title:
An exactly solvable model of two three-dimensional harmonic oscillators
  interacting with the quantum electromagnetic field: the Casimir-Polder
  potential

abstract:
  We consider two three-dimensional isotropic harmonic oscillators interacting
with the quantum electromagnetic field in the Coulomb gauge and within dipole
approximation. Using a Bogoliubov-like transformation, we can obtain
transformed operators such that the Hamiltonian of the system, when expressed
in terms of these operators, assumes a diagonal form. We are also able to
obtain an expression for the energy shift of the ground state, which is valid
at all orders in the coupling constant. From this energy shift the
nonperturbative Casimir-Polder potential energy between the two oscillators can
be obtained. When approximated to the fourth order in the electric charge, the
well-known expression of the Casimir-Polder potential in terms of the
polarizabilities of the oscillators is recovered.


title: On Standards and Specifications in Quantum Cryptography

abstract:
  Quantum cryptography is going to find practically useful applications.
Recently some first quantum cryptographic solutions became available on the
market. For clients it is important to be able to compare the quality and
properties of the proposed products. To this end one needs to elaborate on
specifications and standards of solutions in quantum cryptography. We propose
and discuss a list of characteristics for the specification, which includes
numerical evaluations of the security of solution and can be considered as a
standard for quantum key distribution solutions. The list is based on the
average time of key generation depending on some parameters. In the simplest
case for the user the list includes three characteristics: the security degree,
the length of keys and the key refresh rate.


title:
Decoherence, tunneling and noise-activation in a double-potential well
  at high and zero temperature

abstract:
  We study the effects of the environment on tunneling in an open system
described by a static double-well potential. We describe the evolution of a
quantum state localized in one of the minima of the potential at $t=0$, both in
the limits of high and zero environment temperature. We show that the evolution
of the system can be summarized in terms of three main physical phenomena,
namely decoherence, quantum tunneling and noise-induced activation, and we
obtain analytical estimates for the corresponding time-scales. These analytical
predictions are confirmed by large-scale numerical simulations, providing a
detailed picture of the main stages of the evolution and of the relevant
dynamical processes.


title:
Arbitrary-speed quantum gates within large ion crystals through minimum
  control of laser beams

abstract:
  We propose a scheme to implement arbitrary-speed quantum entangling gates on
two trapped ions immersed in a large linear crystal of ions, with minimal
control of laser beams. For gate speeds slower than the oscillation frequencies
in the trap, a single appropriately-detuned laser pulse is sufficient for
high-fidelity gates. For gate speeds comparable to or faster than the local ion
oscillation frequency, we discover a five-pulse protocol that exploits only the
local phonon modes. This points to a method for efficiently scaling the ion
trap quantum computer without shuttling ions.


title: Complex Rational Numbers in Quantum Mechanics

abstract:
  A binary representation of complex rational numbers and their arithmetic is
described that is not based on qubits. It takes account of the fact that $0s$
in a qubit string do not contribute to the value of a number. They serve only
as place holders. The representation is based on the distribution of four types
of systems, corresponding to $+1,-1,+i,-i,$ along an integer lattice. Complex
rational numbers correspond to arbitrary products of four types of creation
operators acting on the vacuum state. An occupation number representation is
given for both bosons and fermions.


title:
Once more on the equivalence between quantum phase transition phenomena
  in radiation-matter and magnetic systems

abstract:
  In answer to the replies of Reslen {\it et al} [arXiv: quant-ph/0507164
(2005)], and Liberti and Zaffino [arXiv:cond-mat/0507019, (2005)], we comment
once more on the temperature-dependent effective Hamiltonians for the Dicke
model derived by them in [Europhys. Lett., {\bf 69} (2005) 8] and [Eur. Phys.
J., {\bf 44} (2005) 535], respectively. These approximate Hamiltonians cannot
be correct for any finite nonzero temperature because they both violate a
rigorous result. The fact that the Dicke model belongs to the universality
class of, and its thermodynamics is described by the infinitely coordinated
transverse-field XY model is known for more than 30 years.


title:
Teleportation for atomic entangled state by entanglement swapping with
  separate measurements in cavity QED

abstract:
  Experimentally feasible scheme for teleportation of atomic entangled state
via entanglement swapping is proposed in cavity quantum electrodynamics (QED)
without joint Bell-state measurement (BSM). In the teleportation processes the
interaction between atoms and a single-mode nonresonant cavity with the
assistance of a strong classical driving field substitute the joint
measurements. The discussion of the scheme indicates that it can be realized by
current technologies.


title: Reversibility and Irreversibility within the Quantum Formalism

abstract:
  The discussion on time-reversal in quantum mechanics exists at least since
Wigner's ``Uber die Operation der Zeitumkehr in der Quantenmechanik'' paper in
1932. If and how the dynamics of the quantum world is time-reversible has been
the subject of many controversies. Some have seen quantum mechanics as
fundamentally time-irreversible, see for example von Neumann, and some have
seen in that the ultimate cause of time's arrow and second law behavior. In his
best-selling book ``The Emperor's New Mind'', Roger Penrose argues similarly
and concludes that ``our sought-for quantum gravity must be a time-asymmetric
theory'' [p.351]. Not so long ago, we read yet about another project in
Physicalia 26: to extend quantum mechanics into new fundamentally irreversible
equations, thus proposing a new theory giving ``... une description
fondamentale irreversible de tout systeme physique''.


title:
A limit on nonlocality in any world in which communication complexity is
  not trivial

abstract:
  Bell proved that quantum entanglement enables two space-like separated
parties to exhibit classically impossible correlations. Even though these
correlations are stronger than anything classically achievable, they cannot be
harnessed to make instantaneous (faster than light) communication possible.
Yet, Popescu and Rohrlich have shown that even stronger correlations can be
defined, under which instantaneous communication remains impossible. This
raises the question: Why are the correlations achievable by quantum mechanics
not maximal among those that preserve causality? We give a partial answer to
this question by showing that slightly stronger correlations would result in a
world in which communication complexity becomes trivial.


title: Optimal Entanglement Witnesses for Qubits and Qutrits

abstract:
  We study the connection between the Hilbert-Schmidt measure of entanglement
(that is the minimal distance of an entangled state to the set of separable
states) and entanglement witness in terms of a generalized Bell inequality
which distinguishes between entangled and separable states. A method for
checking the nearest separable state to a given entangled one is presented. We
illustrate the general results by considering isotropic states, in particular
2-qubit and 2-qutrit states -- and their generalizations to arbitrary
dimensions -- where we calculate the optimal entanglement witnesses explicitly.


title: Dirac quantization of free motion on curved surfaces

abstract:
  We give an explicit operator realization of Dirac quantization of free
particle motion on a surface of codimension 1. It is shown that the Dirac
recipe is ambiguous and a natural way of fixing this problem is proposed. We
also introduce a modification of Dirac procedure which yields zero quantum
potential. Some problems of abelian conversion quantization are pointed out.


title:
Negativity and Concurrence as complete entanglement measures for two
  arbitrary qudits

abstract:
  Two measures of entanglement, negativity and concurrence are studied for two
arbitrary qudits. We obtain negativity as an expectation value of an operator.
The differences of the squares of negativity and concurrence are invariants of
multilevel entanglement. Explicit results for qutrits and quadrits are
obtained.


title: Proper Time for Spin 1/2 Particles

abstract:
  We find a quantum mechanical formulation of proper time for spin 1/2
particles within the framework of the Dirac theory. It is shown that the rate
of proper time can be represented by an operator called the ` ` tempo
operator'', and that the proper time itself be given by the integral of the
expectation value of the operator. The tempo operator has some terms involving
the Pauli spin matrices, and the evolution of the proper time is influenced by
the spin state via these terms. The relation between the tempo operator and the
metric tensor is elucidated.


title:
Quantum and classical correlations of intense beams of light via joint
  photodetection

abstract:
  We address joint photodetection as a method to discriminate between the
classical correlations of a thermal beam divided by a beam splitter and the
quantum entanglement of a twin-beam obtained by parametric downconversion. We
show that for intense beams of light the detection of the difference
photocurrent may be used, in principle, in order to reveal entanglement, while
the simple measurement of the correlation coefficient is not sufficient. We
have experimentally measured the correlation coefficient and the variance of
the difference photocurrent on several classical and quantum states. Results
are in good agreement with theoretical predictions taking into account the
extra noise in the generated fields that is due to the pump-laser fluctuations.


title: Measuring the parity of an $N$-qubit state

abstract:
  We present a scheme for a projective measurement of the parity operator
$P_z=\prod_{i=1}^N \sigma_z^{(i)}$ of $N$-qubits. Our protocol uses a single
ancillary qubit, or a probe qubit, and involves manipulations of the total spin
of the $N$ qubits without requiring individual addressing. We illustrate our
protocol in terms of an experimental implementation with atomic ions in a
two-zone linear Paul trap, and further discuss its extensions to several more
general cases.


title: Introduction to relativistic quantum information

abstract:
  I discuss the role that relativistic considerations play in quantum
information processing. First I describe how the causality requirements limit
possible multi-partite measurements. Then the Lorentz transformations of
quantum states are introduced, and their implications on physical qubits are
described. This is used to describe relativistic effects in communication and
entanglement.


title: Theory for Raman superradiance in atomic gases

abstract:
  A mean field theory for Raman superradiance (SR) with recoil is presented,
where the typical SR signatures are recovered, such as quadratic dependence of
the intensity on the number of atoms and inverse proportionality of the time
scale to the number of atoms. A comparison with recent experiments and theories
on Rayleigh SR and collective atomic recoil lasing (CARL) are included. The
role of recoil is shown to be in the decay of atomic coherence and breaking of
the symmetry of the SR end-fire modes.


title:
Attacking quantum key distribution with single-photon two-qubit quantum
  logic

abstract:
  The Fuchs-Peres-Brandt (FPB) probe realizes the most powerful individual
attack on Bennett-Brassard 1984 quantum key distribution (BB84 QKD) by means of
a single controlled-NOT (CNOT) gate. This paper describes a complete physical
simulation of the FPB-probe attack on polarization-based BB84 QKD using a
deterministic CNOT constructed from single-photon two-qubit quantum logic.
Adding polarization-preserving quantum nondemolition measurements of photon
number to this configuration converts the physical simulation into a true
deterministic realization of the FPB attack.


title: Resurrection of Schrodinger Cat

abstract:
  Quantum decoherence is the major obstacle in using the potential of
engineered quantum dynamics to revolutionize high-precision measurements,
sensitive detection, or information processing. Here we experimentally
demonstrate that quantum state of a system can be recovered after the state is
destroyed by uncontrollable natural decoherence. Physical system is a cluster
of seven dipolar-coupled nuclear spins of single-labeled 13C-benzene in liquid
crystal. 13C spin plays a role of a device for measuring protons' "cat" state,
a superposition of states with six spins up (alive) and six spins down (dead).
Information about the state, stored in the 13C spin, is used to bring the
protons' subsystem into the alive state, while the excess entropy produced by
decoherence is transferred to the "measuring device", the 13C spin.


title: High fidelity one-qubit operations under random telegraph noise

abstract:
  We address the problem of implementing high fidelity one-qubit operations
subject to time dependent noise in the qubit energy splitting. We show with
explicit numerical results that high fidelity bit flips and one-qubit NOT gates
may be generated by imposing bounded control fields. For noise correlation
times shorter than the time for a pi-pulse, the time optimal pi-pulse yields
the highest fidelity. For very long correlation times, fidelity loss is
approximately due to systematic error, which is efficiently tackled by
compensation for off-resonance with a pulse sequence (CORPSE). For intermediate
ranges of the noise correlation time we find that short CORPSE, which is less
accurate than CORPSE in correcting systematic errors, yields higher fidelities.
Numerical optimization of the pulse sequences using gradient ascent pulse
engineering results in noticeable improvement of the fidelities for the bit
flip and marginal improvement for the NOT gate.


title:
Implementation of non-local operations for arbitrary high-dimensional
  systems with qubit quantum channel

abstract:
  We propose a method to implement a kind of non-local operations between
spatially separated two systems with arbitrary high-dimensions by using only
low-dimensional qubit quantum channels and classical bit communications. The
result may be generalized straightforwardly to apply for multiple systems, each
of them with arbitrary dimensions. Compared with existed approaches, our method
can economize classical resources and the needed low-dimensional quantum
channels may be more easily established in practice. We also show the
construction of the non-local quantum XOR gate for qutrit systems in terms of
the obtained non-local operations as well as some single qutrit local gates.


title: Separating the classical and quantum information via quantum cloning

abstract:
  An application of quantum cloning to optimally interface a quantum system
with a classical observer is presented, in particular we describe a procedure
to perform a minimal disturbance measurement on a single qubit by adopting a
1->2 cloning machine followed by a generalized measurement on a single clone
and the anti-clone or on the two clones. Such scheme has been applied to
enhance the transmission fidelity over a lossy quantum channel.


title: Quantum state reconstruction with binary detectors

abstract:
  I present a simple and robust method of quantum state reconstruction using
non-ideal detectors able to distinguish only between presence and absence of
photons. Using the scheme, one is able to determine a value of Wigner function
in any given point on the phase plane using expectation-maximization estimation
technique.


title: Semiclassical propagator of the Wigner function

abstract:
  Propagation of the Wigner function is studied on two levels of semiclassical
propagation, one based on the van-Vleck propagator, the other on phase-space
path integration. Leading quantum corrections to the classical Liouville
propagator take the form of a time-dependent quantum spot. Its oscillatory
structure depends on whether the underlying classical flow is elliptic or
hyperbolic. It can be interpreted as the result of interference of a
\emph{pair} of classical trajectories, indicating how quantum coherences are to
be propagated semiclassically in phase space. The phase-space path-integral
approach allows for a finer resolution of the quantum spot in terms of Airy
functions.


title:
Shape of the spatial mode function of photons generated in noncollinear
  spontaneous parametric downconversion

abstract:
  We show experimentally how noncollinear geometries in spontaneous parametric
downconversion induce ellipticity of the shape of the spatial mode function.
The degree of ellipticity depends on the pump beam width, especially for highly
focused beams. We also discuss the ellipticity induced by the spectrum of the
pump beam.


title: Logical Structure of Physical Probability Assertions

abstract:
  A modification and generalisation of von Plato's fix of the frequency theory
of probability is presented. It is thermodynamic in nature. Von Plato already
fixed the logical circle in the frequency theory, we generalise his results to
not necessarily ergodic systems of classical and quantum mechanics. This turns
out to be precisely what is needed for the problem of Quantum Measurement and
the problem of induction.


title: Higher order antibunching is not a rare phenomenon

abstract:
  Since the introduction of higher order nonclassical effects, higher order
squeezing has been reported in a number of different physical systems but
higher order antibunching is predicted only in three particular cases. In the
present work, we have shown that the higher order antibunching is not a rare
phenomenon rather it can be seen in many simple optical processes. To establish
our claim, we have shown it in six wave mixing process, four wave mixing
process and in second harmonic generation process.


title:
Polarization Requirements for Ensemble Implementations of Quantum
  Algorithms with a Single Bit Output

abstract:
  We compare the failure probabilities of ensemble implementations of quantum
algorithms which use pseudo-pure initial states, quantified by their
polarization, to those of competing classical probabilistic algorithms.
Specifically we consider a class algorithms which require only one bit to
output the solution to problems. For large ensemble sizes, we present a general
scheme to determine a critical polarization beneath which the quantum algorithm
fails with greater probability than its classical competitor. We apply this to
the Deutsch-Jozsa algorithm and show that the critical polarization is 86.6%.


title: Quantum-Relay-Assisted Key Distribution over High Photon Loss Channels

abstract:
  The maximum distance of quantum communication is limited due to the photon
loss and detector noise. Exploiting entanglement swapping, quantum relay could
offer ways to extend the achievable distance by increasing the signal to noise
ratio. In this letter we present an experimental simulation of long distance
quantum communication, in which the superiority of quantum relay is
demonstrated. Assisted by quantum relay, we greatly extend the distance limit
of unconditional secure quantum communication.


title: Optimal measurements in quantum mechanics

abstract:
  Four common optimality criteria for measurements are formulated using
relations in the set of observables, and their connections are clarified. As
case studies, 1-0 observables, localization observables, and photon counting
observables are considered.


title:
Circular Polarization and Quantum Spin: A Unified Real-Space Picture of
  Photons and Electrons

abstract:
  A classical circularly polarized electromagnetic wave carries angular
momentum, and represents the classical limit of a photon, which carries
quantized spin. It is shown that a very similar picture of a circularly
polarized coherent wave can account for both the spin of an electron and its
quantum wave function, in a Lorentz-invariant fashion. The photon-electron
interaction occurs through the usual electromagnetic potentials, modulating the
frequency and wavevector (energy and momentum) of this rotating spin field.
Other quantum particles can also be represented either as rotating spin fields,
or as composites of such fields. Taken together, this picture suggests an
alternative interpretation of quantum mechanics based solely on coherent wave
packets, with no point particles present.


title:
Security of the Quantum Key Distribution with Blind Polarization Bases
  against Impersonation Attack

abstract:
  In this paper, we briefly show how the quantum key distribution with blind
polarization bases [Kye et al., Phys. Rev. Lett. 95, 040501 (2005)] can be made
secure against the impersonation attack.


title:
General formula for finding Mexican hat wavelets by virtue of Dirac's
  representation theory and coherent state

abstract:
  The admissibility condition of a mother wavelet is explored in the context of
quantum optics theory. By virtue of Dirac's representation theory and the
coherent state' property we derive a general formula for finding Mexican hat
wavelets.


title: New Scheme of Quantum Teleportation

abstract:
  A new scheme for quantum teleportation is presented, in which the complete
teleportation can be occurred even when an entangled state between Alice and
Bob is not maximal.


title: Nonlocal impedances and the Casimir entropy at low temperatures

abstract:
  The problem with the temperature dependence of the Casimir force is
investigated. Specifically, the entropy behavior in the low temperature limit,
which caused debates in the literature, is analyzed. It is stressed that the
behavior of the relaxation frequency in the $T\to0$ limit does not play a
physical role since the anomalous skin effect dominates in this range. In
contrast with the previous works, where the approximate Leontovich impedance
was used for analysis of nonlocal effects, we give description of the problem
in terms of exact nonlocal impedances. It is found that the Casimir entropy is
going to zero at $T\to0$ only in the case when $s$ polarization does not
contribute to the classical part of the Casimir force. However, the entropy
approaching zero from the negative side that, in our opinion, cannot be
considered as thermodynamically satisfactory. The resolution of the negative
entropy problem proposed in the literature is analyzed and it is shown that it
cannot be considered as complete. The crisis with the thermal Casimir effect is
stressed.


title:
Experimental Fault-Tolerant Quantum Cryptography in a Decoherence-Free
  Subspace

abstract:
  we experimentally implement a fault-tolerant quantum key distribution
protocol with two photons in a decoherence-free subspace (DFS). It is
demonstrated that our protocol can yield good key rate even with large bit-flip
error rate caused by collective rotation, while the usual realization of BB84
protocol cannot produce any secure final key given the same channel. Since the
experiment is performed in polarization space and does not need the calibration
of reference frame, important applications in free-space quantum communication
are expected. Moreover, our method can also be used to robustly transmit an
arbitrary two-level quantum state in a type of DFS.


title: Nonbinary stabilizer codes over finite fields

abstract:
  One formidable difficulty in quantum communication and computation is to
protect information-carrying quantum states against undesired interactions with
the environment. In past years, many good quantum error-correcting codes had
been derived as binary stabilizer codes. Fault-tolerant quantum computation
prompted the study of nonbinary quantum codes, but the theory of such codes is
not as advanced as that of binary quantum codes. This paper describes the basic
theory of stabilizer codes over finite fields. The relation between stabilizer
codes and general quantum codes is clarified by introducing a Galois theory for
these objects. A characterization of nonbinary stabilizer codes over GF(q) in
terms of classical codes over GF(q^2) is provided that generalizes the
well-known notion of additive codes over GF(4) of the binary case. This paper
derives lower and upper bounds on the minimum distance of stabilizer codes,
gives several code constructions, and derives numerous families of stabilizer
codes, including quantum Hamming codes, quadratic residue codes, quantum Melas
codes, quantum BCH codes, and quantum character codes. The puncturing theory by
Rains is generalized to additive codes that are not necessarily pure. Bounds on
the maximal length of maximum distance separable stabilizer codes are given. A
discussion of open problems concludes this paper.


title: All entangled states are useful for information processing

abstract:
  The question whether all entangled states can be used as a nonclassical
resource has remained open so far. Here we provide a conclusive answer to this
problem for the case of systems shared by two parties. We show that any
entangled state $\sigma$ can enhance the teleportation power of some other
state. This holds even if the state $\sigma$ is bound entangled.


title: Generic Security Proof of Quantum Key Exchange using Squeezed States

abstract:
  Recently, a Quantum Key Exchange protocol that uses squeezed states was
presented by Gottesman and Preskill. In this paper we give a generic security
proof for this protocol. The method used for this generic security proof is
based on recent work by Christiandl, Renner and Ekert.


title:
Pseudo-Hermiticity and some consequences of a generalized quantum
  condition

abstract:
  We exploit the hidden symmetry structure of a recently proposed non-Hermitian
Hamiltonian and of its Hermitian equivalent one. This sheds new light on the
pseudo-Hermitian character of the former and allows access to a generalized
quantum condition. Special cases lead to hyperbolic and Morse-like potentials
in the framework of a coordinate-dependent mass model.


title:
Self-organization of atoms in a cavity field: threshold, bistability and
  scaling laws

abstract:
  We present a detailed study of the spatial self-organization of laser-driven
atoms in an optical cavity, an effect predicted on the basis of numerical
simulations [P. Domokos and H. Ritsch, Phys. Rev. Lett. 89, 253003 (2002)] and
observed experimentally [A. T. Black et al., Phys. Rev. Lett. 91, 203001
(2003)]. Above a threshold in the driving laser intensity, from a uniform
distribution the atoms evolve into one of two stable patterns that produce
superradiant scattering into the cavity. We derive analytic formulas for the
threshold and critical exponent of this phase transition from a mean-field
approach. Numerical simulations of the microscopic dynamics reveal that, on
laboratory timescale, a hysteresis masks the mean-field behaviour. Simple
physical arguments explain this phenomenon and provide analytical expressions
for the observable threshold. Above a certain density of the atoms a limited
number of ``defects'' appear in the organized phase, and influence the
statistical properties of the system. The scaling of the cavity cooling
mechanism and the phase space density with the atom number is also studied.


title:
Mechanical effects of optical resonators on driven trapped atoms: Ground
  state cooling in a high finesse cavity

abstract:
  We investigate theoretically the mechanical effects of light on atoms trapped
by an external potential, whose dipole transition couples to the mode of an
optical resonator and is driven by a laser. We derive an analytical expression
for the quantum center-of-mass dynamics, which is valid in presence of a tight
external potential. This equation has broad validity and allows for a
transparent interpretation of the individual scattering processes leading to
cooling. We show that the dynamics are a competition of the mechanical effects
of the cavity and of the laser photons, which may mutually interfere. We focus
onto the good-cavity limit and identify novel cooling schemes, which are based
on quantum interference effects and lead to efficient ground state cooling in
experimentally accessible parameter regimes.


title:
Quantum Puzzles in the Set Theoretic Metaworld of Heisenberg, Clauser,
  and Horne

abstract:
  This paper follows up on a recent pre-print (Durham [2005]) by first deriving
a set theoretic relationship between the generalized uncertainty relations and
the Clauser-Horne inequalities. The physical, metaphysical, and
metamathematical implications and problems are then explored. The discussion
builds on previous work by Pitowsky [1994] and suggests that there is a
fundamental problem in quantum correlation that could potentially lead to a
paradox. It leaves open the question of whether the problem is in experiment,
theory, or phenomena.


title: EPR, Bell, GHZ, and Hardy theorems, and quantum mechanics

abstract:
  We review the theorems of Einstein-Podolsky-Rosen (EPR), Bell,
Greenberger-Horne-Zeilinger (GHZ), and Hardy, and present arguments supporting
the idea that quantum mechanics is a complete, causal, non local, and non
separable theory.


title: On Fermion Entanglement

abstract:
  Under the historical definition of entanglement, namely that encountered in
Einstein--Podolski--Rosen (EPR)--type experiments, it is shown that a
particular Slater determinant is entangled. Thus a definition which holds that
any Slater determinant is unentangled, found in the literature, is inconsistent
with the historical definition. A generalization of the historical definition
that embodies its meaning as quantum correlation of observables, in the spirit
of the work of many others, but is much simpler and more physically
transparent, is presented.


title: Fluid Clocks: Emergence of quantum theory from sub-quantum dynamics

abstract:
  It is argued that any operational measure of time is inseparably bound to the
presence of a periodic process in some medium. Since, as first formulated by
Einstein's (1905) equation for the energy, all "particles" (neutrons,
electrons, photons, etc.) are each characterized by a specific "frequency", the
inverse of this frequency is the smallest operational unit of time available in
principle. With a corresponding "coarse graining" of an otherwise practically
idealized, continuous time (i.e., with the latter then holding on time scales
much larger than the coarse grained one), one can show that the basic features
of quantum theory can be derived from a minimal set of assumptions. In
particular, it is shown here how the Schroedinger equation can be derived from
classical physics modified only by said assumption of a coarse grained time and
the presence of so-called "zero-point fluctuations". The latter relate to the
dynamics of a "fluid" vacuum, which is today known to be a far cry from just
being "empty space". Consequently, it is shown that time and matter, when
discussed from a physical point of view, must by necessity be considered in one
common framework.


title: Pulse Control of Decoherence with Population Decay

abstract:
  The pulse control of decoherence in a qubit interacting with a quantum
environment is studied with focus on a general case where decoherence is
induced by both pure dephasing and population decay. To observe how the
decoherence is suppressed by periodic pi pulses, we present a simple method to
calculate the time evolution of a qubit under arbitrary pulse sequences
consisting of bit-flips and/or phase-flips. We examine the effectiveness of the
two typical sequences: bb sequence consisting of only bit-flips, and bp
sequence consisting of both bit- and phase-flips. It is shown that the
effectiveness of the pulse sequences depends on a relative strength of the two
decoherence processes especially when a pulse interval is slightly shorter than
qubit-environment correlation times. In the short-interval limit, however, the
bp sequence is always more effective than, or at least as effective as, the bb
sequence.


title: Grover like Operator Using Only Single-Qubit Gates

abstract:
  We propose a new quantum circuit for the quantum search problem. The quantum
circuit is superior to Grover's algorithm in some realistic cases. The reasons
for the superiority are in short as follows: In the quantum circuit proposed in
this paper, all the operators except for the oracle can be written as direct
products of single-qubit gates. Such separable operators can be executed much
faster than multi-particle operators, such as c-NOT gates and Toffoli gates, in
many realistic systems. The idea of this quantum circuit is inspired by the
Hamiltonian used in the adiabatic quantum computer. In addition, the scaling of
the number of oracle calls for this circuit is the same as that for Grover's
algorithm, i.e. $O(2^{n/2})$.


title: High Resolution Rydberg Spectroscopy of ultracold Rubidium Atoms

abstract:
  We present experiments on two-photon excitation of ${\rm ^{87}}$Rb atoms to
Rydberg states. For this purpose, two continuous-wave (cw)-laser systems for
both 780 nm and 480 nm have been set up. These systems are optimized to a small
linewidth (well below 1 MHz) to get both an efficient excitation process and
good spectroscopic resolution. To test the performance of our laser system, we
investigated the Stark splitting of Rydberg states. For n=40 we were able to
see the hyperfine levels splitting in the electrical field for different
finestructure states. To show the ability of spatially selective excitation to
Rydberg states, we excited rubidium atoms in an electrical field gradient and
investigated both linewidths and lineshifts. Furthermore we were able to excite
the atoms selectively from the two hyperfine ground states to Rydberg states.
Finally, we investigated the Autler-Townes splitting of the
5S$_{1/2}$$\to$5P$_{3/2}$ transition via a Rydberg state to determine the Rabi
frequency of this excitation step.


title: Deletion of imperfect cloned copies

abstract:
  In this work, we design a deleting machine and shown that for some given
condition on machine parameters, it gives slightly better result than P-B
deleting machine [5,6]. Also it is shown that for some particular values of the
machine parameters it acts like Pati-Braunstein deleting machine. We also study
the combined effect of cloning and deleting machine, where at first the cloning
is done by some standard cloning machines such as Wootters-Zurek [1] and
Buzek-Hillery [2] cloning machine and then the copy mode is deleted by
Pati-Braunstein deleting machine or our prescribed deleting machine. After that
we examine the distortion of the input state and the fidelity of deletion .


title:
Optimal reflection-free complex absorbing potentials for quantum
  propagation of wave packets

abstract:
  The conditions for optimal reflection-free complex-absorbing potentials
(CAPs) are discussed. It is shown that the CAPs as derived from the
smooth-exterior-scaling transformation of the Hamiltonian,[J. Phys. B. 31, 1431
(1998)], serve as optimal reflection-free CAPs (RF-CAPs) in wave-packet
propagation calculations of open systems. The initial wave packet, can be
located in the interaction region (as in half collision experiments) where the
CAPs have vanished or in the asymptote where the absorbing potential non zero.
As we show the optimal CAPs can be introduced also in the region where the
physical potential has not vanished. The un-avoided reflections due to the use
of finite number of grid points (or basis functions) are discussed. A simple
way to reduce the "edge grid" reflection effect is described.


title: Many-region vacuum entanglement: Distilling a W state

abstract:
  We investigate the correlations between any number of arbitrarily far-apart
regions of the vacuum of the free Klein-Gordon field by means of its finite
duration coupling to an equal number of localized detectors. We show that the
correlations between any N such regions enable us to distill an N-partite W
state, and therefore exhibit true $N$-fold entanglement. Furthermore, we show
that for N=3, the correlations cannot be reproduced by a hybrid local-nonlocal
hidden-variable model. For N >= 4 the issue remains open.


title: Physical limits on self-replication processes

abstract:
  Using few very general axioms which should be satisfied by any reasonable
theory consistent with general physical principles and some more recent results
concerning "broadcasting" of quantum states we show that: a) only classical
information can self-replicate perfectly, b) "parent" and "offspring" must be
strongly correlated, c) "separation of species" is possible only in a
non-homogeneous environment. To illustrate the existence of theoretical schemes
which possess both classical and quantum features, we present a model based on
the classical probability but with overlapping pure states and "entangled
states" for composite systems.


title: Evolution in Time of Moving Unstable Systems

abstract:
  Relativistic quantum theory shows that the known Einstein time dilation (ED)
approximately holds for the decay law of the unstable particle having definite
momentum p (DP). I use a different definition of the moving particle as the
state with definite velocity v (DV). It is shown that in this case the decay
law is not dilated. On the contrary, it is contracted as compared with the
decay law of the particle at rest. It is demonstrated that ED fails in both DP
and DV cases for time evolution of the simple unstable system of the kind of
oscillating neutrino. Experiments are known which show that ED holds for
mesons. The used theory may explain the fact by supposing that the measured
mesons are in DP state.


title: Retrodictive quantum state engineering

abstract:
  This thesis is concerned with retrodiction and measurement in quantum optics.
The latter of these two concepts is studied in particular form with a general
optical multiport device, consisting of an arbitrary array of beam-splitters
and phase-shifters. I show how such an apparatus generalizes the original
projection synthesis technique, introduced as an in principle technique to
measure the canonical phase distribution. Just as for the original projection
synthesis, it is found that such a generalised device can synthesize any
general projection onto a state in a finite dimensional Hilbert space. One of
the important findings of this thesis is that, unlike the original projection
synthesis technique, the general apparatus described here only requires a
classical, that is a coherent, reference field at the input of the device. Such
an apparatus lends itself much more readily to practical implementation and
would find applications in measurement and predictive state engineering.
  If we relax the above condition to allow for just a single non-classical
reference field, we show that the apparatus is capable of producing a
single-shot measure of canonical phase. That is, the apparatus can project onto
any one of an arbitrarily large subset of phase eigenstates, with a probability
proportional to the overlap of the phase state and the input field. Unlike the
original projection synthesis proposal, this proposal requires a binomial
reference state as opposed to a reciprocal binomial state. We find that such a
reference state can be obtained, to an excellent approximation, from a suitably
squeezed state.
  The analysis of these measurement apparatuses is performed in the less usual,
but completely rigorous, retrodictive formalism of quantum mechanics.


title: Generic Short-Time Propagation of Sharp-Boundaries Wave Packets

abstract:
  A general solution to the "shutter" problem is presented. The propagation of
an arbitrary initially bounded wavefunction is investigated, and the general
solution for any such function is formulated. It is shown that the exact
solution can be written as an expression that depends only on the values of the
function (and its derivatives) at the boundaries. In particular, it is shown
that at short times ($t\ll2mx^2/\hbar$, where $x$ is the distance to the
boundaries) the wavefunction propagation depends only on the wavefunction's
values (or its derivatives) at the boundaries of the region. Finally, we
generalize these findings to a non-singular wavefunction (i.e., for wavepackets
with finite-width boundaries) and suggest an experimental verification.


title: Scheme for generating entangled states of two field modes in a cavity

abstract:
  This paper considers a two-level atom interacting with two cavity modes with
equal frequencies. Applying a unitary transformation, the system reduces to the
analytically solvable Jaynes-Cummings model. For some particular field states,
coherent and squeezed states, the transformation between the two bare basis's,
related by the unitary transformation, becomes particularly simple. It is shown
how to generate, the highly non-classical, entangled coherent states of the two
modes, both in the zero and large detuning cases. An advantage with the zero
detuning case is that the preparation is deterministic and no atomic
measurement is needed. For the large detuning situation a measurement is
required, leaving the field in either of two orthogonal entangled coherent
states.


title: Complementarity and Afshar's experiment

abstract:
  In this article we criticize the experiment realized by S. Afshar [Proc. SPIE
5866, 229-244 (July 2005)]. We analyze Bohr's complementarity and show that the
interpretation proposed by Afshar is misleading.


title: Assumptions that imply quantum dynamics is linear

abstract:
  A basic linearity of quantum dynamics, that density matrices are mapped
linearly to density matrices, is proved very simply for a system that does not
interact with anything else. It is assumed that at each time the physical
quantities and states are described by the usual linear structures of quantum
mechanics. Beyond that, the proof assumes only that the dynamics does not
depend on anything outside the system but must allow the system to be described
as part of a larger system. The basic linearity is linked with previously
established results to complete a simple derivation of the linear Schrodinger
equation. For this it is assumed that density matrices are mapped one-to-one
onto density matrices. An alternative is to assume that pure states are mapped
one-to-one onto pure states and that entropy does not decrease.


title: Sub-Planck phase-space structures and Heisenberg-limited measurements

abstract:
  We show how sub-Planck phase-space structures in the Wigner function can be
used to achieve Heisenberg-limited sensitivity in weak force measurements.
Nonclassical states of harmonic oscillators, consisting of superpositions of
coherent states, are shown to be useful for the measurement of weak forces that
cause translations or rotations in phase space, which is done by entangling the
quantum oscillator with a two-level system. Implementations of this strategy in
cavity QED and ion traps are described.


title:
Single-photon excitation of a coherent state: catching the elementary
  step of stimulated light emission

abstract:
  When a single quantum of electromagnetic field excitation is added to the
same spatio-temporal mode of a coherent state, a new field state is generated
that exhibits intermediate properties between those of the two parents. Such a
single-photon-added coherent state is obtained by the action of the photon
creation operator on a coherent state and can thus be regarded as the result of
the most elementary excitation process of a classical light field. Here we
present and describe in depth the experimental realization of such states and
their complete analysis by means of a novel ultrafast, time-domain, quantum
homodyne tomography technique clearly revealing their non-classical character.


title: Thoughts on Noise and Quantum Computation

abstract:
  We will try to explore, primarily from the complexity-theoretic point of
view, limitations of error-correction and fault-tolerant quantum computation.
We consider stochastic models of quantum computation on $n$ qubits subject to
noise operators that are obtained as products of tiny noise operators acting on
a small number of qubits. We conjecture that for realistic random noise
operators of this kind there will be substantial dependencies between the noise
on individual qubits and, in addition, we propose that the dependence structure
of the noise acting on individual qubits will necessarily depend
(systematically) on the dependence structure of the qubits themselves. We point
out that the majority function can repair, in the classical case, some forms of
stochastic noise of this kind and conjecture that this healing power of
majority has no quantum analog. The main hypothesis of this paper is that these
properties of noise are sufficient to reduce quantum computation to
probabilistic classical computation. Some potentially relevant mathematical
issues and problems will be described. Our line of thought appears to be
related to that of physicists Alicki, Horodecki, Horodecki and Horodecki
[AHHH].


title: Relativistic quantum walks

abstract:
  By pursuing the deep relation between the one-dimensional Dirac equation and
quantum walks, the physical role of quantum interference in the latter is
explained. It is shown that the time evolution of the probability density of a
quantum walker, initially localized on a lattice, is directly analogous to
relativistic wave-packet spreading. Analytic wave-packet solutions reveal a
striking connection between the discrete and continuous time quantum walks.


title:
T-junction ion trap array for two-dimensional ion shuttling, storage and
  manipulation

abstract:
  We demonstrate a two-dimensional 11-zone ion trap array, where individual
laser-cooled atomic ions are stored, separated, shuttled, and swapped. The trap
geometry consists of two linear rf ion trap sections that are joined at a 90
degree angle to form a T-shaped structure. We shuttle a single ion around the
corners of the T-junction and swap the positions of two crystallized ions using
voltage sequences designed to accommodate the nontrivial electrical potential
near the junction. Full two-dimensional control of multiple ions demonstrated
in this system may be crucial for the realization of scalable ion trap quantum
computation and the implementation of quantum networks.


title:
Scheme for implementing quantum information sharing via tripartite
  entangled state in cavity QED

abstract:
  We investigate economic protocol to securely distribute and reconstruct a
single-qubit quantum state between two users via a tripartite entangled state
in cavity QED. Our scheme is insensitive to both the cavity decay and the
thermal field.


title: Photon-number-solving Decoy State Quantum Key Distribution

abstract:
  In this paper, a photon-number-resolving decoy state quantum key distribution
scheme is presented based on recent experimental advancements. A new upper
bound on the fraction of counts caused by multiphoton pulses is given. This
upper bound is independent of intensity of the decoy source, so that both the
signal pulses and the decoy pulses can be used to generate the raw key after
verified the security of the communication. This upper bound is also the lower
bound on the fraction of counts caused by multiphoton pulses as long as faint
coherent sources and high lossy channels are used. We show that Eve's coherent
multiphoton pulse (CMP) attack is more efficient than symmetric individual (SI)
attack when quantum bit error rate is small, so that CMP attack should be
considered to ensure the security of the final key. finally, optimal intensity
of laser source is presented which provides 23.9 km increase in the
transmission distance. 03.67.Dd


title: Notes on Quantum Mechanics and Consciousness

abstract:
  There have lately been a variety of attempts to connect, or even explain, if
not in fact, reduce human consciousness to quantum mechanical processes. Such
attempts tend to draw a sharp and fundamental distinction between the role of
consciousness in classical mechanics, and on the other hand, in quantum
mechanics, with an insistence on the assumed exceptional character of the
latter. What is strangely missed, however, is the role of human consciousness
as such in the very discovery or creation of both of these physical theories.
And this a priori role is far more important than all the possible a posteriori
interplays between consciousness and the mentioned two theories of physics,
interplays which may happen during one or another specific experiment,
measurement, and so on. In this regard it is suggested that the specific
features human consciousness may exhibit during interactions with quantum
mechanical systems may as well have other explanations which do not appear to
be less plausible, or less well founded.


title: Qdensity - a Mathematica Quantum Computer Simulation

abstract:
  This Mathematica 5.2 package~\footnote{QDENSITY is available at
http://www.pitt.edu/~tabakin/QDENSITY} is a simulation of a Quantum Computer.
The program provides a modular, instructive approach for generating the basic
elements that make up a quantum circuit. The main emphasis is on using the
density matrix, although an approach using state vectors is also implemented in
the package. The package commands are defined in {\it Qdensity.m} which
contains the tools needed in quantum circuits, e.g. multiqubit kets,
projectors, gates, etc. Selected examples of the basic commands are presented
here and a tutorial notebook, {\it Tutorial.nb} is provided with the package
(available on our website) that serves as a full guide to the package. Finally,
application is made to a variety of relevant cases, including Teleportation,
Quantum Fourier transform, Grover's search and Shor's algorithm, in separate
notebooks: {\it QFT.nb}, {\it Teleportation.nb}, {\it Grover.nb} and {\it
Shor.nb} where each algorithm is explained in detail. Finally, two examples of
the construction and manipulation of cluster states, which are part of ``one
way computing" ideas, are included as an additional tool in the notebook {\it
Cluster.nb}. A Mathematica palette containing most commands in QDENSITY is also
included: {\it QDENSpalette.nb} .


title: A Transactional Analysis of Interaction Free Measurements

abstract:
  The transactional interpretation of quantum mechanics is applied to the
"interaction-free" measurement scenario of Elitzur and Vaidman and to the
Quantum Zeno Effect version of the measurement scenario by Kwiat, et al. It is
shown that the non-classical information provided by the measurement scheme is
supplied by the probing of the intervening object by incomplete offer and
confirmation waves that do not form complete transactions or lead to real
interactions.


title: On relational time and energy decoherence

abstract:
  Students Alice and Bob take an examination in their quantum mechanics class,
and thereby illustrate some aspects of energy decoherence.


title:
On the geometric potential derived from Hermitian momenta on a curved
  surface

abstract:
  A geometric potential $V_C$ depending on the mean and Gaussian curvatures of
a surface $\Sigma$ arises when confining a particle initially in a
three-dimensional space $\Omega$ onto $\Sigma$ when the particle Hamiltonian
$H_\Omega$ is taken proportional to the Laplacian $L$ on $\Omega$. In this work
rather than assume $H_\Omega \propto L$, momenta $P_\eta$ Hermitian over
$\Omega$ are constructed and used to derive an alternate Hamiltonian $H_\eta$.
The procedure leading to $V_C$, when performed with $H_\eta$, is shown to yield
$V_C = 0$. To obtain a measure of the difference between the two approaches,
numerical results are presented for a toroidal model.


title:
Playing games in quantum mechanical settings: A necessary and sufficient
  condition

abstract:
  A number of recent studies have focused on novel features in game theory when
the games are played using quantum mechanical toolbox (entanglement, unitary
operators, measurement). Researchers have concentrated in two-player-two
strategy, 2x2, dilemma containing classical games, and transferred them into
quantum realm showing that in quantum pure strategies dilemmas in such games
can be resolved if entanglement is distributed between the players armed with
quantum operations. Moreover, it became clear that the players receive the
highest sum of payoffs available in the game, which are otherwise impossible in
classical pure strategies. Encouraged by the observation of rich dynamics of
physical systems with many interacting parties and the power of entanglement in
quantum versions of 2x2 games, it became generally accepted that quantum
versions can be easily extended to N-player situations by simply allowing
N-partite entangled states. In this article, however, we show that this is not
generally true because the reproducibility of classical tasks in quantum domain
imposes limitations on the type of entanglement and quantum operators. We
propose a benchmark for the evaluation of quantum and classical versions of
games, and derive the necessary and sufficient conditions for a physical
realization. We give examples of entangled states that can and cannot be used,
and the characteristics of quantum operators used as strategies.


title:
Concurrence vs. purity: Influence of local channels on Bell states of
  two qubits

abstract:
  We analyze how a maximally entangled state of two-qubits (e.g., the singlet
$\psi_s$) is affected by action of local channels described by completely
positive maps $\cE$ . We analyze the concurrence and the purity of states
$\varrho_\cE=\cE\otimes\cI[\psi_s]$.Using the concurrence-{\it vs}-purity phase
diagram we characterize local channels $\cE$ by their action on the singlet
state $\psi_s$. We specify a region of the concurrence-{\it vs.}-purity diagram
that is achievable from the singlet state via the action of unital channels. We
show that even most general (including non-unital) local channels acting just
on a single qubit of the original singlet state cannot generate the maximally
entangled mixed states (MEMS). We study in detail various time evolutions of
the original singlet state induced by local Markovian semigroups. We show that
the decoherence process is represented in the concurrence-{\it vs.}-purity
diagram by a line that forms the lower bound of the achievable region for
unital maps. On the other hand, the depolarization process is represented by a
line that forms the upper bound of the region of maps induced by unital maps.


title: Quantum electromdynamics in a linear absorbing dielectric medium

abstract:
  The eletromagnetic field in a linear absorptive dielectric medium, is
quantized in the framework of the damped polarization model. A Hamiltonian
containing a reservoir with continuous degrees of freedom, is proposed. The
reservoir minimally interacts with the dielectric polarization and the
electromagnetic field. The Lagevin-Schrodinger equation is obtained as the
equation of motion of the polarization field. The radiation reaction
electromagnetic field is considered. For a homogeneous medium, the equations of
motion are solved using the Laplace transformation method.


title: The Groverian Measure of Entanglement for Mixed States

abstract:
  The Groverian entanglement measure introduced earlier for pure quantum states
[O. Biham, M.A. Nielsen and T. Osborne, Phys. Rev. A 65, 062312 (2002)] is
generalized to the case of mixed states, in a way that maintains its
operational interpretation. The Groverian measure of a mixed state of n qubits
is obtained by a purification procedure into a pure state of 2n qubits,
followed by an optimization process based on Uhlmann's theorem, before the
resulting state is fed into Grover's search algorithm. The Groverian measure,
expressed in terms of the maximal success probability of the algorithm,
provides an operational measure of entanglement of both pure and mixed quantum
states of multiple qubits. These results may provide further insight into the
role of entanglement in making quantum algorithms powerful.


title: The Analogue of Bohm-Bell Processes on a Graph

abstract:
  Bohm-Bell processes, of interest in the foundations of quantum field theory,
form a class of Markov processes $Q_t$ generalizing in a natural way both
Bohm's dynamical system in configuration space for nonrelativistic quantum
mechanics and Bell's jump process for lattice quantum field theories. They are
such that at any time $t$ the distribution of $Q_t$ is $|\psi_t|^2$ with $\psi$
the wave function of quantum theory. We extend this class here by introducing
the analogous Markov process for quantum mechanics on a graph (also called a
network, i.e., a space consisting of line segments glued together at their
ends). It is a piecewise deterministic process whose innovations occur only
when it passes through a vertex.


title:
The Role of Doppler Broadening in Electromagnetically Induced
  Transparency and Autler-Townes Splitting in Open Molecular Systems

abstract:
  We describe in this Letter how inhomogeneous line broadening affects the
Autler-Townes (AT) splitting in a three level open molecular cascade system.
For moderate Rabi frequencies in the range of 300 to 500 MHz the fluorescence
line shape from the uppermost level |3> in this system depends strongly on the
frequency ratio of the two laser fields. However, the fluorescence spectrum of
the intermediate level |2> appears as expected. We provide a description of the
conditions for optimally resolved AT splitting in terms of the probe
laser/coupling field frequency ratio and laser propagation geometry based on
our theoretical analysis of the Doppler integral. This is important for
applications such as molecular angular momentum alignment as well as for the
measurement of the transition dipole moment matrix element.


title: Thin layer quantization in higher dimensions and codimensions

abstract:
  We consider the thin layer quantization with use of only the most elementary
notions of differential geometry. We consider this method in higher dimensions
and get an explicit formula for quantum potential. For codimension 1 surfaces
the quantum potential is presented in terms of principal curvatures, and
equivalence with Prokhorov quantization method is proved. It is shown that, in
contrast with original da Costa method, Prokhorov quantization can be
generalized directly to higher codimensions.


title:
Security of differential phase shift quantum key distribution against
  individual attacks

abstract:
  We derive a proof of security for the Differential Phase Shift Quantum Key
Distribution (DPSQKD) protocol under the assumption that Eve is restricted to
individual attacks. The security proof is derived by bounding the average
collision probability, which leads directly to a bound on Eve's mutual
information on the final key. The security proof applies to realistic sources
based on pulsed coherent light. We then compare individual attacks to
sequential attacks and show that individual attacks are more powerful.


title:
High-fidelity linear optical quantum computing with polarization
  encoding

abstract:
  We show that the KLM scheme [Knill, Laflamme and Milburn, Nature {\bf 409},
46] can be implemented using polarization encoding, thus reducing the number of
path modes required by half. One of the main advantages of this new
implementation is that it naturally incorporates a loss detection mechanism
that makes the probability of a gate introducing a non-detected error, when
non-ideal detectors are considered, dependent only on the detector dark-count
rate and independent of its efficiency. Since very low dark-count rate
detectors are currently available, a high-fidelity gate (probability of error
of order $10^{-6}$ conditional on the gate being successful) can be implemented
using polarization encoding. The detector efficiency determines the overall
success probability of the gate but does not affect its fidelity. This can be
applied to the efficient construction of optical cluster states with very high
fidelity for quantum computing.


title: Entanglement dynamics under decoherence: from qubits to qudits

abstract:
  We investigate the time evolution of entanglement for bipartite systems of
arbitrary dimensions under the influence of decoherence. For qubits, we
determine the precise entanglement decay rates under different
system-environment couplings, including finite temperature effects. For qudits,
we show how to obtain upper bounds for the decay rates and also present exact
solutions for various classes of states.


title: Entanglement and quantum phase transition in quantum mixed spin chains

abstract:
  The ground entanglement and thermal entanglement in quantum mixed spin chains
consisting of two integer spins 1 and two half integer spins 1/2 arrayed as
${1/2}-{1/2}-1-1$ in a unit cell with antiferromagnetic nearest-neighbor
couplings $J_1$($J_2$) between the spins of equal (different) magnitudes, are
investigated by adopting the log-negativity. The ground entanglement transition
found here is closely related with the valence bond state transition, and the
thermal entanglement near the critical point is calculated and shown that two
distinct behaviors exist in the nearest neighbor same kind of spins and
different kind of spins, respectively. The potential application of our results
on the quantum information processing is also discussed.


title: A probabilistic branching bisimulation for quantum processes

abstract:
  Full formal descriptions of algorithms making use of quantum principles must
take into account both quantum and classical computing components and assemble
them so that they communicate and cooperate.Moreover, to model concurrent and
distributed quantum computations, as well as quantum communication protocols,
quantum to quantum communications which move qubits physically from one place
to another must also be taken into account.
  Inspired by classical process algebras, which provide a framework for
modeling cooperating computations, a process algebraic notation is defined,
which provides a homogeneous style to formal descriptions of concurrent and
distributed computations comprising both quantum and classical parts.Based upon
an operational semantics which makes sure that quantum objects, operations and
communications operate according to the postulates of quantum mechanics, a
probabilistic branching bisimulation is defined among processes considered as
having the same behavior.


title: Reflectionless Potentials and PT Symmetry

abstract:
  Large families of Hamiltonians that are non-Hermitian in the conventional
sense have been found to have all eigenvalues real, a fact attributed to an
unbroken PT symmetry. The corresponding quantum theories possess an
unconventional scalar product. The eigenvalues are determined by differential
equations with boundary conditions imposed in wedges in the complex plane. For
a special class of such systems, it is possible to impose the PT-symmetric
boundary conditions on the real axis, which lies on the edges of the wedges.
The PT-symmetric spectrum can then be obtained by imposing the more transparent
requirement that the potential be reflectionless.


title: Multiparty quantum secret splitting and quantum state sharing

abstract:
  A protocol for multiparty quantum secret splitting is proposed with an
ordered $N$ EPR pairs and Bell state measurements. It is secure and has the
high intrinsic efficiency and source capacity as almost all the instances are
useful and each EPR pair carries two bits of message securely. Moreover, we
modify it for multiparty quantum state sharing of an arbitrary $m$-particle
entangled state based on quantum teleportation with only Bell state
measurements and local unitary operations which make this protocol more
convenient in a practical application than others.


title:
Controlled photon emission and Raman transition experiments with a
  single trapped atom

abstract:
  We present recent results on the coherent control of an optical transition in
a single rubidium atom, trapped in an optical tweezer. We excite the atom using
resonant light pulses that are short (4 ns) compared with the lifetime of the
excited state (26 ns). By varying the intensity of the laser pulses, we can
observe an adjustable number of Rabi oscillations, followed by free decay once
the light is switched off. To generate the pulses we have developed a novel
laser system based on frequency doubling a telecoms laser diode at 1560 nm. By
setting the laser intensity to make a pi-pulse, we use this coherent control to
make a high quality triggered source of single photons. We obtain an average
single photon rate of 9600 s-1 at the detector. Measurements of the
second-order temporal correlation function show almost perfect antibunching at
zero delay. In addition, we present preliminary results on the use of Raman
transitions to couple the two hyperfine levels of the ground state of our
trapped atom. This will allow us to prepare and control a qubit formed by two
hyperfine sub-levels.


title: Entanglement swapping for generalized non-local correlations

abstract:
  We consider an analogue of entanglement-swapping for a set of black boxes
with the most general non-local correlations consistent with relativity
(including correlations which are stronger than any attainable in quantum
theory). In an attempt to incorporate this phenomenon, we consider expanding
the space of objects to include not only correlated boxes, but `couplers',
which are an analogue for boxes of measurements with entangled eigenstates in
quantum theory. Surprisingly, we find that no couplers exist for two
binary-input/binary-output boxes, and hence that there is no analogue of
entanglement-swapping for such boxes.


title: Decoherence induced by a composite environment

abstract:
  We study the decoherence induced by the environment over a composite quantum
system, comprising two coupled subsystems A and B, which may be a harmonic or
an upside-down oscillators. We analyze the case in which the B-subsystem is in
direct interaction with a thermal bath, while the other remains isolated from
the huge reservoir. We compare the results concerning the decoherence suffered
by the A-subsystem.


title: Quantum theory of light and noise polarization in nonlinear optics

abstract:
  We present a consistent quantum theory of the electromagnetic field in
nonlinearly responding causal media, with special emphasis on $\chi^{(2)}$
media. Starting from QED in linearly responding causal media, we develop a
method to construct the nonlinear Hamiltonian expressed in terms of the complex
nonlinear susceptibility in a quantum mechanically consistent way. In
particular we show that the method yields the nonlinear noise polarization,
which together with the linear one is responsible for intrinsic quantum
decoherence.


title: Entanglement of Trapped-Ion Clock States

abstract:
  A M{\o}lmer-S{\o}rensen entangling gate is realized for pairs of trapped
$^{111}$Cd$^+$ ions using magnetic-field insensitive "clock" states and an
implementation offering reduced sensitivity to optical phase drifts. The gate
is used to generate the complete set of four entangled states, which are
reconstructed and evaluated with quantum-state tomography. An average
target-state fidelity of 0.79 is achieved, limited by available laser power and
technical noise. The tomographic reconstruction of entangled states
demonstrates universal quantum control of two ion-qubits, which through
multiplexing can provide a route to scalable architectures for trapped-ion
quantum computing.


title: An introduction to measurement based quantum computation

abstract:
  In the formalism of measurement based quantum computation we start with a
given fixed entangled state of many qubits and perform computation by applying
a sequence of measurements to designated qubits in designated bases. The choice
of basis for later measurements may depend on earlier measurement outcomes and
the final result of the computation is determined from the classical data of
all the measurement outcomes. This is in contrast to the more familiar gate
array model in which computational steps are unitary operations, developing a
large entangled state prior to some final measurements for the output. Two
principal schemes of measurement based computation are teleportation quantum
computation (TQC) and the so-called cluster model or one-way quantum computer
(1WQC). We will describe these schemes and show how they are able to perform
universal quantum computation. We will outline various possible relationships
between the models which serve to clarify their workings. We will also discuss
possible novel computational benefits of the measurement based models compared
to the gate array model, especially issues of parallelisability of algorithms.


title: A Physical Axiomatic Approach to Schrodinger's Equation

abstract:
  The Schrodinger equation for non-relativistic quantum systems is derived from
some classical physics axioms within an ensemble hamiltonian framework. Such an
approach enables one to understand the structure of the equation, in particular
its linearity, in intuitive terms. Furthermore it allows for a physically
motivated and systematic investigation of potential generalisations which are
briefly discussed.


title: Scalable Quantum Computing with "Enhancement" Quantum Dots

abstract:
  We propose a novel scheme of solid state realization of a quantum computer
based on single spin "enhancement mode" quantum dots as building blocks. In the
enhancement quantum dots, just one electron can be brought into initially empty
dot, in contrast to depletion mode dots based on expelling of electrons from
multi-electron dots by gates. The quantum computer architectures based on
depletion dots are confronted by several challenges making scalability
difficult. These challenges can be successfully met by the approach based on
ehnancement mode, capable of producing square array of dots with versatile
functionalities. These functionalities allow transportation of qubits,
including teleportation, and error correction based on straightforward one- and
two-qubit operations. We describe physical properties and demonstrate
experimental characteristics of enhancement quantum dots and single-electron
transistors based on InAs/GaSb composite quantum wells. We discuss the
materials aspects of quantum dot quantum computing, including the materials
with large spin splitting such as InAs, as well as perspectives of enhancement
mode approach in materials such as Si.


title:
Quantum State Reconstruction of Many Body System Based on Complete Set
  of Quantum Correlations Reduced by Symmetry

abstract:
  We propose and study a universal approach for the reconstruction of quantum
states of many body systems from symmetry analysis. The concept of minimal
complete set of quantum correlation functions (MCSQCF) is introduced to
describe the state reconstruction. As an experimentally feasible physical
object, the MCSQCF is mathematically defined through the minimal complete
subspace of observables determined by the symmetry of quantum states under
consideration. An example with broken symmetry is analyzed in detail to
illustrate the idea.


title: Experimental Analysis of a 4-Qubit Cluster State

abstract:
  Linear optics quantum logic operations enabled the observation of a
four-photon cluster state. We prove genuine four-partite entanglement and study
its persistency, demonstrating remarkable differences to the usual GHZ state.
Efficient analysis tools are introduced in the experiment, which will be of
great importance in further studies on multi-particle entangled states.


title: On the structure of the sets of mutually unbiased bases for N qubits

abstract:
  For a system of N qubits, spanning a Hilbert space of dimension d=2^N, it is
known that there exists d+1 mutually unbiased bases. Different construction
algorithms exist, and it is remarkable that different methods lead to sets of
bases with different properties as far as separability is concerned. Here we
derive the four sets of nine bases for three qubits, and show how they are
unitarily related. We also briefly discuss the four-qubit case, give the
entanglement structure of sixteen sets of bases,and show some of them, and
their interrelations, as examples. The extension of the method to the general
case of N qubits is outlined.


title: Quantum Kaleidoscopes and Bell's theorem

abstract:
  A quantum kaleidoscope is defined as a set of observables, or states,
consisting of many different subsets that provide closely related proofs of the
Bell-Kochen-Specker (BKS) and Bell nonlocality theorems. The kaleidoscopes
prove the BKS theorem through a simple parity argument, which also doubles as a
proof of Bell's nonlocality theorem if use is made of the right sort of
entanglement. Three closely related kaleidoscopes are introduced and discussed
in this paper: a 15-observable kaleidoscope, a 24-state kaleidoscope and a
60-state kaleidoscope. The close relationship of these kaleidoscopes to a
configuration of 12 points and 16 lines known as Reye's configuration is
pointed out. The "rotations" needed to make each kaleidoscope yield all its
apparitions are laid out. The 60-state kaleidoscope, whose underlying
geometrical structure is that of ten interlinked Reye's configurations
(together with their duals), possesses a total of 1120 apparitions that provide
proofs of the two Bell theorems. Some applications of these kaleidoscopes to
problems in quantum tomography and quantum state estimation are discussed.


title: Stabilizer Formalism for Operator Quantum Error Correction

abstract:
  Operator quantum error correction is a recently developed theory that
provides a generalized framework for active error correction and passive error
avoiding schemes. In this paper, we describe these codes in the stabilizer
formalism of standard quantum error correction theory. This is achieved by
adding a "gauge" group to the standard stabilizer definition of a code that
defines an equivalence class between encoded states. Gauge transformations
leave the encoded information unchanged; their effect is absorbed by virtual
gauge qubits that do not carry useful information. We illustrate the
construction by identifying a gauge symmetry in Shor's 9-qubit code that allows
us to remove 4 of its 8 stabilizer generators, leading to a simpler decoding
procedure and a wider class of logical operations without affecting its
essential properties. This opens the path to possible improvements of the error
threshold of fault-tolerant quantum computing.


title: Inseparability criteria for bipartite quantum states

abstract:
  We provide necessary and sufficient conditions for the partial transposition
of bipartite harmonic quantum states to be nonnegative. The conditions are
formulated as an infinite series of inequalities for the moments of the state
under study. The violation of any inequality of this series is a sufficient
condition for entanglement. Previously known entanglement conditions are shown
to be special cases of our approach.


title: Geodesics and the best measurement for distinguishing quantum states

abstract:
  From statistical distinguishability of probability distributions, one can
define distinguishability of quantum states. A corresponding measurement to
perform, optimal in a definite sense, for distinguishing between two given
states rho_A and rho_B, has been derived by Fuchs and Caves. We show that the
Bures-Uhlmann geodesic through the two states singles out this measurement. The
geodesic `bounces' at the boundary of the set of quantum states. Whenever the
geodesic hits the boundary, the state orthogonal to that boundary state is one
of the basis states for the measurement.


title:
Effects of random localizing events on matter waves: formalism and
  examples

abstract:
  A formalism is introduced to describe a number of physical processes that may
break down the coherence of a matter wave over a characteristic length scale l.
In a second-quantized description, an appropriate master equation for a set of
bosonic "modes" (such as atoms in a lattice, in a tight-binding approximation)
is derived. Two kinds of "localizing processes" are discussed in some detail
and shown to lead to master equations of this general form: spontaneous
emission (more precisely, light scattering), and modulation by external random
potentials. Some of the dynamical consequences of these processes are
considered: in particular, it is shown that they generically lead to a damping
of the motion of the matter-wave currents, and may also cause a "flattening" of
the density distribution of a trapped condensate at rest.


title: Superradiance in ultracold Rydberg gases

abstract:
  Experiments in dense, ultracold gases of rubidium Rydberg atoms show a
considerable decrease of the radiative excited state lifetimes compared to
dilute gases. This accelerated decay is explained by collective and cooperative
effects, leading to superradiance. A novel formalism to calculate effective
decay times in a dense Rydberg gas shows that for these atoms the decay into
nearby levels increases by up to three orders of magnitude. Excellent agreement
between theory and experiment follows from this treatment of Rydberg decay
behavior.


title:
Thermodynamics of a quantized electromagnetic field in rectangular
  cavities with perfectly conducting walls

abstract:
  The thermodynamical properties of a quantized electromagnetic field inside a
box with perfectly conducting walls are studied using a regularization scheme
that permits to obtain finite expressions for the thermodynamic potentials. The
source of ultraviolet divergences is directly isolated in the expression for
the density of modes, and the logarithmic infrared divergences are regularized
imposing the uniqueness of vacuum and, consequently, the vanishing of the
entropy in the limit of zero temperature. We thus obtain corrections to the
Casimir energy and pressures, and to the specific heat that are due to
temperature effects; these results suggest effects that could be tested
experimentally.


title: Remote which-way-choice scheme: proposed foundations experiments

abstract:
  Twin photons from spontaneous parametric down-conversion with preselected
polarization are used as spatially disjoint subsystems. One photon is subject
to an interference measurement, while a projective measurement of the second
photon induces the way-choice of the first photon. This would be an example of
way-choice free of direct action on the interfering photon. Two further
applications of the proposed scheme are considered: a new method of quantum
information speed measurement, and a test of commutation of space-like remote
measurements.


title:
Jensen-Shannon divergence as a measure of distinguishability between
  mixed quantum states

abstract:
  We discuss an alternative to relative entropy as a measure of distance
between mixed quantum states. The proposed quantity is an extension to the
realm of quantum theory of the Jensen-Shannon divergence (JSD) between
probability distributions. The JSD has several interesting properties. It
arises in information theory and, unlike the Kullback-Leibler divergence, it is
symmetric, always well defined and bounded. We show that the quantum JSD (QJSD)
shares with the relative entropy most of the physically relevant properties, in
particular those required for a "good" quantum distinguishability measure. We
relate it to other known quantum distances and we suggest possible applications
in the field of the quantum information theory.


title: Efficient quantum algorithms for simulating sparse Hamiltonians

abstract:
  We present an efficient quantum algorithm for simulating the evolution of a
sparse Hamiltonian H for a given time t in terms of a procedure for computing
the matrix entries of H. In particular, when H acts on n qubits, has at most a
constant number of nonzero entries in each row/column, and |H| is bounded by a
constant, we may select any positive integer $k$ such that the simulation
requires O((\log^*n)t^{1+1/2k}) accesses to matrix entries of H. We show that
the temporal scaling cannot be significantly improved beyond this, because
sublinear time scaling is not possible.


title:
The harmonic oscillator with dissipation within the theory of open
  quantum systems

abstract:
  Time evolution of the expectation values of various dynamical operators of
the harmonic oscillator with dissipation is analitically obtained within the
framework of the Lindblad theory for open quantum systems. We deduce the
density matrix of the damped harmonic oscillator from the solution of the
Fokker-Planck equation for the coherent state representation, obtained from the
master equation for the density operator. The Fokker-Planck equation for the
Wigner distribution function, subject to either the Gaussian type or the
$\delta$-function type of initial conditions, is also solved by using the
Wang-Uhlenbeck method. The obtained Wigner functions are two-dimensional
Gaussians with different widths.


title: Density operator and entropy of the damped quantum harmonic oscillator

abstract:
  The expression for the density operator of the damped harmonic oscillator is
derived from the master equation in the framework of the Lindblad theory for
open quantum systems. Then the von Neumann entropy and effective temperature of
the system are obtained. The entropy for a state characterized by a Wigner
distribution function which is Gaussian in form is found to depend only on the
variance of the distribution function.


title: Quantum search algorithm as an open system

abstract:
  We study the quantum search algorithm as an open system. More specifically,
we analyze the responses of that algorithm to an external monochromatic field,
and to the decoherences introduced by the measurement process. We find that the
search algorithm is robust with respect to many external interactions.


title:
Direct Observation of Sub-Poissonian Number Statistics in a Degenerate
  Bose Gas

abstract:
  We report the direct observation of sub-Poissonian number fluctuation for a
degenerate Bose gas confined in an optical trap. Reduction of number
fluctuations below the Poissonian limit is observed for average numbers that
range from 300 to 60 atoms.


title: Quantum measurement of a mesoscopic spin ensemble

abstract:
  We describe a method for precise estimation of the polarization of a
mesoscopic spin ensemble by using its coupling to a single two-level system.
Our approach requires a minimal number of measurements on the two-level system
for a given measurement precision. We consider the application of this method
to the case of nuclear spin ensemble defined by a single electron-charged
quantum dot: we show that decreasing the electron spin dephasing due to nuclei
and increasing the fidelity of nuclear-spin-based quantum memory could be
within the reach of present day experiments.


title: Certainty relations between local and nonlocal observables

abstract:
  We demonstrate that for an arbitrary number of identical particles, each
defined on a Hilbert-space of arbitrary dimension, there exists a whole ladder
of relations of complementarity between local, and every conceivable kind of
joint (or nonlocal) measurements. E.g., the more accurate we can know (by a
measurement) some joint property of three qubits (projecting the state onto a
tripartite entangled state), the less accurate some other property, local to
the three qubits, become. We also show that the corresponding complementarity
relations are particularly tight for particles defined on prime dimensional
Hilbert spaces.


title: Witnessing Entanglement of EPR States With Second-Order Interference

abstract:
  The separability of the continuous-variable EPR state can be tested with
Hanbury-Brown and Twiss type interference. The second-order visibility of such
interference can provide an experimental test of entanglement. It is shown that
time-resolved interference leads to the Hong, Ou and Mandel deep, that provides
a signature of quantum non-separability for pure and mixed EPR states. A
Hanbury-Brown and Twiss type witness operator can be constructed to test the
quantum nature of the EPR entanglement.


title: Fault Models for Quantum Mechanical Switching Networks

abstract:
  The difference between faults and errors is that, unlike faults, errors can
be corrected using control codes. In classical test and verification one
develops a test set separating a correct circuit from a circuit containing any
considered fault. Classical faults are modelled at the logical level by fault
models that act on classical states. The stuck fault model, thought of as a
lead connected to a power rail or to a ground, is most typically considered. A
classical test set complete for the stuck fault model propagates both binary
basis states, 0 and 1, through all nodes in a network and is known to detect
many physical faults. A classical test set complete for the stuck fault model
allows all circuit nodes to be completely tested and verifies the function of
many gates. It is natural to ask if one may adapt any of the known classical
methods to test quantum circuits. Of course, classical fault models do not
capture all the logical failures found in quantum circuits. The first obstacle
faced when using methods from classical test is developing a set of realistic
quantum-logical fault models. Developing fault models to abstract the test
problem away from the device level motivated our study. Several results are
established. First, we describe typical modes of failure present in the
physical design of quantum circuits. From this we develop fault models for
quantum binary circuits that enable testing at the logical level. The
application of these fault models is shown by adapting the classical test set
generation technique known as constructing a fault table to generate quantum
test sets. A test set developed using this method is shown to detect each of
the considered faults.


title: Precision frequency measurements with entangled states

abstract:
  We demonstrate how quantum entanglement can be used for precision frequency
measurements with trapped ions. In particular, we show how to suppress linear
Zeeman shifts in optical frequency measurements by using maximally entangled
states of two ions even if the individual ions do not have any
field-independent transition. In addition, this technique allows for an
accurate measurement of small external field frequency shifts such as the
electric quadrupole shift which are important for ion clock experiments.


title: Variable Bias Coin Tossing

abstract:
  Alice is a charismatic quantum cryptographer who believes her parties are
unmissable; Bob is a (relatively) glamorous string theorist who believes he is
an indispensable guest. To prevent possibly traumatic collisions of
self-perception and reality, their social code requires that decisions about
invitation or acceptance be made via a cryptographically secure variable bias
coin toss (VBCT). This generates a shared random bit by the toss of a coin
whose bias is secretly chosen, within a stipulated range, by one of the
parties; the other party learns only the random bit. Thus one party can
secretly influence the outcome, while both can save face by blaming any
negative decisions on bad luck.
  We describe here some cryptographic VBCT protocols whose security is
guaranteed by quantum theory and the impossibility of superluminal signalling,
setting our results in the context of a general discussion of secure two-party
computation. We also briefly discuss other cryptographic applications of VBCT.


title: Controlling Entanglement Generation in External Quantum Fields

abstract:
  Two, non-interacting two-level atoms immersed in a common bath can become
mutually entangled when evolving with a Markovian, completely positive
dynamics. For an environment made of external quantum fields, this phenomenon
can be studied in detail: one finds that entanglement production can be
controlled by varying the bath temperature and the distance between the atoms.
Remarkably, in certain circumstances, the quantum correlations can persist in
the asymptotic long-time regime.


title: Raman Adiabatic Transfer of Optical States

abstract:
  We analyze electromagnetically induced transparency and light storage in an
ensemble of atoms with multiple excited levels (multi-Lambda configuration)
which are coupled to one of the ground states by quantized signal fields and to
the other one via classical control fields. We present a basis transformation
of atomic and optical states which reduces the analysis of the system to that
of EIT in a regular 3-level configuration. We demonstrate the existence of dark
state polaritons and propose a protocol to transfer quantum information from
one optical mode to another by an adiabatic control of the control fields.


title:
Impact of entanglement on the game-theoretical concept of evolutionary
  stability

abstract:
  An example of a quantum game is presented that explicitly shows the impact of
entanglement on the game-theoretical concept of evolutionary stability.


title: On the Role of Hadamard Gates in Quantum Circuits

abstract:
  We study a reduced quantum circuit computation paradigm in which the only
allowable gates either permute the computational basis states or else apply a
"global Hadamard operation", i.e. apply a Hadamard operation to every qubit
simultaneously. In this model, we discuss complexity bounds (lower-bounding the
number of global Hadamard operations) for common quantum algorithms : we
illustrate upper bounds for Shor's Algorithm, and prove lower bounds for
Grover's Algorithm. We also use our formalism to display a gate that is neither
quantum-universal nor classically simulable, on the assumption that Integer
Factoring is not in BPP.


title: A detector for continuous measurement of ultra-cold atoms in real time

abstract:
  We present the first detector capable of recording high-bandwidth real time
atom number density measurements of a Bose Einstein condensate. Based on a
two-color Mach-Zehnder interferometer, our detector has a response time that is
six orders of magnitude faster than current detectors based on CCD cameras
while still operating at the shot-noise limit. With this minimally destructive
system it may be possible to implement feedback to stabilize a Bose-Einstein
condensate or an atom laser.


title: A two reservoir model of quantum error correction

abstract:
  We consider a two reservoir model of quantum error correction with a hot bath
causing errors in the qubits and a cold bath cooling the ancilla qubits to a
fiducial state. We consider error correction protocols both with and without
measurement of the ancilla state. The error correction acts as a kind of
refrigeration process to maintain the data qubits in a low entropy state by
periodically moving the entropy to the ancilla qubits and then to the cold
reservoir. We quantify the performance of the error correction as a function of
the reservoir temperatures and cooling rate by means of the fidelity and the
residual entropy of the data qubits. We also make a comparison with the
continuous quantum error correction model of Sarovar and Milburn [Phys. Rev. A
72 012306].


title: Using Quantum Mechanics to Cope with Liars

abstract:
  We propose the use of a quantum algorithm to deal with the problem of
searching with errors in the framework of two-person games. Specifically, we
present a solution to the Ulam's problem that polynomially reduces its query
complexity and makes it independent from the dimension of the search space.


title: Decoherence induced by a fluctuating Aharonov-Casher phase

abstract:
  Dipoles interference is studied when atomic systems are coupled to classical
electromagnetic fields. The interaction between the dipoles and the classical
fields induces a time-varying Aharonov-Casher phase. Averaging over the phase
generates a suppression of fringe visibility in the interference pattern. We
show that, for suitable experimental conditions, the loss of contrast for
dipoles can be observable and almost as large as the corresponding one for
coherent electrons. We analyze different trajectories in order to show the
dependence of the decoherence factor with the velocity of the particles.


title: Mach Zehnder Interferometry with NOON Quantum States

abstract:
  The paper has been withdrawn by the authors. See newer and expanded version
quant-ph/0606221, published in Europhysics Letters 78, 30004 (2007).


title: Robust state preparation of a single trapped ion by adiabatic passage

abstract:
  We report adiabatic passage experiments with a single trapped $^{40}$Ca$^+$
ion. By applying a frequency chirped laser pulse with a Gaussian amplitude
envelope we reach a transfer efficiency of 0.990(10) on an optical transition
from the electronic ground state S$_{1/2}$ to the metastable state D$_{5/2}$.
This transfer method is shown to be insensitive to the accurate setting of
laser parameters, and therefore is suitable as a robust tool for ion based
quantum computing.


title: Entanglement in bosonic systems

abstract:
  We present a technique to resolve a Gaussian density matrix and its time
evolution through known expectation values in position and momentum. Further we
find the full spectrum of this density matrix and apply the technique to a
chain of harmonic oscillators to find agreement with conformal field theory in
this domain. We also observe that a non-conformal state has a divergent
entanglement entropy.


title:
The second law, Maxwell's daemon and work derivable from quantum heat
  engines

abstract:
  With a class of quantum heat engines which consists of two-energy-eigenstate
systems undergoing, respectively, quantum adiabatic processes and energy
exchanges with heat baths at different stages of a cycle, we are able to
clarify some important aspects of the second law of thermodynamics. The quantum
heat engines also offer a practical way, as an alternative to Szilard's engine,
to physically realise Maxwell's daemon. While respecting the second law on the
average, they are also capable of extracting more work from the heat baths than
is otherwise possible in thermal equilibrium.


title: Phase transitions and quantum measurements

abstract:
  In a quantum measurement, a coupling $g$ between the system S and the
apparatus A triggers the establishment of correlations, which provide
statistical information about S. Robust registration requires A to be
macroscopic, and a dynamical symmetry breaking of A governed by S allows the
absence of any bias. Phase transitions are thus a paradigm for quantum
measurement apparatuses, with the order parameter as pointer variable. The
coupling $g$ behaves as the source of symmetry breaking. The exact solution of
a model where S is a single spin and A a magnetic dot (consisting of $N$
interacting spins and a phonon thermal bath) exhibits the reduction of the
state as a relaxation process of the off-diagonal elements of S+A, rapid due to
the large size of $N$. The registration of the diagonal elements involves a
slower relaxation from the initial paramagnetic state of A to either one of its
ferromagnetic states. If $g$ is too weak, the measurement fails due to a
``Buridan's ass'' effect. The probability distribution for the magnetization
then develops not one but two narrow peaks at the ferromagnetic values. During
its evolution it goes through wide shapes extending between these values.


title:
Conditions for separability in generalized Laplacian matrices and
  nonnegative matrices as density matrices

abstract:
  Recently, Laplacian matrices of graphs are studied as density matrices in
quantum mechanics. We continue this study and give conditions for separability
of generalized Laplacian matrices of weighted graphs with unit trace. In
particular, we show that the Peres-Horodecki positive partial transpose
separability condition is necessary and sufficient for separability in
${\mathbb C}^2\otimes {\mathbb C}^q$. In addition, we present a sufficient
condition for separability of generalized Laplacian matrices and diagonally
dominant nonnegative matrices.


title: Models of Quantum Cellular Automata

abstract:
  In this paper we present a systematic view of Quantum Cellular Automata
(QCA), a mathematical formalism of quantum computation. First we give a general
mathematical framework with which to study QCA models. Then we present four
different QCA models, and compare them. One model we discuss is the traditional
QCA, similar to those introduced by Shumacher and Werner, Watrous, and Van Dam.
We discuss also Margolus QCA, also discussed by Schumacher and Werner. We
introduce two new models, Coloured QCA, and Continuous-Time QCA. We also
compare our models with the established models. We give proofs of computational
equivalence for several of these models. We show the strengths of each model,
and provide examples of how our models can be useful to come up with
algorithms, and implement them in real-world physical devices.


title: A Processor Core Model for Quantum Computing

abstract:
  We describe an architecture based on a processing 'core' where multiple
qubits interact perpetually, and a separate 'store' where qubits exist in
isolation. Computation consists of single qubit operations, swaps between the
store and the core, and free evolution of the core. This enables computation
using physical systems where the entangling interactions are 'always on'.
Alternatively, for switchable systems our model constitutes a prescription for
optimizing many-qubit gates. We discuss implementations of the quantum Fourier
transform, Hamiltonian simulation, and quantum error correction.


title:
Binomial states and the phase distribution measurement of weak optical
  fields

abstract:
  We show that the eight-port interferometer used by Noh, Foug\`{e}res, and
Mandel [Phys. Rev. Lett. {\bf 71}, 2579 (1993)] to measure their operational
phase distribution of light can also be used to measure the canonical phase
distribution of weak optical fields, where canonical phase is defined as the
complement of photon number. A binomial reference state is required for this
purpose, which we show can be obtained to an excellent degree of approximation
from a suitably squeezed state. The proposed method requires only
photodetectors that can distinguish among zero, one and more than one photons
and is not particularly sensitive to photodetector imperfections.