title:
Shor's Factoring Algorithm and Modern Cryptography. An Illustration of
  the Capabilities Inherent in Quantum Computers

abstract:
  The security of messages encoded via the widely used RSA public key
encryption system rests on the enormous computational effort required to find
the prime factors of a large number N using classical (i.e., conventional)
computers. In 1994, however, Peter Shor showed that for sufficiently large N a
quantum computer would be expected to perform the factoring with much less
computational effort. This paper endeavors to explain, in a fashion
comprehensible to the non-expert readers of this journal: (i) the RSA
encryption protocol; (ii) the various quantum computer manipulations
constituting the Shor algorithm; (iii) how the Shor algorithm performs the
factoring; and (iv) the precise sense in which a quantum computer employing
Shor's algorithm can be said to accomplish the factoring of very large numbers
with less computational effort than a classical computer can. It is made
apparent that factoring $N$ generally requires many successive runs of the
algorithm. The careful analysis herein reveals, however, that the probability
of achieving a successful factorization on a single run is about twice as large
as commonly quoted in the literature.


title: The time-reversal test for stochastic quantum dynamics

abstract:
  The calculation of quantum dynamics is currently a central issue in
theoretical physics, with diverse applications ranging from ultra-cold atomic
Bose-Einstein condensates (BEC) to condensed matter, biology, and even
astrophysics. Here we demonstrate a conceptually simple method of determining
the regime of validity of stochastic simulations of unitary quantum dynamics by
employing a time-reversal test. We apply this test to a simulation of the
evolution of a quantum anharmonic oscillator with up to $6.022\times10^{23}$
(Avogadro's number) of particles. This system is realisable as a Bose-Einstein
condensate in an optical lattice, for which the time-reversal procedure could
be implemented experimentally.


title:
Berry's phase with quantized field driving: effects of inter-subsystem
  coupling

abstract:
  The effect of inter-subsystem couplings on the Berry phase of a composite
system as well as that of its subsystem is investigated in this paper. We
analyze two coupled spin-$\frac 1 2 $ particles with one driven by a quantized
field as an example, the pure state geometric phase of the composite system as
well as the mixed state geometric phase for the subsystem is calculated and
discussed.


title:
Atomic theory methods for the polarization in photon and electron
  interactions with atoms

abstract:
  An alternative method to the density matrix formalism for the derivation of
general expressions of the interaction of polarized atoms with polarized
photons and electrons is presented. The expression for the cross-section
describing the polarization states of all particles taking part in the process
are obtained in the form of an expansion via irreducible tensors that have the
most simplest possible behaviour under changes of directions. The ways of the
application of the general expressions suitable for the specific experimental
conditions are outlined by deriving asymmetry parameters of the angular
distributions of photoelectrons and Auger electrons following photoionization
as well as the parameters of the angular correlations between photo- and Auger
electrons.


title: Quantum computer with dipole-dipole interacting two-level systems

abstract:
  A scalable, high-performance quantum processor can be implemented using
near-resonant dipole-dipole interacting dopants in a solid state host. In this
scheme, the qubits are represented by ground and subradiant states of effective
dimers formed by pairs of closely spaced two-level systems, while the two-qubit
entanglement either relies on the coherent excitation exchange between the
dimers or is mediated by external laser fields.


title: Open quantum systems

abstract:
  The damping of the harmonic oscillator is studied in the framework of the
Lindblad theory for open quantum systems. A generalization of the fundamental
constraints on quantum mechanical diffusion coefficients which appear in the
master equation for the damped quantum oscillator is presented; the
Schr\"odinger, Heisenberg and Weyl-Wigner-Moyal representations of the Lindblad
equation are given explicitly. On the basis of these representations it is
shown that various master equations for the damped quantum oscillator used in
the literature are particular cases of the Lindblad equation and that not all
of these equations are satisfying the constraints on quantum mechanical
diffusion coefficients. The master equation is transformed into Fokker-Planck
equations for quasiprobability distributions and a comparative study is made
for the Glauber $P$ representation, the antinormal ordering $Q$ representation
and the Wigner $W$ representation. The density matrix is represented via a
generating function, which is obtained by solving a time-dependent linear
partial differential equation derived from the master equation. The damped
harmonic oscillator is applied for the description of the charge equilibration
mode observed in deep inelastic reactions. For a system consisting of two
harmonic oscillators the time dependence of expectation values, Wigner function
and Weyl operator are obtained and discussed. In addition models for the
damping of the angular momentum are studied. Using this theory to the quantum
tunneling through the nuclear barrier, besides Gamow's transitions with energy
conservation, additional transitions with energy loss, are found. When this
theory is used to the resonant atom-field interaction, new optical equations
describing the coupling through the environment are obtained.


title: Communication cost of breaking the Bell barrier

abstract:
  Correlations in an Einstein-Podolsky-Rosen-Bohm experiment can be made
stronger than quantum correlations by allowing a single bit of classical
communication between the two sides of the experiment.


title: Continuous Variable Quantum State Sharing via Quantum Disentanglement

abstract:
  Quantum state sharing is a protocol where perfect reconstruction of quantum
states is achieved with incomplete or partial information in a multi-partite
quantum networks. Quantum state sharing allows for secure communication in a
quantum network where partial information is lost or acquired by malicious
parties. This protocol utilizes entanglement for the secret state distribution,
and a class of "quantum disentangling" protocols for the state reconstruction.
We demonstrate a quantum state sharing protocol in which a tripartite entangled
state is used to encode and distribute a secret state to three players. Any two
of these players can collaborate to reconstruct the secret state, whilst
individual players obtain no information. We investigate a number of quantum
disentangling processes and experimentally demonstrate quantum state
reconstruction using two of these protocols. We experimentally measure a
fidelity, averaged over all reconstruction permutations, of F = 0.73. A result
achievable only by using quantum resources.


title: Preparation of arbitrary qutrit state based on biphotons

abstract:
  The novel experimental realization of three-state optical quantum systems is
presented. We use the polarization state of biphotons,propagating in single
frequency- and spatial mode, to generate an arbitrary qutrits. In particular
the specific sequence of states that are used in the extended version of BB84
quantum key distribution protocol was generated and tested. We experimentally
verify the orthogonality of the 12 basic states and demonstrate the ability of
switching between them. The tomography procedure is applied to reconstruct the
density matrices of generated states.


title:
A Simple Scheme to Entangle Distant Qubits from a Mixed State via an
  Entanglement Mediator

abstract:
  A simple scheme to prepare an entanglement between two separated qubits from
a given mixed state is proposed. A single qubit (entanglement mediator) is
repeatedly made to interact locally and consecutively with the two qubits
through rotating-wave couplings and is then measured. It is shown that we need
to repeat this kind of process only three times to establish a maximally
entangled state directly from an arbitrary initial mixed state, with no need to
prepare the state of the qubits in advance or to rearrange the setup step by
step. Furthermore, the maximum yield realizable with this scheme is compatible
with the maximum entanglement, provided that the coupling constants are
properly tuned.


title: Quantum Algorithm to Solve Satisfiability Problems

abstract:
  A new quantum algorithm is proposed to solve Satisfiability(SAT) problems by
taking advantage of non-unitary transformation in ground state quantum
computer. The energy gap scale of the ground state quantum computer is analyzed
for 3-bit Exact Cover problems. The time cost of this algorithm on general SAT
problems is discussed.


title:
Scheme for deterministic Bell-state-measurement-free quantum
  teleportation

abstract:
  A deterministic teleportation scheme for unknown atomic states is proposed in
cavity QED. The Bell state measurement is not needed in the teleportation
process, and the success probability can reach 1.0. In addition, the current
scheme is insensitive to the cavity decay and thermal field.


title: Behaviour of the wave function near the origin in the radial case

abstract:
  We give one more proof in two and three space dimensions that the irregular
solution of the Schrodinger equation, for zero angular momentum, is in fact the
solution of an equation containing an extra 'delta function'. We propose
another criterium to eliminate the irregular solution which is to require the
validity of the virial theorem of which we give a general proof in the
classical and quantum cases.


title: Spin & Statistics in Nonrelativistic Quantum Mechanics, II

abstract:
  Recently a sufficient and necessary condition for Pauli's spin- statistics
connection in nonrelativistic quantum mechanics has been established
[quant-ph/0208151]. The two-dimensional part of this result is extended to
n-particle systems and reformulated and further simplified in a more geometric
language.


title: A new strategy to find bound states in anharmonic oscillators

abstract:
  A very simple procedure to calculate eigenenergies of quantum anharmonic
oscillators is presented. The method, exact but for numerical computations,
consists merely in requiring the vanishing of the Wronskian of two solutions
which are regular respectively at the origin and at infinity. The first one can
be represented by its series expansion; for the second one, an asymptotic
expansion is available. The procedure is illustrated by application to quartic
and sextic oscillators.


title: Path Integration on Darboux Spaces

abstract:
  In this paper the Feynman path integral technique is applied to
two-dimensional spaces of non-constant curvature: these spaces are called
Darboux spaces $\DI$--$\DIV$. We start each consideration in terms of the
metric and then analyze the quantum theory in the separable coordinate systems.
The path integral in each case is formulated and then solved in the majority of
cases, the exceptions being quartic oscillators where no closed solution is
known. The required ingredients are the path integral solutions of the linear
potential, the harmonic oscillator, the radial harmonic oscillator, the
modified P\"oschl--Teller potential, and for spheroidal wave-functions,
respectively. The basic path integral solutions, which appear here in a
complicated way, have been developed in recent work and are known. The final
solutions are represented in terms of the corresponding Green's functions and
the expansions into the wave-functions, respectively. We also sketch some
limiting cases of the Darboux spaces, where spaces of constant negative and
zero curvature emerge.


title:
Inefficiency and classical communication bounds for conversion between
  partially entangled pure bipartite states

abstract:
  We derive lower limits on the inefficiency and classical communication costs
of dilution between two-term bipartite pure states that are partially
entangled. We first calculate explicit relations between the allowable error
and classical communication costs of entanglement dilution using the protocol
of Lo-Popescu and then consider a two-stage dilution from singlets with this
protocol followed by some unknown protocol for conversion between partially
entangled states. Applying the lower bounds on classical communication and
inefficiency of Harrow-Lo and Hayden-Winter to this two-stage protocol, we
derive bounds for the unknown protocol. In addition we derive analogous (but
looser) bounds for general pure states.


title: A model of quantum reduction with decoherence

abstract:
  The problem of reduction (wave packet reduction) is reexamined under two
simple conditions: Reduction is a last step completing decoherence. It acts in
commonplace circumstances and should be therefore compatible with the
mathematical frame of quantum field theory and the standard model.
  These conditions lead to an essentially unique model for reduction.
Consistency with renormalization and time-reversal violation suggest however a
primary action in the vicinity of Planck's length. The inclusion of quantum
gravity and the uniqueness of space-time point moreover to generalized quantum
theory, first proposed by Gell-Mann and Hartle, as a convenient framework for
developing this model into a more complete theory.


title:
Characteristic parameters and dynamics of two-qubit system in
  self-assembled monolayers

abstract:
  We suggest the application of nitronylnitroxide substituted with methyl group
and 2,2,6,6-tetramethylpiperidin organic radicals as 1/2-spin qubits for
self-assembled monolayer quantum devices. We show that the oscillating
cantilever driven adiabatic reversals technique can provide the read-out of the
spin states. We compute components of the $g$-tensor and dipole-dipole
interaction tensor for these radicals. We show that the delocalization of the
spin in the radical may significantly influence the dipole-dipole interaction
between the spins.


title: Finite Quantum Kinematics of the Harmonic Oscillator

abstract:
  Arbitrarily small changes in the commutation relations suffice to transform
the usual singular quantum theories into regular quantum theories. This process
is an extension of canonical quantization that we call general quantization.
Here we apply general quantization to the time-independent linear harmonic
oscillator. The unstable Heisenberg group becomes the stable group SO(3). This
freezes out the zero-point energy of very soft or very hard oscillators, like
those responsible for the infrared or ultraviolet divergencies of usual field
theories, without much changing the medium oscillators. It produces pronounced
violations of equipartition and of the usual uncertainty relations for soft or
hard oscillators,and interactions between the previously uncoupled excitation
quanta of the oscillator, weakly attractive for medium quanta, strongly
repulsive for soft or hard quanta.


title: Robust Quantum Algorithms for Oracle Identification

abstract:
  The oracle identification problem (OIP) was introduced by Ambainis et al.
\cite{AIKMRY04}. It is given as a set $S$ of $M$ oracles and a blackbox oracle
$f$. Our task is to figure out which oracle in $S$ is equal to the blackbox $f$
by making queries to $f$. OIP includes several problems such as the Grover
Search as special cases. In this paper, we improve the algorithms in
\cite{AIKMRY04} by providing a mostly optimal upper bound of query complexity
for this problem: ($i$) For any oracle set $S$ such that $|S| \le 2^{N^d}$ ($d
< 1$), we design an algorithm whose query complexity is
$O(\sqrt{N\log{M}/\log{N}})$, matching the lower bound proved in
\cite{AIKMRY04}. ($ii$) Our algorithm also works for the range between
$2^{N^d}$ and $2^{N/\log{N}}$ (where the bound becomes O(N)), but the gap
between the upper and lower bounds worsens gradually. ($iii$) Our algorithm is
robust, namely, it exhibits the same performance (up to a constant factor)
against the noisy oracles as also shown in the literatures
\cite{AC02,BNRW03,HMW03} for special cases of OIP.


title:
Classical simulation of quantum algorithms using the tensor product
  representation

abstract:
  Using the tensor product representation in the density matrix renormalization
group, we show that a quantum circuit of Grover's algorithm, which has
one-qubit unitary gates, generalized Toffoli gates, and projective
measurements, can be efficiently simulated by a classical computer. It is
possible to simulate quantum circuits with several ten qubits.


title:
Constructing arbitrary Steane code single logical qubit fault-tolerant
  gates

abstract:
  We present a simple method for constructing optimal fault-tolerant
approximations of arbitrary unitary gates using an arbitrary discrete universal
gate set. The method presented is numerical and scales exponentially with the
number of gates used in the approximation. However, for the specific case of
arbitrary single-qubit gates and the fault-tolerant gates permitted by the
concatenated 7-qubit Steane code, we find gate sequences sufficiently long and
accurate to permit the fault-tolerant factoring of numbers thousands of bits
long. A general scaling law of how rapidly these fault-tolerant approximations
converge to arbitrary single-qubit gates is also determined.


title:
On Disagreement about Nonperturbative Corrections in Triple-well
  Potential

abstract:
  We examine in detail nonperturbative corrections for low lying energies of a
symmetric triple-well potential with non-equivalent vacua, for which there have
been disagreement about asymptotic formulas and controversy over the validity
of the dilute gas approximation. We carry out investigations from various
points of view, including not only a numerical comparison of the
nonperturbative corrections with the exact values but also the prediction of
the large order behavior of the perturbation series, consistency with the
perturbative corrections, and comparison with the WKB approximation. We show
that all the results support our formula previously obtained from the valley
method calculation beyond the dilute gas approximation.


title: Non-Markovian Particle Dynamics in Continuously Controlled Quantum Gases

abstract:
  For a quantum gas, being subject to continuous feedback of a macroscopic
observable, the single-particle dynamics is studied. Albeit feedback-induced
particle correlations, it is shown that analytic solutions are obtained by
formally extending the single-particle Hilbert space by an auxiliary degree of
freedom. The particle's motion is then fed by colored noise, which effectively
maps quantum-statistical correlations onto the single particle. Thus, the
single particle in the continuously controlled gas follows a non-Markovian
trajectory in phase-space.


title: Multipartite secure state distribution

abstract:
  We introduce the distribution of a secret multipartite entangled state in a
real-world scenario as a quantum primitive. We show that in the presence of
noisy quantum channels (and noisy control operations) any state chosen from the
set of two-colorable graph states (CSS codewords) can be created with high
fidelity while it remains unknown to all parties. This is accomplished by
either blind multipartite entanglement purification, which we introduce in this
paper, or by multipartite entanglement purification of enlarged states, which
offers advantages over an alternative scheme based on standard channel
purification and teleportation. The parties are thus provided with a secret
resource of their choice for distributed secure applications.


title:
Finite dimensional quantizations of the (q,p) plane : new space and
  momentum inequalities

abstract:
  We present a N-dimensional quantization a la Berezin-Klauder or frame
quantization of the complex plane based on overcomplete families of states
(coherent states) generated by the N first harmonic oscillator eigenstates. The
spectra of position and momentum operators are finite and eigenvalues are
equal, up to a factor, to the zeros of Hermite polynomials. From numerical and
theoretical studies of the large $N$ behavior of the product $\lambda\_m(N)
\lambda\_M(N)$ of non null smallest positive and largest eigenvalues, we infer
the inequality $\delta\_N(Q) \Delta\_N(Q) = \sigma\_N \overset{<}{\underset{N
\to \infty}{\to}} 2 \pi$ (resp. $\delta\_N(P) \Delta\_N(P) = \sigma\_N
\overset{<}{\underset{N \to \infty}{\to}} 2 \pi $) involving, in suitable
units, the minimal ($\delta\_N(Q)$) and maximal ($\Delta\_N(Q)$) sizes of
regions of space (resp. momentum) which are accessible to exploration within
this finite-dimensional quantum framework. Interesting issues on the
measurement process and connections with the finite Chern-Simons matrix model
for the Quantum Hall effect are discussed.


title:
Frequency Measurement of an Ar+ Laser Stabilized on Narrow Lines of
  Molecular Iodine at 501.7 nm

abstract:
  A spectrometer for ultra high-resolution spectroscopy of molecular iodine at
wave length 501.7 nm, near the dissociation limit is described. Line shapes
about 30 kHz wide (HWHM) were obtained using saturation spectroscopy in a
pumped cell. The frequency of an Ar+ laser was locked to a hyperfine component
of the R(26)62-0 transition and the first absolute frequency measurement of
this line is reported.


title: On "Inconsistency in the Application of the Adiabatic Theorem"

abstract:
  It is shown where the proof of "inconsistency in the application of the
adiabatic theorem" goes wrong.


title: Elementary Operations

abstract:
  A Clifford algebra over the binary field 2 = {0,1} is a second-order
classical logic that is substantially richer than Boolean algebra. We use it as
a bridge to a Clifford algebraic quantum logic that is richer than the usual
Hilbert space quantum logic and admits iteration. This leads to a higher-order
Clifford-algebraic logic. We formulate a toy Dirac equation with this logic. It
isexactly Lorentz-invariant, yet it approximates the usual Dirac equation as
closely as desired and all its variables have finite spectra. It is worth
considering as a Lorentz-invariant improvement on lattice space-times.


title: SIC-POVMs and the Extended Clifford Group

abstract:
  We describe the structure of the extended Clifford Group (defined to be the
group consisting of all operators, unitary and anti-unitary, which normalize
the generalized Pauli group (or Weyl-Heisenberg group as it is often called)).
We also obtain a number of results concerning the structure of the Clifford
Group proper (i.e. the group consisting just of the unitary operators which
normalize the generalized Pauli group). We then investigate the action of the
extended Clifford group operators on symmetric informationally complete POVMs
(or SIC-POVMs) covariant relative to the action of the generalized Pauli group.
We show that each of the fiducial vectors which has been constructed so far
(including all the vectors constructed numerically by Renes et al) is an
eigenvector of one of a special class of order 3 Clifford unitaries. This
suggests a strengthening of a conjuecture of Zauner's. We give a complete
characterization of the orbits and stability groups in dimensions 2-7. Finally,
we show that the problem of constructing fiducial vectors may be expected to
simplify in the infinite sequence of dimensions 7, 13, 19, 21, 31,... . We
illustrate this point by constructing exact expressions for fiducial vectors in
dimensions 7 and 19.


title: A new mechanism for electron spin echo envelope modulation

abstract:
  Electron spin echo envelope modulation (ESEEM) has been observed for the
first time from a coupled hetero-spin pair of electron and nucleus in liquid
solution. Previously, modulation effects in spin echo experiments have only
been described in liquid solutions for a coupled pair of homonuclear spins in
NMR or a pair of resonant electron spins in EPR. We observe low-frequency ESEEM
(26 and 52 kHz) due to a new mechanism present for any electron spin with S>1/2
that is hyperfine coupled to a nuclear spin. In our case these are electron
spin (S=3/2) and nuclear spin (I=1) in the endohedral fullerene N@C60. The
modulation is shown to arise from second order effects in the isotropic
hyperfine coupling of an electron and 14N nucleus.


title:
Influence of molecular temperature on the coherence of fullerenes in a
  near-field interferometer

abstract:
  We study C70 fullerene matter waves in a Talbot-Lau interferometer as a
function of their temperature. While the ideal fringe visibility is observed at
moderate molecular temperatures, we find a gradual degradation of the
interference contrast if the molecules are heated before entering the
interferometer. A method is developed to assess the distribution of the
micro-canonical temperatures of the molecules in free flight. This way the
heating-dependent reduction of interference contrast can be compared with the
predictions of quantum theory. We find that the observed loss of coherence
agrees quantitatively with the expected decoherence rate due to the thermal
radiation emitted by the hot molecules.


title: Gravity-induced resonances in a rotating trap

abstract:
  It is shown that in an anisotropic harmonic trap that rotates with the
properly chosen rotation rate, the force of gravity leads to a resonant
behavior. Full analysis of the dynamics in an anisotropic, rotating trap in 3D
is presented and several regions of stability are identified. On resonance, the
oscillation amplitude of a single particle, or of the center of mass of a
many-particle system (for example, BEC), grows linearly with time and all
particles are expelled from the trap. The resonances can only occur when the
rotation axis is tilted away from the vertical position. The positions of the
resonances (there are always two of them) do not depend on the mass but only on
the characteristic frequencies of the trap and on the direction of the angular
velocity of rotation.


title: Quantum Electrodynamics in Media with Negative Refraction

abstract:
  We consider the interaction of atoms with the quantized electromagnetic field
in the presence of materials with negative index of refraction. Spontaneous
emission of an atom embedded in a negative index material is discussed. It is
shown furthermore that the possibility of a vanishing optical path length
between two spatially separated points provided by these materials can lead to
complete suppression of spontaneous emission of an atom in front of a perfect
mirror even if the distance between atom and mirror is large compared to the
transition wavelength. Two atoms put in the focal points of a lens formed by a
parallel slab of ideal negative index material are shown to exhibit perfect
sub- and superradiance. The maximum length scale in both cases is limited only
by the propagation distance within the free-space radiative decay time.
Limitations of the predicted effects arising from absorption, finite
transversal extension and dispersion of the material are analyzed.


title:
A bound on the mutual information, and properties of entropy reduction,
  for quantum channels with inefficient measurements

abstract:
  The Holevo bound is a bound on the mutual information for a given quantum
encoding. In 1996 Schumacher, Westmoreland and Wootters [Schumacher,
Westmoreland and Wootters, Phys. Rev. Lett. 76, 3452 (1996)] derived a bound
which reduces to the Holevo bound for complete measurements, but which is
tighter for incomplete measurements. The most general quantum operations may be
both incomplete and inefficient. Here we show that the bound derived by SWW can
be further extended to obtain one which is yet again tighter for inefficient
measurements. This allows us in addition to obtain a generalization of a bound
derived by Hall, and to show that the average reduction in the von Neumann
entropy during a quantum operation is concave in the initial state, for all
quantum operations. This is a quantum version of the concavity of the mutual
information. We also show that both this average entropy reduction, and the
mutual information for pure state ensembles, are Schur-concave for unitarily
covariant measurements; that is, for these measurements, information gain
increases with initial uncertainty.


title: On infinite walls in deformation quantization

abstract:
  We examine the deformation quantization of a single particle moving in one
dimension (i) in the presence of an infinite potential wall, (ii) confined by
an infinite square well, and (iii) bound by a delta function potential energy.
In deformation quantization, considered as an autonomous formulation of quantum
mechanics, the Wigner function of stationary states must be found by solving
the so-called $\*$-genvalue (``stargenvalue'') equation for the Hamiltonian.
For the cases considered here, this pseudo-differential equation is difficult
to solve directly, without an ad hoc modification of the potential. Here we
treat the infinite wall as the limit of a solvable exponential potential.
Before the limit is taken, the corresponding $\*$-genvalue equation involves
the Wigner function at momenta translated by imaginary amounts. We show that it
can be converted to a partial differential equation, however, with a
well-defined limit. We demonstrate that the Wigner functions calculated from
the standard Schr\"odinger wave functions satisfy the resulting new equation.
Finally, we show how our results may be adapted to allow for the presence of
another, non-singular part in the potential.


title: A Lower Bound for Quantum Phase Estimation

abstract:
  We obtain a query lower bound for quantum algorithms solving the phase
estimation problem. Our analysis generalizes existing lower bound approaches to
the case where the oracle Q is given by controlled powers Q^p of Q, as it is
for example in Shor's order finding algorithm. In this setting we will prove a
log (1/epsilon) lower bound for the number of applications of Q^p1, Q^p2, ...
This bound is tight due to a matching upper bound. We obtain the lower bound
using a new technique based on frequency analysis.


title: Protocol for universal gates in optimally biased superconducting qubits

abstract:
  We present a new experimental protocol for performing universal gates in a
register of superconducting qubits coupled by fixed on-chip linear reactances.
The qubits have fixed, detuned Larmor frequencies and can remain, during the
entire gate operation, biased at their optimal working point where decoherence
due to fluctuations in control parameters is suppressed to first order.
Two-qubit gates are performed by simultaneously irradiating two qubits at their
respective Larmor frequencies with appropriate amplitude and phase, while
one-qubit gates are performed by the usual single-qubit irradiation pulses.


title:
Brownian motion of a charged test particle in vacuum between two
  conducting plates

abstract:
  The Brownian motion of a charged test particle caused by quantum
electromagnetic vacuum fluctuations between two perfectly conducting plates is
examined and the mean squared fluctuations in the velocity and position of the
test particle are calculated. Our results show that the Brownian motion in the
direction normal to the plates is reinforced in comparison to that in the
single-plate case. The effective temperature associated with this normal
Brownian motion could be three times as large as that in the single-plate case.
However, the negative dispersions for the velocity and position in the
longitudinal directions, which could be interpreted as reducing the quantum
uncertainties of the particle, acquire positive corrections due to the presence
of the second plate, and are thus weakened.


title: Hidden Variables and Nonlocality in Quantum Mechanics

abstract:
  In this paper, we show that Erwin Schroedinger's generalization of the
Einstein Podolsky Rosen argument can be connected to certain mathematical
theorems - Gleason's and also Kochen and Specker's - in a manner analogous to
the relation of EPR itself with Bell's theorem. In both cases, the conclusion
is quantum nonlocality, as we discuss. The "Schroedinger nonlocality" proofs
share some features with the Greenberger, Horne, and Zeilinger
quantum-nonlocality work, yet also differ in significant ways.
  For clarity and completeness, we begin with a detailed discussion of the
topic of hidden variable theorems. We argue, in agreement with John S. Bell,
that 'impossibility' does not follow.


title:
Uniform Semiclassical Approach to Fidelity Decay: from Weak to Strong
  Perturbation

abstract:
  We study fidelity decay by a uniform semiclassical approach, in the three
perturbation regimes, namely, the perturbative regime, the Fermi-golden-rule
(FGR) regime, and the Lyapunov regime.
  A semiclassical expression is derived for fidelity of initial Gaussian wave
packets with width of the order $\sqrt{\hbar}$
  ($\hbar$ being the effective Planck constant).
  Short time decay of fidelity of initial Gaussian wave packets is also
studied, with respect to two time scales introduced in the semiclassical
approach.
  In the perturbative regime, it is confirmed numerically that fidelity has the
FGR decay before the Gaussian decay sets in.
  An explanation is suggested to a non-FGR decay in the FGR regime, which has
been observed in a system with weak chaos in the classical limit, by using the
Levy distribution as an approximation for the distribution of action
difference.
  In the Lyapunov regime, it is shown that the average of the logarithm of
fidelity may have roughly the Lyapunov decay within some time interval, in
systems possessing large fluctuation of the finite-time Lyapunov exponent in
the classical limit.


title: Instability, Isolation, and the Tridecompositional Uniqueness Theorem

abstract:
  The tridecompositional uniqueness theorem of Elby and Bub (1994) shows that a
wavefunction in a triple tensor product Hilbert space has at most one
decomposition into a sum of product wavefunctions with each set of component
wavefunctions linearly independent. I demonstrate that, in many circumstances,
the unique component wavefunctions and the coefficients in the expansion are
both hopelessly unstable, both under small changes in global wavefunction and
under small changes in global tensor product structure. In my opinion, this
means that the theorem cannot underlie law-like solutions to the problems of
the interpretation of quantum theory. I also provide examples of circumstances
in which there are open sets of wavefunctions containing no states with various
decompositions.


title:
A quantum key distribution and identification protocol based on
  entanglement swapping

abstract:
  A quantum key distribution and identification protocol is proposed, which is
based on entanglement swapping. Through choosing particles by twos from the
sequence and performing Bell measurements, two communicators can detect
eavesdropping, identify each other and obtain the secure key according to the
measurement results. Because the two particles measured together are selected
out randomly, we need neither alternative measurements nor rotation of the Bell
states. Furthermore, less Bell measurements are needed in our protocol than in
the previous similar ones.


title:
Relationships Between Quantum and Classical Mechanics using the
  Representation Theory of the Heisenberg Group

abstract:
  This thesis is concerned with the representation theory of the Heisenberg
group and its applications to both classical and quantum mechanics. We continue
the development of $p$-mechanics which is a consistent physical theory capable
of describing both classical and quantum mechanics simultaneously.
$p$-Mechanics starts from the observation that the one dimensional
representations of the Heisenberg group play the same role in classical
mechanics which the infinite dimensional representations play in quantum
mechanics.
  In this thesis we introduce the idea of states to $p$-mechanics.
$p$-Mechanical states come in two forms: elements of a Hilbert space and
integration kernels. In developing $p$-mechanical states we show that quantum
probability amplitudes can be obtained using solely functions/distributions on
the Heisenberg group. This theory is applied to the examples of the forced,
harmonic and coupled oscillators. In doing so we show that both the quantum and
classical dynamics of these systems can be derived from the same source. Also
using $p$-mechanics we simplify some of the current quantum mechanical
calculations.
  We also analyse the role of both linear and non-linear canonical
transformations in $p$-mechanics. We enhance a method derived by Moshinsky for
studying the passage of canonical transformations from classical to quantum
mechanics. The Kepler/Coulomb problem is also examined in the $p$-mechanical
context. In analysing this problem we show some limitations of the current
$p$-mechanical approach. We then use Klauder's coherent states to generate a
Hilbert space which is particularly useful for the Kepler/Coulomb problem.


title:
Deformed shape invariance and exactly solvable Hamiltonians with
  position-dependent effective mass

abstract:
  Known shape-invariant potentials for the constant-mass Schrodinger equation
are taken as effective potentials in a position-dependent effective mass (PDEM)
one. The corresponding shape-invariance condition turns out to be deformed. Its
solvability imposes the form of both the deformed superpotential and the PDEM.
A lot of new exactly solvable potentials associated with a PDEM background are
generated in this way. A novel and important condition restricting the
existence of bound states whenever the PDEM vanishes at an end point of the
interval is identified. In some cases, the bound-state spectrum results from a
smooth deformation of that of the conventional shape-invariant potential used
in the construction. In others, one observes a generation or suppression of
bound states, depending on the mass-parameter values. The corresponding
wavefunctions are given in terms of some deformed classical orthogonal
polynomials.


title:
Experimental realization of optimal asymmetric cloning and telecloning
  via partial teleportation

abstract:
  We report an experimental realization of both optimal asymmetric cloning and
telecloning of single photons by making use of partial teleportation of an
unknown state. In the experiment, we demonstrate that, conditioned on the
success of partial teleportation of single photons, not only the optimal
asymmetric cloning can be accomplished, but also one of two outputs can be
transfered to a distant location, realizing the telecloning. The experimental
results represent a novel way to achieve the quantum cloning and may have
potential applications in the context of quantum communication.


title: Transient dynamics of linear quantum amplifiers

abstract:
  The transient dynamics of a quantum linear amplifier during the transition
from damping to amplification regime is studied. The master equation for the
quantized mode of the field is solved, and the solution is used to describe the
statistics of the output field. The conditions under which a nonclassical input
field may retain nonclassical features at the output of the amplifier are
analyzed and compared to the results of earlier theories. As an application we
give a dynamical description of the departure of the system from thermal
equilibrium.


title: Quantum diffusion in the quasiperiodic kicked rotor

abstract:
  We study the mechanisms responsible for quantum diffusion in the
quasiperiodic kicked rotor. We report experimental measurements of the
diffusion constant on the atomic version of the system and develop a
theoretical approach (based on the Floquet theorem) explaining the
observations, especially the ``sub-Fourier'' character of the resonances
observed in the vicinity of exact periodicity, i.e. the ability of the system
to distinguish two neighboring driving frequencies in a time shorter than the
inverse of the difference of the two frequencies.


title:
Non-Markovian master equations from entanglement with stationary
  unobserved degrees of freedom

abstract:
  We deduce a class of non-Markovian completely positive master equations which
describe a system in a composite bipartite environment, consisting of a
Markovian reservoir and additional stationary unobserved degrees of freedom
that modulate the dissipative coupling. The entanglement-induced memory effects
can persist for arbitrary long times and affect the relaxation to equilibrium,
as well as induce corrections to the quantum-regression theorem. By considering
the extra degrees of freedom as a discrete manifold of energy levels, strong
non-exponential behavior can arise, as for example power law and stretched
exponential decays.


title: Manipulating quantum states with aspheric lenses

abstract:
  We present an experimental demonstration to manipulate the width and position
of the down-converted beam waist. Our results can be used to engineer the
two-photon orbital angular momentum (OAM) entangled states (such as
concentrating OAM entangled states) and generate Hermite-Gaussian (HG) modes
entangled states.


title: Multimode Hong-Ou-Mandel Interferometry

abstract:
  We review some recent experiments based upon multimode two-photon
interference of photon pairs created by spontaneous parametric down-conversion.
The new element provided by these experiments is the inclusion of the
transverse spatial profiles of the pump, signal and idler fields. We discuss
multimode Hong-Ou-Mandel interference, and show that the transverse profile of
the pump beam can be manipulated in order to control two-photon interference.
We present the basic theory and experimental results as well as several
applications to the field of quantum information.


title:
Intrinsic-Stabilization Uni-Directional Quantum Key Distribution Between
  Beijing and Tianjin

abstract:
  Quantum key distribution provides unconditional security for communication.
Unfortunately, current experiment schemes are not suitable for long-distance
fiber transmission because of instability or backscattering. We present a
uni-directional intrinsic-stabilization scheme that is based on
Michelson-Faraday interferometers, in which reflectors are replaced with 90
degree Faraday mirrors. With the scheme, key exchange from Beijing to Tianjin
over 125 kilometers with an average error rate is below 6% has been achieved
and its limited distance exceeds 150 kilometers. Experimental result shows the
system is insensitive to environment and can run over day and night without any
break even in the noise workshop.


title: Decoherence properties of arbitrarily long histories

abstract:
  Within the decoherent histories formulation of quantum mechanics, we consider
arbitrarily long histories constructed from a fixed projective partition of a
finite-dimensional Hilbert space. We review some of the decoherence properties
of such histories including simple necessary decoherence conditions and the
dependence of decoherence on the initial state. Here we make a first step
towards generalization of our earlier results [Scherer and Soklakov, e-print:
quant-ph/0405080, (2004) and Scherer et al., Phys. Lett. A, vol. 326, 307,
(2004)] to the case of approximate decoherence.


title: Hypothesis elimination on a quantum computer

abstract:
  Hypothesis elimination is a special case of Bayesian updating, where each
piece of new data rules out a set of prior hypotheses. We describe how to use
Grover's algorithm to perform hypothesis elimination for a class of probability
distributions encoded on a register of qubits, and establish a lower bound on
the required computational resources.


title: Dynamics of Two-Level System Interacting with Random Classical Field

abstract:
  The dynamics of a particle interacting with random classical field in a
two-well potential is studied by the functional integration method. The
probability of particle localization in either of the wells is studied in
detail. Certain field-averaged correlation functions for quantum-mechanical
probabilities and the distribution function for the probabilities of final
states (which can be considered as random variables in the presence of a random
field) are calculated. The calculated correlators are used to discuss the
dependence of the final state on the initial state. One of the main results of
this work is that, although the off-diagonal elements of density matrix
disappear with time, a particle in the system is localized incompletely
(wave-packet reduction does not occur), and the distribution function for the
probability of finding particle in one of the wells is a constant at infinite
time.


title:
Estimation of pure qubit states with collective and individual
  measurements

abstract:
  We analyze the estimation of a qubit pure state by means of local
measurements on $N$ identical copies and compare its averaged fidelity for an
isotropic prior probability distribution to the absolute upper bound given by
collective measurements. We discuss two situations: the first one, where the
state is restricted to lie on the equator of the Bloch sphere, is formally
equivalent to phase estimation; the second one, where there is no constrain on
the state, can also be regarded as the estimation of a direction in space using
a quantum arrow made out of $N$ parallel spins. We discuss various schemes with
and without classical communication and compare their efficiency. We show that
the fidelity of the most general collective measurement can always be achieved
asymptotically with local measurements and no classical communication.


title: Information vs. Disturbance in Dimension D

abstract:
  We show that for Eve to get information in one basis about a state, she must
cause errors in all bases that are mutually unbiased to that basis. Our result
holds in any dimension. We also show that this result holds for all functions
of messages that are encrypted with a key.


title: The DARPA Quantum Network

abstract:
  A team from BBN Technologies, Boston University, and Harvard University has
recently built and begun to operate the world's first Quantum Key Distribution
(QKD)network under DARPA sponsorship. The DARPA Quantum Network became fully
operational on October 23, 2003 in BBN's laboratories, and in June 2004 was
fielded through dark fiber under the streets of Cambridge, Mass., to link our
campuses with non-stop quantum cryptography, twenty-four hours per day. As of
December 2004, it consists of six nodes. Four are 5 MHz, BBN-built BB84 systems
designed for telecommunications fiber and inter-connected by a photonic switch.
Two are the electronics subsystems for a high speed free-space system designed
and built by NIST. This paper describes the motivation for our work, the
current status of the DARPA Quantum Network, its unique optical switching and
key relay protocols, and our future plans.


title:
Generalized uncertainty relations and efficient measurements in quantum
  systems

abstract:
  We consider two variants of a quantum-statistical generalization of the
Cramer-Rao inequality that establishes an invariant lower bound on the mean
square error of a generalized quantum measurement. The proposed complex variant
of this inequality leads to a precise formulation of a generalized uncertainty
principle for arbitrary states, in contrast to Helstrom's symmetric variant in
which these relations are obtained only for pure states. A notion of canonical
states is introduced and the lower mean square error bound is found for
estimating of the parameters of canonical states, in particular, the canonical
parameters of a Lie group. It is shown that these bounds are globally
attainable only for canonical states for which there exist efficient
measurements or quasimeasurements.


title:
Design of Optimal Dynamic Analyzers: Mathematical Aspects of Wave
  Pattern Recognition

abstract:
  We give a review of the most important results on optimal tomography as
mathematical wave-pattern recognition theory emerged in the 70's in connection
with the problems of optimal estimation and hypothesis testing in quantum
theory. In quantum theory such problems are sometimes referred as the problem
of optimal measurement of an unknown quantum state, and are the main subject of
the emerging mathematical theory of quantum statistics.
  We develop the results of quantum pattern recognition theory, most of which
belong to VPB, further into the direction of wave, rather than particle
statistical estimation and hypothesis testing theory, with the aim to include
not only quantum matter waves but also classical wave patterns like optical and
acoustic waves. We conclude that Hilbert space and operator methods developed
in quantum theory are equally useful in the classical wave theory, as soon as
the possible observations are restricted to only intensity distributions of
waves, i.e. when the wave states are not the allowed observables, as they are
not the observables of individual particles in the quantum theory. We show that
all characteristic attributes of quantum theory such as complementarity,
entanglement or Heisenberg uncertainty relations are also attributes of the
generalized wave pattern recognition theory.


title: Quantum state reconstruction via continuous measurement

abstract:
  We present a new procedure for quantum state reconstruction based on weak
continuous measurement of an ensemble average. By applying controlled evolution
to the initial state new information is continually mapped onto the measured
observable. A Bayesian filter is then used to update the state-estimate in
accordance with the measurement record. This generalizes the standard paradigm
for quantum tomography based on strong, destructive measurements on separate
ensembles. This approach to state estimation can be non-destructive and
real-time, giving information about observables whose evolution cannot be
described classically, opening the door to new types of quantum feedback
control.


title:
Efficient Quantum Algorithms for the Hidden Subgroup Problem over a
  Class of Semi-direct Product Groups

abstract:
  In this paper, we consider the hidden subgroup problem (HSP) over the class
of semi-direct product groups $\mathbb{Z}_{p^r}\rtimes\mathbb{Z}_q$, for p and
q prime. We first present a classification of these groups in five classes.
Then, we describe a polynomial-time quantum algorithm solving the HSP over all
the groups of one of these classes: the groups of the form
$\mathbb{Z}_{p^r}\rtimes\mathbb{Z}_p$, where p is an odd prime. Our algorithm
works even in the most general case where the group is presented as a black-box
group with not necessarily unique encoding. Finally, we extend this result and
present an efficient algorithm solving the HSP over the groups
$\mathbb{Z}^m_{p^r}\rtimes\mathbb{Z}_p$.


title: Additivity for transpose depolarizing channels

abstract:
  Additivity of the minimal output entropy for the family of transpose
depolarizing channels introduced by Fannes et al. [quant-ph/0410195] is
considered. It is shown that using the method of our previous paper
[quant-ph/0403072] allows us to prove the additivity for the range of the
parameter values for which the problem was left open in [quant-ph/0410195].
Together with the result of [quant-ph/0410195], this covers the whole family of
transpose depolarizing channels.


title: Unconditionally secure key distillation from multi-photons

abstract:
  In this paper, we prove that the unconditionally secure key can be
surprisingly extracted from {\it multi}-photon emission part in the photon
polarization-based QKD. One example is shown by explicitly proving that one can
indeed generate an unconditionally secure key from Alice's two-photon emission
part in ``Quantum cryptography protocols robust against photon number splitting
attacks for weak laser pulses implementations'' proposed by V. Scarani {\it et
al.,} in Phys. Rev. Lett. {\bf 92}, 057901 (2004), which is called SARG04. This
protocol uses the same four states as in BB84 and differs only in the classical
post-processing protocol. It is, thus, interesting to see how the classical
post-processing of quantum key distribution might qualitatively change its
security. We also show that one can generate an unconditionally secure key from
the single to the four-photon part in a generalized SARG04 that uses six
states. Finally, we also compare the bit error rate threshold of these
protocols with the one in BB84 and the original six-state protocol assuming a
depolarizing channel.


title: Squeezing and entanglement of matter-wave gap solitons

abstract:
  We study quantum squeezing and entanglement of gap solitons in a
Bose-Einstein condensate loaded into a one-dimensional optical lattice. By
employing a linearized quantum theory we find that quantum noise squeezing of
gap solitons, produced during their evolution, is enhanced compared with the
atomic solitons in a lattice-free case due to intra-soliton structure of
quantum correlations induced by the Bragg scattering in the periodic potential.
We also show that nonlinear interaction of gap solitons in dynamically stable
bound states can produce strong soliton entanglement.


title: States for phase estimation in quantum interferometry

abstract:
  Ramsey interferometry allows the estimation of the phase $\phi$ of rotation
of the pseudospin vector of an ensemble of two-state quantum systems. For
$\phi$ small, the noise-to-signal ratio scales as the spin-squeezing parameter
$\xi$, with $\xi<1$ possible for an entangled ensemble. However states with
minimum $\xi$ are not optimal for single-shot measurements of an arbitrary
phase. We define a phase-squeezing parameter, $\zeta$, which is an appropriate
figure-of-merit for this case. We show that (unlike the states that minimize
$\xi$), the states that minimize $\zeta$ can be created by evolving an
unentangled state (coherent spin state) by the well-known 2-axis
counter-twisting Hamiltonian. We analyse these and other states (for example
the maximally entangled state, analogous to the optical "NOON" state $|\psi> =
(|N,0>+|0,N>)/\sqrt{2}$) using several different properties, including $\xi$,
$\zeta$, the coefficients in the pseudo angular momentum basis (in the three
primary directions) and the angular Wigner function $W(\theta,\phi)$. Finally
we discuss the experimental options for creating phase squeezed states and
doing single-shot phase estimation.


title:
Non-cyclic Geometric Phase due to Spatial Evolution in a Neutron
  Interferometer

abstract:
  We present a split-beam neutron interferometric experiment to test the
non-cyclic geometric phase tied to the spatial evolution of the system: the
subjacent two-dimensional Hilbert space is spanned by the two possible paths in
the interferometer and the evolution of the state is controlled by phase
shifters and absorbers. A related experiment was reported previously by
Hasegawa et al. [Phys. Rev. A 53, 2486 (1996)] to verify the cyclic spatial
geometric phase. The interpretation of this experiment, namely to ascribe a
geometric phase to this particular state evolution, has met severe criticism
from Wagh [Phys. Rev. A 59, 1715 (1999)]. The extension to a non-cyclic
evolution manifests the correctness of the interpretation of the previous
experiment by means of an explicit calculation of the non-cyclic geometric
phase in terms of paths on the Bloch-sphere.


title: Probabilistic Super Dense Coding

abstract:
  We explore the possibility of performing super dense coding with
non-maximally entangled states as a resource. Using this we find that one can
send two classical bits in a probabilistic manner by sending a qubit. We
generalize our scheme to higher dimensions and show that one can communicate
2log_2 d classical bits by sending a d-dimensional quantum state with a certain
probability of success. The success probability in super dense coding is
related to the success probability of distinguishing non-orthogonal states. The
optimal average success probabilities are explicitly calculated. We consider
the possibility of sending 2 log_2 d classical bits with a shared resource of a
higher dimensional entangled state (D X D, D > d). It is found that more
entanglement does not necessarily lead to higher success probability. This also
answers the question as to why we need log_2 d ebits to send 2 log_2 d
classical bits in a deterministic fashion.


title: Realization of a General Multi-step Quantum Cloning Machine

abstract:
  A general multi-step N->M probabilistic optimal universal cloning protocol is
presented together with the experimental realization of the (1 -> 3) and (2 ->
3) machines. Since the present method exploits the bosonic nature of the
photons, it can be applied to any particle obeying to the Bose statistics. On a
technological perspective, the present protocol is expected to find
applications as a novel, multi-qubit symmetrizator device to be used in modern
quantum information networks.


title: Realization of the 1->3 optimal phase-covariant quantum cloning machine

abstract:
  The 1->3 quantum phase covariant cloning, which optimally clones qubits
belonging to the equatorial plane of the Bloch sphere, achieves the fidelity
Fcov(1->3)=0.833, larger than for the 1->3 universal cloning Funiv(1->3)=0.778.
We show how the 1->3 phase covariant cloning can be implemented by a smart
modification of the standard universal quantum machine by a projection of the
output states over the symmetric subspace. A complete experimental realization
of the protocol for polarization encoded qubits based on non-linear and linear
methods will be discussed.


title:
Four-level quantum teleportation, swapping and collective translations
  of multipartite quantum entanglement

abstract:
  In this paper, an optimal scheme of four-level quantum teleportation and
swapping of quantum entanglement is given. We construct a complete orthogonal
basis of the bipartite ququadrit systems. Using this basis, the four-level
quantum teleportation and swapping can be achieved according to the standard
steps. In addition, associate the above bases with the unextendible product
bases and the exact entanglement bases, we prove that in the $2\times 2\times
2$ systems or $3\times 3$ systems the collective translations of multipartite
quantum entanglement can be realized.
  PACC numbers: 03.67.Mn, 03.65.Ud, 03.67.Hk.
  Keywords: Ququadrit systems, Bases, Four-level teleportation, Swapping,
Collective translations.


title: Detuning effects in the one-photon mazer

abstract:
  The quantum theory of the mazer in the non-resonant case (a detuning between
the cavity mode and the atomic transition frequencies is present) is written.
The generalization from the resonant case is far from being direct. Interesting
effects of the mazer physics are pointed out. In particular, it is shown that
the cavity may slow down or speed up the atoms according to the sign of the
detuning and that the induced emission process may be completely blocked by use
of a positive detuning. It is also shown that the detuning adds a potential
step effect not present at resonance and that the use of positive detunings
defines a well-controlled cooling mechanism. In the special case of a mesa
cavity mode function, generalized expressions for the reflection and
transmission coefficients have been obtained. The general properties of the
induced emission probability are finally discussed in the hot, intermediate and
cold atom regimes. Comparison with the resonant case is given.


title: Transmission of ultracold atoms through a micromaser: detuning effects

abstract:
  The transmission probability of ultracold atoms through a micromaser is
studied in the general case where a detuning between the cavity mode and the
atomic transition frequencies is present. We generalize previous results
established in the resonant case (zero detuning) for the mesa mode function. In
particular, it is shown that the velocity selection of cold atoms passing
through the micromaser can be very easily tuned and enhanced using a
non-resonant field inside the cavity. Also, the transmission probability
exhibits with respect to the detuning very sharp resonances that could define
single cavity devices for high accuracy metrology purposes (atomic clocks).


title: Dynamics of a quantum measurement

abstract:
  We work out an exactly solvable hamiltonian model which retains all the
features of realistic quantum measurements. In order to use an interaction
process involving a system and an apparatus as a measurement, it is necessary
that the apparatus is macroscopic. This implies to treat it with quantum
statistical mechanics. The relevant time scales of the process are exhibited.
It begins with a very rapid disappearance of the off-diagonal blocks of the
overall density matrix of the tested system and the apparatus. Possible
recurrences are hindered by the large size of the latter. On a much larger time
scale the apparatus registers the outcome: Correlations are established between
the final values of the pointer and the initial diagonal blocks of the density
matrix of the tested system. We thus derive Born's rule and von Neumann's
reduction of the state from the dynamical process.


title: An application of a matrix inequality in quantum information theory

abstract:
  Quantum information theory has generated several interesting conjectures
involving products of completely positive maps on matrix algebras, also known
as quantum channels. In particular it is conjectured that the output state with
maximal p-norm from a product channel is always a product state. It is shown
here that the Lieb-Thirring inequality can be used to prove this conjecture for
one special case, namely when one of the components of the product channel is
of the type known as a diagonal channel, which acts on a state by taking the
Hadamard product with a positive matrix.


title: Modal logic approach to preferred bases in the quantum universe

abstract:
  We present a modal logic based approach to the so-called endophysical quantum
universe. In particular, we treat the problem of preferred bases and that of
state reduction by employing an eclectic collection of methods including
Baltag's analytic non-wellfounded set theory, a modal logic interpretation of
Dempster-Shafer theory, and results from the theory of isometric embeddings of
discrete metrics. Two basic principles, the bisimulation principle and the
principle of imperfection, are derived that permit us to conduct an inductive
proof showing that a preferred basis emerges at each evolutionary stage of the
quantum universe. These principles are understood as theoretical realizations
of the paradigm according to which the physical universe is a simulation on a
quantum computer and a second paradigm saying that physical degrees of freedom
are a model of Poincare's physical continuum. Several comments are given
related to communication theory, to evolutionary biology, and to quantum
gravity.


title: A quantum cellular automaton for universal quantum computation

abstract:
  I describe a quantum cellular automaton capable of performing universal
quantum computation. The automaton has an elementary transition function that
acts on Margolus cells of $2\times 2$ qubits, and both the ``quantum input''
and the program are encoded in the initial state of the system.


title:
Experimental Test of the Kochen-Specker Theorem for Single Qubits using
  Positive Operator-Valued Measures

abstract:
  We present an experimental scheme for the implementation of arbitrary
generalized measurements, represented by positive-operator valued measures, on
the polarization of single photons, using linear optical devices. Further, we
experimentally test a Kochen-Specker theorem for single qubits using positive
operator-valued measures. Our experimental results for the first time disprove
non-contextual hidden-variable theories, even for single qubits.


title: A Bohmian approach to quantum fractals

abstract:
  A quantum fractal is a wavefunction with a real and an imaginary part
continuous everywhere, but differentiable nowhere. This lack of
differentiability has been used as an argument to deny the general validity of
Bohmian mechanics (and other trajectory--based approaches) in providing a
complete interpretation of quantum mechanics. Here, this assertion is overcome
by means of a formal extension of Bohmian mechanics based on a limiting
approach. Within this novel formulation, the particle dynamics is always
satisfactorily described by a well defined equation of motion. In particular,
in the case of guidance under quantum fractals, the corresponding trajectories
will also be fractal.


title: Complex multi-projective variety and entanglement

abstract:
  In this paper, we will show that a vanishing generalized concurrence of a
separable state can be seen as an algebraic variety called the Segre variety.
This variety define a quadric space which gives a geometric picture of
separable states. For pure, bi- and three-partite states the variety equals the
generalized concurrence. Moreover, we generalize the Segre variety to a general
multipartite state by relating to a quadric space defined by two-by-two
subdeterminants.


title: Fundamental Aspects of Quantum Brownian Motion

abstract:
  With this work we elaborate on the physics of quantum noise in thermal
equilibrium and in stationary non-equilibrium. Starting out from the celebrated
quantum fluctuation-dissipation theorem we discuss some important consequences
that must hold for open, dissipative quantum systems in thermal equilibrium.
The issue of quantum dissipation is exemplified with the fundamental problem of
a damped harmonic quantum oscillator. The role of quantum fluctuations is
discussed in the context of both, the nonlinear generalized quantum Langevin
equation and the path integral approach. We discuss the consequences of the
time-reversal symmetry for an open dissipative quantum dynamics and,
furthermore, point to a series of subtleties and possible pitfalls. The path
integral methodology is applied to the decay of metastable states assisted by
quantum Brownian noise.


title: Quantum state estimation and large deviations

abstract:
  In this paper we propose a method to estimate the density matrix \rho of a
d-level quantum system by measurements on the N-fold system. The scheme is
based on covariant observables and representation theory of unitary groups and
it extends previous results concerning the estimation of the spectrum of \rho.
We show that it is consistent (i.e. the original input state \rho is recovered
with certainty if N \to \infty), analyze its large deviation behavior, and
calculate explicitly the corresponding rate function which describes the
exponential decrease of error probabilities in the limit N \to \infty. Finally
we discuss the question whether the proposed scheme provides the fastest
possible decay of error probabilities.


title: Quantum optical time-of-arrival model in three dimensions

abstract:
  We investigate the three-dimensional formulation of a recently proposed
operational arrival-time model. It is shown that within typical conditions for
optical transitions the results of the simple one-dimensional version are
generally valid. Differences that may occur are consequences of Doppler and
momentum-transfer effects. Ways to minimize these are discussed.


title:
Squeezing generation and revivals in a cavity-ion system in contact with
  a reservoir

abstract:
  We consider a system consisting of a single two-level ion in a harmonic trap,
which is localized inside a non-ideal optical cavity at zero temperature and
subjected to the action of two external lasers. We are able to obtain an
analytical solution for the total density operator of the system and show that
squeezing in the motion of the ion and in the cavity field is generated. We
also show that complete revivals of the states of the motion of the ion and of
the cavity field occur periodically.


title: Entanglement in quantum critical spin systems

abstract:
  We study the field dependence of the entanglement of formation in anisotropic
S=1/2 antiferromagnetic chains and two-leg ladders displaying a T=0
field-driven quantum phase transition. The analysis is carried out via Quantum
Monte Carlo simulations. At zero temperature the entanglement estimators show
abrupt changes at and around criticality, vanishing below the critical field,
in correspondence with an exactly factorized state, and then immediately
recovering a finite value upon passing through the quantum phase transition. At
the quantum critical point, a deep minimum in the pairwise-to-global
entanglement ratio shows that multi-spin entanglement is strongly enhanced;
moreover this signature represents a novel way of detecting the quantum phase
transition of the system, relying entirely on entanglement estimators.


title:
Generation of a superposition of multiple mesoscopic states of radiation
  in a resonant cavity

abstract:
  Using resonant interaction between atoms and the field in a high quality
cavity, we show how to generate a superposition of many mesoscopic states of
the field. We study the quasi-probability distributions and demonstrate the
nonclassicality of the superposition in terms of the zeroes of the Q-function
as well as the negativity of the Wigner function. We discuss the decoherence of
the generated superposition state. We propose homodyne techniques of the type
developed by Auffeves et al [Phys. Rev. Lett. 91, 230405 (2003)] to monitor the
superposition of many mesoscopic states.


title: The fundamental problem of quantum cryptography

abstract:
  It is known that statistical predictions of quantum theory do not depend on
its interpretation. In particular, an experiment cannot distinguish between the
Copenhagen interpretation (involving no hidden variables) and the de
Broglie-Bohm interpretation based on nonlocal hidden variables. Quantum
cryptographic protocols, such as BB84 or E91, are secure and mutually
equivalent as long as one works within the framework of Copenhagen
interpretation. But they are inequivalent and insecure if one considers attacks
allowed by the de Broglie-Bohm interpretation. The fundametal problem of
quantum cryptography is therefore this: Are all the statements about security
of quantum protocols based on our belief in one of the two allowed
interpretations of quantum mechanics? We show that this is not the case.
Ekert-type protocols can be modified in a way that makes them secure even if
the de Broglie-Bohm nonlocal hidden variables exist. Bennett-Brassard-type
cryptography does not seem to allow for such a correction.


title: Encoding a qubit into multilevel subspaces

abstract:
  We present a formalism for encoding the logical basis of a qubit into
subspaces of multiple physical levels. The need for this multilevel encoding
arises naturally in situations where the speed of quantum operations exceeds
the limits imposed by the addressability of individual energy levels of the
qubit physical system. A basic feature of the multilevel encoding formalism is
the logical equivalence of different physical states and correspondingly, of
different physical transformations. This logical equivalence is a source of a
significant flexibility in designing logical operations, while the multilevel
structure inherently accommodates fast and intense broadband controls thereby
facilitating faster quantum operations. Another important practical advantage
of multilevel encoding is the ability to maintain full quantum-computational
fidelity in the presence of mixing and decoherence within encoding subspaces.
The formalism is developed in detail for single-qubit operations and
generalized for multiple qubits. As an illustrative example, we perform a
simulation of closed-loop optimal control of single-qubit operations for a
model multilevel system, and subsequently apply these operations at finite
temperatures to investigate the effect of decoherence on operational fidelity.


title: Complementarity and Entanglement in Quantum Information Theory

abstract:
  The restrictions that nature places on the distribution of correlations in a
multipartite quantum system play fundamental roles in the evolution of such
systems, and yield vital insights into the design of protocols for the quantum
control of ensembles with potential applications in the field of quantum
computing. We show how this entanglement sharing behavior may be studied in
increasingly complex systems of both theoretical and experimental significance
and demonstrate that entanglement sharing, as well as other unique features of
entanglement, e.g. the fact that maximal information about a multipartite
quantum system does not necessarily entail maximal information about its
component subsystems, may be understood as specific consequences of the
phenomenon of complementarity extended to composite quantum systems. We also
present a local hidden-variable model supplemented by an efficient amount of
classical communication that reproduces the quantum-mechanical predictions for
the entire class of Gottesman-Knill circuits. The success of our simulation
provides strong evidence that the power of quantum computation arises not
directly from entanglement, but rather from the nonexistence of an efficient,
local realistic description of the computation, even when augmented by an
efficient amount of nonlocal, but classical communication. Finally, we note
that the findings presented in this thesis support the conjecture that Hilbert
space dimension is an objective property of a quantum system since it
constrains the number of valid conceptual divisions of the system into
subsystems.


title: Dynamic decoherence control of a solid-state nuclear quadrupole qubit

abstract:
  We report on the application of a dynamic decoherence control pulse sequence
on a nuclear quadrupole transition in $Pr^{3+}:Y_2SiO_5$ . Process tomography
is used to analyse the effect of the pulse sequence. The pulse sequence was
found to increase the decoherence time of the transition to over 30 seconds.
Although the decoherence time was significantly increased, the population terms
were found to rapidly decay on the application of the pulse sequence. The
increase of this decay rate is attributed to inhomogeneity in the ensemble.
Methods to circumvent this limit are discussed.


title: Multi pulse control of entanglement

abstract:
  We study the effectiveness of multi pulse control to suppress the degradation
of entanglement. Based on a linearly interacting spin-boson model, we show that
the multi pulse application recovers the decay of concurrence when an entangled
pair of spins interacts with a reservoir that has the non-Markovian nature. We
present the effectiveness of multi pulse control for both the common bath case
and the individual bath case.


title: Quantum Information Theory and the Foundations of Quantum Mechanics

abstract:
  This thesis is a contribution to the debate on the implications of quantum
information theory for the foundations of quantum mechanics.
  In Part 1, the logical and conceptual status of various notions of
information is assessed. It is emphasized that the everyday notion of
information is to be firmly distinguished from the technical notions arising in
information theory; however it is maintained that in both settings
`information' functions as an abstract noun, hence does not refer to a
particular or substance (the worth of this point is illustrated in application
to quantum teleportation). The claim that `Information is Physical' is assessed
and argued to face a destructive dilemma. Accordingly, the slogan may not be
understood as an ontological claim, but at best, as a methodological one. The
reflections of Bruckner and Zeilinger (2001) and Deutsch and Hayden (2000) on
the nature of information in quantum mechanics are critically assessed and some
results presented on the characterization of entanglement in the Deutsch-Hayden
formalism. Some philosophical aspects of quantum computation are discussed and
general morals drawn concerning the nature of quantum information theory.
  In Part II, following some preliminary remarks, two particular
information-theoretic approaches to the foundations of quantum mechanics are
assessed in detail. It is argued that Zeilinger's (1999) Foundational Principle
is unsuccessful as a foundational principle for quantum mechanics. The
information-theoretic characterization theorem of Clifton, Bub and Halvorson
(2003) is assessed more favourably, but the generality of the approach is
questioned and it is argued that the implications of the theorem for the
traditional foundational problems in quantum mechanics remains obscure.


title:
Matter Wave Diffraction from an Inclined Transmission Grating: Searching
  for the Elusive He-4 Trimer Efimov State

abstract:
  The size of the helium trimer is determined by diffracting a beam of He-4
clusters from a 100 nm grating inclined by 21 degree. Due to the bar thickness
the projected slit width is roughly halved to 27 nm, increasing the sensitivity
to the trimer size. The peak intensities measured out to the 8th order are
evaluated via a few-body scattering theory. The trimer pair distance is found
to be 1.1+0.4/-0.5 nm in agreement with predictions for the ground state. No
evidence for a significant amount of Efimov trimers is found. Their
concentration is estimated to be less than 6%.


title: Optimal coupling of entangled photons into single-mode optical fibers

abstract:
  We present a consistent multimode theory that describes the coupling of
single photons generated by collinear Type-I parametric down-conversion into
single-mode optical fibers. We have calculated an analytic expression for the
fiber diameter which maximizes the pair photon count rate. For a given focal
length and wavelength, a lower limit of the fiber diameter for satisfactory
coupling is obtained.


title: The limitations of nice mutually unbiased bases

abstract:
  Mutually unbiased bases of a Hilbert space can be constructed by partitioning
a unitary error basis. We consider this construction when the unitary error
basis is a nice error basis. We show that the number of resulting mutually
unbiased bases can be at most one plus the smallest prime power contained in
the dimension, and therefore that this construction cannot improve upon
previous approaches. We prove this by establishing a correspondence between
nice mutually unbiased bases and abelian subgroups of the index group of a nice
error basis and then bounding the number of such subgroups. This bound also has
implications for the construction of certain combinatorial objects called nets.


title:
Extending the Promise of the Deutsch--Jozsa--Hoyer Algorithm for Finite
  Groups

abstract:
  Hoyer has given a generalisation of the Deutsch--Jozsa algorithm which uses
the Fourier transform on a group G which is (in general) non-Abelian. His
algorithm distinguishes between functions which are either perfectly balanced
(m-to-one) or constant, with certainty, and using a single quantum query. Here,
we show that this algorithm (which we call the Deutsch--Jozsa--Hoyer algorithm)
can in fact deal with a broader range of promises, which we define in terms of
the irreducible representations of G.


title: Time and Ensemble Averages in Bohmian Mechanics

abstract:
  We show that in the framework of one-dimensional Bohmian Quantum
Mechanics[1], for a particle subject to a potential undergoing a weak adiabatic
change, the time averages of the particle's positions typically differ markedly
from the ensemble averages. We Apply this result to the case where the weak
perturbing potential is the back-action of a measuring device (i.e. a
protective measurement). It is shown that under these conditions, most
trajectories never cross the position measured (as already shown for a
particular example in [3]).


title: Spin-glasses in optical cavity

abstract:
  Recent advances in nanofabrication and optical control have garnered
tremendous interest in multi-qubit-cavity systems. Here we analyze a spin-glass
version of such a nanostructure, solving analytically for the phase diagrams in
both the matter and radiation subsystems in the replica symmetric regime.
Interestingly, the resulting phase transitions turn out to be tunable simply by
varying the matter-radiation coupling strength.


title: Noise Tolerance of the BB84 Protocol with Random Privacy Amplification

abstract:
  We prove that BB84 protocol with random privacy amplification is secure with
a higher key rate than Mayers' estimate with the same error rate. Consequently,
the tolerable error rate of this protocol is increased from 7.5 % to 11 %. We
also extend this method to the case of estimating error rates separately in
each basis, which enables us to securely share a longer key.


title: Complexity of Graph State Preparation

abstract:
  The graph state formalism is a useful abstraction of entanglement. It is used
in some multipartite purification schemes and it adequately represents
universal resources for measurement-only quantum computation. We focus in this
paper on the complexity of graph state preparation. We consider the number of
ancillary qubits, the size of the primitive operators, and the duration of
preparation. For each lexicographic order over these parameters we give upper
and lower bounds for the complexity of graph state preparation. The first part
motivates our work and introduces basic notions and notations for the study of
graph states. Then we study some graph properties of graph states,
characterizing their minimal degree by local unitary transformations, we
propose an algorithm to reduce the degree of a graph state, and show the
relationship with Sutner sigma-game.
  These properties are used in the last part, where algorithms and lower bounds
for each lexicographic order over the considered parameters are presented.


title: Quantum Compiling with Approximation of Multiplexors

abstract:
  A quantum compiling algorithm is an algorithm for decomposing ("compiling")
an arbitrary unitary matrix into a sequence of elementary operations (SEO).
Suppose $U_{in}$ is an $\nb$-bit unstructured unitary matrix (a unitary matrix
with no special symmetries) that we wish to compile. For $\nb>10$, expressing
$U_{in}$ as a SEO requires more than a million CNOTs. This calls for a method
for finding a unitary matrix that: (1)approximates $U_{in}$ well, and (2) is
expressible with fewer CNOTs than $U_{in}$. The purpose of this paper is to
propose one such approximation method. Various quantum compiling algorithms
have been proposed in the literature that decompose an arbitrary unitary matrix
into a sequence of U(2)-multiplexors, each of which is then decomposed into a
SEO. Our strategy for approximating $U_{in}$ is to approximate these
intermediate U(2)-multiplexors. In this paper, we will show how one can
approximate a U(2)-multiplexor by another U(2)-multiplexor that is expressible
with fewer CNOTs.


title: Spectral analysis of short time signals

abstract:
  The very old problem of extracting frequencies from time signals is addressed
in the case of signals that are very short as compared to their intrinsic time
scales. The solution of the problem is not only important to the classic signal
processing but also helps to disqualify several common formulations of the
quantum mechanical time-energy uncertainty principle.


title: Quantum physics with a hidden variable

abstract:
  Every quantum physical system can be considered the ''shadow'' of a special
kind of classical system. The system proposed here is classical mainly because
each observable function has a well precise value on each state of the system:
an hypothetical observer able to prepare the system exactly in an assigned
state and able to build a measuring apparatus perfectly corresponding to a
required observable gets always the same real value. The same system considered
instead by an unexpert observer, affected by the ignorance of a hidden
variable, is described by a statistical theory giving exactly and without
exception the states, the observables, the dynamics and the probabilities
prescribed for the usual quantum system.


title:
Efficient and Robust Quantum Key Distribution With Minimal State
  Tomography

abstract:
  We introduce the Singapore protocol, a qubit protocol for quantum key
distribution that is fully tomographic, more efficient than other tomographic
protocols, and very robust. Under ideal circumstances the efficiency is
log_2(4/3)=0.415 key bits per qubit sent. This is 25% more than the efficiency
of 1/3=0.333 for the standard six-state protocol, which sets the benchmark. We
describe a simple two-way communication scheme that extracts 0.4 key bits per
qubit and thus gets close to the information-theoretical limit. The noise
thresholds that we report for a hierarchy of eavesdropping attacks demonstrate
the robustness of the protocol: A secure key can be extracted if there is less
than 38.9% noise.


title: A Unified and Generalized Approach to Quantum Error Correction

abstract:
  We present a unified approach to quantum error correction, called operator
quantum error correction. This scheme relies on a generalized notion of
noiseless subsystems that is not restricted to the commutant of the interaction
algebra. We arrive at the unified approach, which incorporates the known
techniques -- i.e. the standard error correction model, the method of
decoherence-free subspaces, and the noiseless subsystem method -- as special
cases, by combining active error correction with this generalized noiseless
subsystem method. Moreover, we demonstrate that the quantum error correction
condition from the standard model is a necessary condition for all known
methods of quantum error correction.


title:
Entanglement-assisted transformation is asymptotically equivalent to
  multiple-copy transformation

abstract:
  We show that two ways of manipulation of quantum entanglement, namely,
entanglement-assisted local transformation [D. Jonathan and M. B. Plenio, Phys.
Rev. Lett. {\bf 83}, 3566 (1999)] and multiple-copy transformation [S.
Bandyopadhyay, V. Roychowdhury, and U. Sen, Phys. Rev. A {\bf 65}, 052315
(2002)], are equivalent in the sense that they can asymptotically simulate each
other's ability to implement a desired transformation from a given source state
to another given target state with the same optimal success probability. As a
consequence, this yields a feasible method to evaluate the optimal conversion
probability of an entanglement-assisted transformation.


title: Quantum-enhanced measurements: beating the standard quantum limit

abstract:
  Quantum mechanics, through the Heisenberg uncertainty principle, imposes
limits to the precision of measurement. Conventional measurement techniques
typically fail to reach these limits. Conventional bounds to the precision of
measurements such as the shot noise limit or the standard quantum limit are not
as fundamental as the Heisenberg limits, and can be beaten using quantum
strategies that employ `quantum tricks' such as squeezing and entanglement.


title:
Measurement of the total energy of an isolated system by an internal
  observer

abstract:
  We consider the situation in which an observer internal to an isolated system
wants to measure the total energy of the isolated system (this includes his own
energy, that of the measuring device and clocks used, etc...). We show that he
can do this in an arbitrarily short time, as measured by his own clock. This
measurement is not subjected to a time-energy uncertainty relation. The
properties of such measurements are discussed in detail with particular
emphasis on the relation between the duration of the measurement as measured by
internal clocks versus external clocks.


title:
A New Form of Path Integral for the Coherent States Representation and
  its Semiclassical Limit

abstract:
  The overcompleteness of the coherent states basis leads to a multiplicity of
representations of Feynman's path integral. These different representations,
although equivalent quantum mechanically, lead to different semiclassical
limits. Two such semiclassical formulas were derived in \cite{Bar01} for the
two corresponding path integral forms suggested by Klauder and Skagerstan in
\cite{Klau85}. Each of these formulas involve trajectories governed by a
different classical representation of the Hamiltonian operator: the P
representation in one case and the Q representation in other. In this paper we
construct a third representation of the path integral whose semiclassical limit
involves directly the Weyl representation of the Hamiltonian operator, i.e.,
the classical Hamiltonian itself.


title: Single spin detection by qubit SWAP to a molecular nanomagnet

abstract:
  Spin state detection is a key but very challenging step for any spin-based
solid-state quantum computing technology. In fullerene based quantum computer
technologies, we here propose to detect the single spin inside a fullerene by
transferring the quantum information from the endohedral spin to the ground
states of a molecular nanomagnet Fe$_{8}$, with large spin S=10. We show how to
perform the required SWAP operation and how to read out the information through
state-of-the-art techniques such as micro-SQUID.


title:
A non-perturbative method for time-dependent problems in quantum
  mechanics

abstract:
  A powerful method for calculating the eigenvalues of a Hamiltonian operator
consists of converting the energy eigenvalue equation into a matrix equation by
means of an appropriate basis set of functions. The convergence of the method
can be greatly improved by means of a variational parameter in the basis
functions determined by the principle of minimal sensitivity. In the case of
the quartic anharmonic oscillator and of a symmetrical double-well potential we
choose an effective oscillator frequency. In the case of nonsymmetrical
potential we add a coordinate shift in a two-parameter variational calculation.
The method not only gives the spectrum, but also an approximation to the energy
eigenfunctions. Consequently it can be used to solve the time-dependent
Schr\"odinger equation using the method of stationary states. We apply it to
the time development of two different initial wave functions in the double-well
slow roll potential.


title:
Entropic uncertainty relations for incomplete sets of mutually unbiased
  observables

abstract:
  Entropic uncertainty relations, based on sums of entropies of probability
distributions arising from different measurements on a given pure state, can be
seen as a generalization of the Heisenberg uncertainty relation that is in many
cases a more useful way to quantify incompatibility between observables. Of
particular interest are relationships between `mutually unbiased' observables,
which are maximally incompatible. Lower bounds on the sum of entropies for sets
of two such observables, and for complete sets of observables within a space of
given dimension, have been found. This paper explores relations in the
intermediate regime of large, but far from complete, sets of unbiased
observables.


title: Optimized design of universal two-qubit gates

abstract:
  We construct optimized implementations of the CNOT and other universal
two-qubit gates that, unlike many of the previously proposed protocols, are
carried out in a single step. The new protocols require tunable inter-qubit
couplings but, in return, show a significant improvements in the quality of
gate operations. Our optimization procedure can be further extended to the
combinations of elementary two-qubit as well as irreducible many-qubit gates.


title:
Optical loss and lasing characteristics of high-quality-factor AlGaAs
  microdisk resonators with embedded quantum dots

abstract:
  Optical characterization of AlGaAs microdisk resonant cavities with a quantum
dot active region is presented. Direct passive measurement of the optical loss
within AlGaAs microdisk resonant structures embedded with InAs/InGaAs
dots-in-a-well (DWELL) is performed using an optical-fiber-based probing
technique at a wavelength (lambda~1400 nm) that is red-detuned from the dot
emission wavelength (lambda~1200 nm). Measurements in the 1400 nm wavelength
band on microdisks of diameter D = 4.5 microns show that these structures
support modes with cold-cavity quality factors as high as 360,000.
DWELL-containing microdisks are then studied through optical pumping at room
temperature. Pulsed lasing at lambda ~ 1200 nm is seen for cavities containing
a single layer of InAs dots, with threshold values of ~ 17 microWatts,
approaching the estimated material transparency level. Room-temperature
continuous wave operation is also observed.


title:
Stimulated Raman Adiabatic Passage (STIRAP) Among Degenerate-Level
  Manifolds

abstract:
  We examine the conditions needed to accomplish stimulated Raman adiabatic
passage (STIRAP) when the three levels (g, e and f) are degenerate, with
arbitrary couplings contributing to the pump-pulse interaction (g - e) and to
the Stokes-pulse interaction (e-f). We show that in general a sufficient
condition for complete population removal from the g set of degenerate states
for arbitrary, pure or mixed, initial state is that the degeneracies should not
decrease along the sequence g, e and f. We show that when this condition holds
it is possible to achieve the degenerate counterpart of conventional STIRAP,
whereby adiabatic passage produces complete population transfer. Indeed, the
system is equivalent to a set of independent three-state systems, in each of
which a STIRAP procedure can be implemented. We describe a scheme of unitary
transformations that produces this result. We also examine the cases when this
degeneracy constraint does not hold, and show what can be accomplished in those
cases. For example, for angular momentum states when the degeneracy of the g
and f levels is less than that of the e level we show how a special choice for
the pulse polarizations and phases can produce complete removal of population
from the g set. Our scheme can be a powerful tool for coherent control in
degenerate systems, because of its robustness when selective addressing of the
states is not required or impossible. We illustrate the analysis with several
analytically solvable examples, in which the degeneracies originate from
angular momentum orientation, as expressed by magnetic sublevels.


title: Engineering mixed states in a degenerate four-state system

abstract:
  A method is proposed for preparing any pure and a wide class of mixed quantum
states in the decoherence-free ground-state subspace of a degenerate multilevel
lambda system. The scheme is a combination of optical pumping and a series of
coherent excitation processes, and for a given pulse sequence the same final
state is obtained regardless of the initial state of the system. The method is
robust with respect to the fluctuation of the pulse areas, like in adiabatic
methods, however, the field amplitude can be adjusted in a larger range.


title:
Quantum and Classical Communication-Space Tradeoffs from Rectangle
  Bounds

abstract:
  We derive lower bounds for tradeoffs between the communication C and space S
for communicating circuits. The first such bound applies to quantum circuits.
If for any function f with image Z the multicolor discrepancy of the
communication matrix of f is 1/2^d, then any bounded error quantum protocol
with space S, in which Alice receives some l inputs, Bob r inputs, and they
compute f(x_i,y_j) for the lr pairs of inputs (x_i,y_j) needs communication
C=\Omega(lrd \log |Z|/S). In particular, n\times n-matrix multiplication over a
finite field F requires C=\Theta(n^3\log^2 |F|/S). We then turn to randomized
bounded error protocols, and derive the bound C=\Omega(n^3/S^2) for Boolean
matrix multiplication, utilizing a new direct product result for the one-sided
rectangle lower bound on randomized communication complexity. This implies a
separation between quantum and randomized protocols.


title:
Quantum entanglement enhances the capacity of bosonic channels with
  memory

abstract:
  The bosonic quantum channels have recently attracted a growing interest,
motivated by the hope that they open a tractable approach to the generally hard
problem of evaluating quantum channel capacities. These studies, however, have
always been restricted to memoryless channels. Here, it is shown that the
classical capacity of a bosonic Gaussian channel with memory can be
significantly enhanced if entangled symbols are used instead of product
symbols. For example, the capacity of a photonic channel with 70%-correlated
thermal noise of one third the shot noise is enhanced by about 11% when using
3.8-dB entangled light with a modulation variance equal to the shot noise.


title:
Klauder's coherent states for the radial Coulomb problem in a uniformly
  curved space and their flat-space limits

abstract:
  First a set of coherent states a la Klauder is formally constructed for the
Coulomb problem in a curved space of constant curvature. Then the flat-space
limit is taken to reduce the set for the radial Coulomb problem to a set of
hydrogen atom coherent states corresponding to both the discrete and the
continuous portions of the spectrum for a fixed \ell sector.


title: A Quantum Langevin Formulation of Risk-Sensitive Optimal Control

abstract:
  In this paper we formulate a risk-sensitive optimal control problem for
continuously monitored open quantum systems modelled by quantum Langevin
equations. The optimal controller is expressed in terms of a modified
conditional state, which we call a risk-sensitive state, that represents
measurement knowledge tempered by the control purpose. One of the two
components of the optimal controller is dynamic, a filter that computes the
risk-sensitive state.
  The second component is an optimal control feedback function that is found by
solving the dynamic programming equation. The optimal controller can be
implemented using classical electronics.
  The ideas are illustrated using an example of feedback control of a two-level
atom.


title: Wigner-Yanase skew information as tests for quantum entanglement

abstract:
  A Bell-type inequality is proposed in terms of Wigner-Yanase skew
information, which is quadratic and involves only one local spin observable at
each site. This inequality presents a hierarchic classification of all states
of multipartite quantum systems from separable to fully entangled states, which
is more powerful than the one presented by quadratic Bell inequalities from
two-entangled to fully entangled states. In particular, it is proved that the
inequality provides an exact test to distinguish entangled from nonentangled
pure states of two qubits. Our inequality sheds considerable light on
relationships between quantum entanglement and information theory.