large quantum systems are considered.


title: Non-Holonomic Control IV : Coherence Protection in a Rubidium isotope

abstract:
  In this paper, we present a realistic application of the coherence protection
method proposed in the previous article. A qubit of information encoded on the
two spin states of a Rubidium isotope is protected from the action of electric
and magnetic fields.


title: SUSY transformation of the Green function and a trace formula

abstract:
  An integral relation is established between the Green functions corresponding
to two Hamiltonians which are supersymmetric (SUSY) partners and in general may
possess both discrete and continuous spectra. It is shown that when the
continuous spectrum is present the trace of the difference of the Green
functions for SUSY partners is a finite quantity which may or may not be equal
to zero despite the divergence of the traces of each Green function. Our
findings are illustrated by using the free particle example considered both on
the whole real line and on a half line.


title: Entanglement of a photon and a collective atomic excitation

abstract:
  We describe a new experimental approach to probabilistic atom-photon (signal)
entanglement. Two qubit states are encoded as orthogonal collective spin
excitations of an unpolarized atomic ensemble. After a programmable delay, the
atomic excitation is converted into a photon (idler). Polarization states of
both the signal and the idler are recorded and are found to be in violation of
the Bell inequality. Atomic coherence times exceeding several microseconds are
achieved by switching off all the trapping fields - including the quadrupole
magnetic field of the magneto-optical trap - and zeroing out the residual
ambient magnetic field.


title: Quantum Anti-Piracy Storage of Classical Data

abstract:
  A scheme is proposed which stores classical data in 4-state quantum
registers. It can achieve the following goal: the classical data can always be
read unambiguously, while the quantum registers cannot be copied. Therefore the
data provider can always distinguish the original quantum registers from piracy
copies. Examples of application are also given.


title: Quantum Computation Beyond the "Standard Circuit Model"

abstract:
  Construction of explicit quantum circuits follows the notion of the "standard
circuit model" introduced in the solid and profound analysis of elementary
gates providing quantum computation. Nevertheless the model is not always
optimal (e.g. concerning the number of computational steps) and it neglects
physical systems which cannot follow the "standard circuit model" analysis. We
propose a computational scheme which overcomes the notion of the transposition
from classical circuits providing a computation scheme with the least possible
number of Hamiltonians in order to minimize the physical resources needed to
perform quantum computation and to succeed a minimization of the computational
procedure (minimizing the number of computational steps needed to perform an
arbitrary unitary transformation). It is a general scheme of construction,
independent of the specific system used for the implementation of the quantum
computer. The open problem of controllability in Lie groups is directly related
and rises to prominence in an effort to perform universal quantum computation.


title:
Reply to Brankov et al.'s "Comment on equivalence between quantum phase
  transition phenomena in radiation-matter and magnetic systems"

abstract: Reply to Comment quant-ph/0506207 by J.G.Brankov et al.


title:
Bound states of the Dirac equation for the PT-symmetric generalized
  Hulthen potential by the Nikiforov-Uvarov method

abstract:
  The one-dimensional Dirac equation is solved for the PT-symmetric generalized
Hulthen potential. The Nikiforov-Uvarov method which is based on solving the
second-order linear differential equations by reduction to a generalized
equation of hypergeometric type is used to obtain exact energy eigenvalues and
corresponding eigenfunctions.


title: Quantum teleprotation with sonic black holes

abstract:
  We show a new property of sonic black holes. After deriving the metric of a
sonic black hole from the Schrodinger equation and quantizing the perturbation
fields near the sonic event horizon, we show particles of Hawking radiation can
act as a source of entanglement: two-mode squeezed entanglement is produced
near the event horizon, which can be used in quantum teleportation. The
fidelity of the teleportation is closely related to the temperature of the
sonic black holes, but high fidelity seems difficult to reach in our case.


title: No approximate complex fermion coherent states

abstract:
  Whereas boson coherent states with complex parametrization provide an
elegant, and intuitive representation, there is no counterpart for fermions
using complex parametrization. However, a complex parametrization provides a
valuable way to describe amplitude and phase of a coherent beam. Thus we pose
the question of whether a fermionic beam can be described, even approximately,
by a complex-parametrized coherent state and define, in a natural way,
approximate complex-parametrized fermion coherent states. Then we identify four
appealing properties of boson coherent states (eigenstate of annihilation
operator, displaced vacuum state, preservation of product states under linear
coupling, and factorization of correlators) and show that these approximate
complex fermion coherent states fail all four criteria. The inapplicability of
complex parametrization supports the use of Grassman algebras as an appropriate
alternative.


title: Entanglement conditions for two-mode states

abstract:
  We provide a class of inequalities whose violation shows the presence of
entanglement in two-mode systems. We initially consider observables that are
quadratic in the mode creation and annihilation operators and find conditions
under which a two-mode state is entangled. Further examination allows us to
formulate additional conditions for detecting entanglement. We conclude by
showing how the methods used here can be extended to find entanglement in
systems of more than two modes.


title: Fast Quantum Computing with Buckyballs

abstract:
  We have found that encapsulated atoms in fullerene molecules, which carry a
spin, can be used for fast quantum computing. We describe the scheme for
performing quantum computations, going through the preparation of the qubit
state and the realization of a two-qubit quantum gate. When we apply a static
magnetic field to each encased spin, we find out the ideal design for the
preparation of the quantum state. Therefore, adding to our system a time
dependent magnetic field, we can perform a phase-gate. The operational time
related to a $\pi-$phase gate is of the order of $ns$. This finding shows that,
during the decoherence time, which is proportional to $\mu s$, we can perform
many thousands of gate operations. In addition, the two-qubit state which
arises after a $\pi-$gate is characterized by a high degree of entanglement.
This opens a new avenue for the implementation of fast quantum computation.


title: Without the Born Rule

abstract:
  The auxiliary rules of quantum mechanics have always included the Born rule
that connects probability with square modulus. This need not be the case, for
it is possible to introduce probability into the theory through probability
current alone. When this is done, other rules can provide for stochastically
triggered measurements within a system of any size, microscopic or macroscopic;
and solutions to the Schrodinger equation can be consistently applied to
individual trials, not just to ensembles of trials. Other advantages appear.
The rules can then resolve the paradox associated with the Schrodinger cat
experiment, and remove the possibility of the many world thesis of Everett. As
a result, the system can accommodate any conscious observer, including the
principal investigator who cannot otherwise be included in a quantum mechanical
system.


title: An Introduction to Cartan's KAK Decomposition for QC Programmers

abstract:
  This paper presents no new results; its goals are purely pedagogical. A
special case of the Cartan Decomposition has found much utility in the field of
quantum computing, especially in its sub-field of quantum compiling. This
special case allows one to factor a general 2-qubit operation (i.e., an element
of U(4)) into local operations applied before and after a three parameter,
non-local operation. In this paper, we give a complete and rigorous proof of
this special case of Cartan's Decomposition. From the point of view of QC
programmers who might not be familiar with the subtleties of Lie Group Theory,
the proof given here has the virtues, that it is constructive in nature, and
that it uses only Linear Algebra. The constructive proof presented in this
paper is implemented in some Octave/Matlab m-files that are included with the
paper. Thus, this paper serves as documentation for the attached m-files.


title: Quantum Information Processing in Disordered and Complex Quantum Systems

abstract:
  We investigate quantum information processing and manipulations in disordered
systems of ultracold atoms and trapped ions. First, we demonstrate generation
of entanglement and local realization of quantum gates in a quantum spin glass
system. Entanglement in such systems attains significantly high values, after
quenched averaging, and has a stable positive value for arbitrary times.
Complex systems with long range interactions, such as ion chains or dipolar
atomic gases, can be modeled by neural network Hamiltonians. In such systems,
we find the characteristic time of persistence of quenched averaged
entanglement, and also find the time of its revival.


title: Natural three-qubit interactions in one-way quantum computing

abstract:
  We address the effects of natural three-qubit interactions on the
computational power of one-way quantum computation (\QC). A benefit of using
more sophisticated entanglement structures is the ability to construct compact
and economic simulations of quantum algorithms with limited resources. We show
that the features of our study are embodied by suitably prepared optical
lattices, where effective three-spin interactions have been theoretically
demonstrated. We use this to provide a compact construction for the Toffoli
gate. Information flow and two-qubit interactions are also outlined, together
with a brief analysis of relevant sources of imperfection.


title: Quantum Error Correction and Fault-Tolerance

abstract:
  I give an overview of the basic concepts behind quantum error correction and
quantum fault tolerance. This includes the quantum error correction conditions,
stabilizer codes, CSS codes, transversal gates, fault-tolerant error
correction, and the threshold theorem.


title: Reply to "Comment on 'Measuring a Photonic Qubit without Destroying It'"

abstract:
  In our Letter we proposed a scheme for nondeterministic quantum nondemolition
(QND) measurement of the polarization of a single photon--a photonic
qubit--using linear optics and photodetection. The scheme works with nonunit
probability, but success is heralded by the detection of a single photon in the
meter output. We provided an experimental demonstration of this scheme and
introduced three universally applicable fidelity measures--the measurement
fidelity F_M, the quantum state preparation fidelity F_QSP, and the QND
fidelity F_QND--to quantify its performance. The claim of Kok and Munro in
their Comment [quant-ph/0406120] is that one of our fidelity measures F_M is
not appropriate because it relies on coincidence measurements. We show why this
claim is wrong from both a fundamental and an operational perspective.


title: Reasoning about quantum knowledge

abstract:
  We construct a formal framework for investigating epistemic and temporal
notions in the context of distributed quantum computation. While we rely on
structures developed earlier, we stress that our notion of quantum knowledge
makes sense more generally in any agent-based model for distributed quantum
systems. Several arguments are given to support our view that an agent's
possibility relation should not be based on the reduced density matrix, but
rather on local classical states and local quantum operations. In this way, we
are able to analyse distributed primitives such as superdense coding and
teleportation, obtaining interesting conclusions as to how the knowledge of
individual agents evolves. We show explicitly that the knowledge transfer in
teleportation is essentially classical, in that eventually, the receiving agent
knows that its state is equal to the initial state of the sender. The relevant
epistemic statements for teleportation deal with this correlation rather than
with the actual quantum state, which is unknown throughout the protocol.


title:
Non-Markovian Quantum Error Deterrence by Dynamical Decoupling in a
  General Environment

abstract:
  A dynamical decoupling scheme for the deterrence of errors in the
non-Markovian (usually corresponding to low temperature, short time, and strong
coupling) regimes suitable for qubits constructed out of a multilevel structure
is studied. We use the effective spin-boson model (ESBM) introduced recently
[K. Shiokawa and B. L. Hu, Phys. Rev. A70, 062106 (2004)] as a low temperature
limit of the quantum Brownian oscillator model, where one can obtain exact
solutions for a general environment with colored noises. In our decoupling
scheme a train of pairs of strong pulses are used to evolve the interaction
Hamiltonian instantaneously. Using this scheme we show that the dynamical
decoupling method can suppress $1/f$ noise with slower and hence more
accessible pulses than previously studied, but it still fails to decouple
super-Ohmic types of environments.