title: Retrodictive quantum optical state engineering

abstract:
  Although it has been known for some time that quantum mechanics can be
formulated in a way that treats prediction and retrodiction on an equal
footing, most attention in engineering quantum states has been devoted to
predictive states, that is, states associated with the a preparation event.
Retrodictive states, which are associated with a measurement event and
propagate backwards in time, are also useful, however. In this paper we show
how any retrodictive state of light that can be written to a good approximation
as a finite superposition of photon number states can be generated by an
optical multiport device. The composition of the state is adjusted by
controlling predictive coherent input states. We show how the probability of
successful state generation can be optimised by adjusting the multiport device
and also examine a versatile configuration that is useful for generating a
range of states.


title:
Theory and experiment of entanglement in a quasi-phase-matched
  two-crystal source

abstract:
  We report new results regarding a source of polarization entangled
photon-pairs created by the process of spontaneous parametric downconversion in
two orthogonally oriented, periodically poled, bulk KTiOPO4 crystals (PPKTP).
The source emits light colinearly at the non-degenerate wavelengths of 810 nm
and 1550 nm, and is optimized for single-mode optical fiber collection and
long-distance quantum communication. The configuration favors long crystals,
which promote a high photon-pair production rate at a narrow bandwidth,
together with a high pair-probability in fibers. The quality of entanglement is
limited by chromatic dispersion, which we analyze by determining the output
state. We find that such a decoherence effect is strongly material dependent,
providing for long crystals an upper bound on the visibility of the coincidence
fringes of 41% for KTiOPO4, and zero for LiNbO3. The best obtained raw
visibility, when canceling decoherence with an extra piece of crystal, was 91
\pm 0.2%, including background counts. We confirm by a violation of the
CHSH-inequality (S = 2.679 \pm 0.004 at 55 s^{-1/2} standard deviations) and by
complete quantum state tomography that the fibers carry high-quality entangled
pairs at a maximum rate of 55 x 10^3 s^{-1}THz^{-1}mW^{-1}.


title:
Development of an approximate method for quantum optical models and
  their pseudo-Hermicity

abstract:
  An approximate method is suggested to obtain analytical expressions for the
eigenvalues and eigenfunctions of the some quantum optical models. The method
is based on the Lie-type transformation of the Hamiltonians. In a particular
case it is demonstrated that $E\times \epsilon $ Jahn-Teller Hamiltonian can
easily be solved within the framework of the suggested approximation. The
method presented here is conceptually simple and can easily be extended to the
other quantum optical models. We also show that for a purely imaginary coupling
the $E\times \epsilon $ Hamiltonian becomes non-Hermitian but $P\sigma
_{0}$-symmetric. Possible generalization of this approach is outlined.


title:
Electromagnetically induced transparency and dark fluorescence in a
  cascade three-level Lithium molecule

abstract:
  We observed electromagnetically induced transparency (EIT) and dark
fluorescence in a cascade three-level diatomic Lithium system using
Optical-Optical Double Resonance (OODR) spectroscopy. When a strong coupling
laser couples the intermediate state $A^{1}\Sigma^{+}_{u}(v=13, J=14)$ to the
upper state $G^{1}\Pi_{g}(v=11, J=14)$ of $^7Li_2$, the fluorescence from both
$A^{1}\Sigma^{+}_{u}$ and $G^{1}\Pi_{g}$ states was drastically reduced as the
weak probe laser was tuned through the resonance transition between the ground
state $X^{1}\Sigma^{+}_{g}(v=4, J=15)$ and the excited state
$A^{1}\Sigma^{+}_{u}(v=13, J=14)$. The strong coupling laser makes an optically
thick medium transparent for the probe transition. In addition, The fact that
fluorescence from the upper state $G^{1}\Pi_{g}(v=11, J=14)$ was also dark when
both lasers were tuned at resonance implies that the molecules were trapped in
the ground state. We used density matrix methods to simulate the response of an
open molecular three-level system to the action of a strong coupling field and
a weak probe field. The analytical solutions were obtained under the
steady-state condition. We have incorporated the magnetic sublevel (M)
degeneracy of the rotational levels in the lineshape analysis and report $|M|$
dependent lineshape splitting. The theoretical calculations are in excellent
agreement with the observed fluorescence spectra. We show that the coherence is
remarkably preserved even when the coupling field was detuned far from the
resonance.


title: Non Existence of Quantum Mechanical Self Replicating Machine

abstract:
  In this letter we establish the impossibility of existence of self
replicating machine in the quantum world. We establish this result by three
different but consistent approaches of linearity of quantum mechanics, no
signalling condition and conservation of entanglement under local unitary
operations.


title:
Almost Global Stochastic Feedback Stabilization of Conditional Quantum
  Dynamics

abstract:
  We propose several parametrization-free solutions to the problem of quantum
state reduction control by means of continuous measurement and smooth quantum
feedback. In particular, we design a feedback law for which almost global
stochastic feedback stabilization can be proved analytically by means of
Lyapunov techinques. This synthesis arises very naturally from the physics of
the problem, as it relies on the variance associated with the quantum filtering
process.


title: Foundations Of Quantum Theory Revisited

abstract:
  After giving a panoramic view of the " text-book " interpretation of the new
quantum mechanics, as a sequel to the old quantum theory, the conceptual basis
of quantum theory since the Copenhagen Interpretation is reviewed in the
context of various proposals since Einstein and Niels Bohr, designed to throw
light on possible new facets bearing on its foundations, the key issues to its
inherent "incompleteness" being A) measurement, and B) quantum non-locality. A
related item on measurement, namely Quantum Zeno (as well as anti-Zeno) effect
is also reviewed briefly. The inputs for the new facets are from some key
Indian experts : S.M. Roy, V. Singh ; D. Home; B. Misra; C.S. Unnikrishnan


title: On quantum Lyapunov exponents

abstract:
  It was shown that quantum analysis constitutes the proper analytic basis for
quantization of Lyapunov exponents in the Heisenberg picture. Differences among
various quantizations of Lyapunov exponents are clarified.


title: Exactly solvable approximating models for Rabi Hamiltonian dynamics

abstract:
  The interaction between an atom and a one mode external driving field is an
ubiquitous problem in many branches of physics and is often modeled using the
Rabi Hamiltonian. In this paper we present a series of analytically solvable
Hamiltonians that approximate the Rabi Hamiltonian and compare our results to
the Jaynes-Cummings model which neglects the so-called counter-rotating term in
the Rabi Hamiltonian. Through a unitary transformation that diagonlizes the
Jaynes-Cummings model, we transform the counter-rotating term into separate
terms representing several different physical processes. By keeping only
certain terms, we can achieve an excellent approximation to the exact dynamics
within specified parameter ranges.


title: Robust gates for holonomic quantum computation

abstract:
  Non Abelian geometric phases are attracting increasing interest because of
possible experimental application in quantum computation. We study the effects
of the environment (modelled as an ensemble of harmonic oscillators) on a
holonomic transformation and write the corresponding master equation. The
solution is analytically and numerically investigated and the behavior of the
fidelity analyzed: fidelity revivals are observed and an optimal finite
operation time is determined at which the gate is most robust against noise.


title: Atomic Coherence Induced Macroscopical Entangled Coherent State

abstract: This paper had been withdrawed


title: Dipole induced transparency in drop-filter cavity-waveguide systems

abstract:
  We show that a waveguide that is normally opaque due to interaction with a
drop-filter cavity can be made transparent when the drop filter is also coupled
to a dipole. A transparency condition is derived between the cavity lifetime
and vacuum Rabi frequency of the dipole. This condition is much weaker than
strong coupling, and amounts to simply achieving large Purcell factors. Thus,
we can observe transparency in the weak coupling regime. We describe how this
effect can be useful for designing quantum repeaters for long distance quantum
communication.


title: Coherent States with SU(2) and SU(3) Charges

abstract:
  We define coherent states carrying SU(2) charges by exploiting Schwinger
boson representation of SU(2) Lie algebra. These coherent states satisfy
continuity property and provide resolution of identity on $S^{3}$. We further
generalize these techniques to construct the corresponding SU(3) charge
coherent states. The SU(N) extension is discussed.


title: QMA/qpoly Is Contained In PSPACE/poly: De-Merlinizing Quantum Protocols

abstract:
  This paper introduces a new technique for removing existential quantifiers
over quantum states. Using this technique, we show that there is no way to pack
an exponential number of bits into a polynomial-size quantum state, in such a
way that the value of any one of those bits can later be proven with the help
of a polynomial-size quantum witness. We also show that any problem in QMA with
polynomial-size quantum advice, is also in PSPACE with polynomial-size
classical advice. This builds on our earlier result that BQP/qpoly is contained
in PP/poly, and offers an intriguing counterpoint to the recent discovery of
Raz that QIP/qpoly = ALL. Finally, we show that QCMA/qpoly is contained in
PP/poly and that QMA/rpoly = QMA/poly.


title: Fault-tolerant quantum computation with long-range correlated noise

abstract:
  We prove a new version of the quantum accuracy threshold theorem that applies
to non-Markovian noise with algebraically decaying spatial correlations. We
consider noise in a quantum computer arising from a perturbation that acts
collectively on pairs of qubits and on the environment, and we show that an
arbitrarily long quantum computation can be executed with high reliability in D
spatial dimensions, if the perturbation is sufficiently weak and decays with
the distance r between the qubits faster than 1/r^D.


title: Typical entanglement of stabilizer states

abstract:
  How entangled is a randomly chosen bipartite stabilizer state? We show that
if the number of qubits each party holds is large the state will be close to
maximally entangled with probability exponentially close to one. We provide a
similar tight characterization of the entanglement present in the maximally
mixed state of a randomly chosen stabilizer code. Finally, we show that
typically very few GHZ states can be extracted from a random multipartite
stabilizer state via local unitary operations. Our main tool is a new
concentration inequality which bounds deviations from the mean of random
variables which are naturally defined on the Clifford group.


title:
Quantum Measurements for Graph Isomorphism Require Entanglement: Tight
  Results on Multiregister Fourier Sampling (Withdrawn)

abstract: This article has been withdrawn by the authors.


title:
Quantization of the canonically conjugate pair angle and orbital angular
  momentum

abstract:
  The question how to quantize a classical system where an angle phi is one of
the basic canonical variables has been controversial since the early days of
quantum mechanics. The problem is that the angle is a multivalued or
discontinuous variable on the corresponding phase space. The remedy is to
replace phi by the smooth periodic functions cos phi and sin phi. In the case
of the canonical pair (phi,l),l: orbital angular momentum (OAM), the phase
space S_(phi,l) ={phi in R mod 2pi, l in R} has the global structure S^1 x R of
a cylinder on which the Poisson brackets of the 3 functions cos phi, sin phi
and l obey the Lie algebra of the euclidean group E(2) in the plane. This
property provides the basis for the quantization of the system in terms of
irreducible unitary representations of the group E(2) or of its covering
groups. A crucial point is that - due to the fact that the subgroup SO(2) = S^1
is multiply connected - these representations allow for fractional OAM l = n +
c, c in [0,1). Such c not 0 have already been observed in cases like the
Aharonov-Bohm and the fractional quantum Hall effects and they correspond to
the quasi-momenta of Bloch waves in ideal crystals. The proposal of the present
paper is to look for fractional OAM in connection with the quantum optics of
Laguerre-Gaussian laser modes in external magnetic fields. The quantum theory
of the phase space S_(phi,l) in terms of unitary representations of E(2) allows
for two types of "coherent" states the properties of which are discussed in
detail: Non-holomorphic minimal uncertainty states and holomorphic ones
associated with Bargmann-Segal Hilbert spaces.


title:
Practical purification scheme for decohered coherent-state
  superpositions via partial homodyne detection

abstract:
  We present a simple protocol to purify a coherent-state superposition that
has undergone a linear lossy channel. The scheme constitutes only a single beam
splitter and a homodyne detector, and thus is experimentally feasible. In
practice, a superposition of coherent states is transformed into a classical
mixture of coherent states by linear loss, which is usually the dominant
decoherence mechanism in optical systems. We also address the possibility of
producing a larger amplitude superposition state from decohered states, and
show that in most cases the decoherence of the states are amplified along with
the amplitude.


title: Classification of mixed high-dimensional multiparticle systems

abstract:
  We present an inequality that classifies mixed multipartite systems of an
arbitrary dimension with respect to separability and positivity of partial
transpose properties. This inequality gives a way to experimentally classify
the observed state of multipartite systems of an arbitrary dimension. The
inequality also implies that a sufficient condition for a density operator to
have no positive partial transpose with respect to any subsystem is that the
fidelity to a generalized Greenberger-Horne-Zeilinger state {[A. Cabello, Phys.
Rev. A {\bf 63}, 022104 (2001)]} is larger than 1/2 for mixed multipartite
systems of an arbitrary dimension.


title:
Observables suitable for restricting the fidelity to multipartite
  maximally entangled states

abstract:
  We present a class of observables which are suitable for determining the
fidelity of a state to the multipartite Greenberger-Horne-Zeilinger (GHZ)
state. Given an expectation value of an observable belonging to the class, we
give a simple formula that gives a lower bound and an upper bound for the
fidelity. Applying the formula to the GHZ-state preparation experiment by Pan
{\it et al}. {[Nature (London) {\bf 403}, 515 (2000)]}, we show that the
observed state lies outside of the class of biseparable mixed three-qubit
states. We also show that for this class of operators, adopting the principle
of minimum variance {[Phys. Rev. A {\bf 60}, 4338 (1999)]} in the state
estimation always results in the state with the minimum fidelity.


title: Quantum Replicator Dynamics

abstract:
  We propose quantization relationships which would let us describe and
solution problems originated by conflicting or cooperative behaviors among the
members of a system from the point of view of quantum mechanical interactions.
The quantum analogue of the replicator dynamics is the equation of evolution of
mixed states from quantum statistical mechanics. A system and all its members
will cooperate and rearrange its states to improve their present condition.
They strive to reach the best possible state for each of them which is also the
best possible state for the whole system. This led us to propose a quantum
equilibrium in which a system is stable only if it maximizes the welfare of the
collective above the welfare of the individual. If it is maximized the welfare
of the individual above the welfare of the collective the system gets unstable
and eventually it collapses.


title: Perfect A/D conversion of entanglement

abstract:
  We investigate how entanglement can be perfectly transfered between
continuous variable and qubits system. We find that a two-mode squeezed vacuum
state can be converted to the product state of an infinitive number of
two-qubit states while keeping the entanglement. The reverse process is also
possible. The interaction Hamitonian is a kind of non-linear Jaynes-Cumings
Hamiltonian.


title: Indistinguishable Particles in Quantum Mechanics: An Introduction

abstract:
  In this article, we discuss the identity and indistinguishability of quantum
systems and the consequent need to introduce an extra postulate in Quantum
Mechanics to correctly describe situations involving indistinguishable
particles. This is, for electrons, the Pauli Exclusion Principle, or in
general, the Symmetrization Postulate. Then, we introduce fermions and bosons
and the distributions respectively describing their statistical behaviour in
indistinguishable situations. Following that, we discuss the spin-statistics
connection, as well as alternative statistics and experimental evidence for all
these results, including the use of bunching and antibunching of particles
emerging from a beam splitter as a signature for some bosonic or fermionic
states.


Comment on "Topological Transitions in Berry's Phase Interference
  Effects"


title: Equiangular lines, mutually unbiased bases, and spin models

abstract:
  We use difference sets to construct interesting sets of lines in complex
space. Using (v,k,1)-difference sets, we obtain k^2-k+1 equiangular lines in
C^k when k-1 is a prime power. Using semiregular relative difference sets with
parameters (k,n,k,l) we construct sets of n+1 mutually unbiased bases in C^k.
We show how to construct these difference sets from commutative semifields and
that several known maximal sets of mutually unbiased bases can be obtained in
this way, resolving a conjecture about the monomiality of maximal sets. We also
relate mutually unbiased bases to spin models.


title:
Towards a precision measurement of the Casimir force in a cylinder-plane
  geometry

abstract:
  We report on a proposal aimed at measuring the Casimir force in a
cylinder-plane configuration. The Casimir force is evaluated including
corrections due to finite parallelism, conductivity, and temperature. The range
of validity of the proximity force approximation is also discussed. An
apparatus to test the feasibility of a precision measurement in this
configuration has been developed, and we describe both a procedure to control
the parallelism and the results of the electrostatic calibration. Finally, we
discuss the possibility of measuring the thermal contribution to the Casimir
force and deviations from the proximity force approximation, both of which are
expected at relatively large distances.


title:
Additivity and multiplicativity properties of some Gaussian channels for
  Gaussian inputs

abstract:
  We prove multiplicativity of maximal output $p$ norm of classical noise
channels and thermal noise channels of arbitrary modes for all $p>1$ under the
assumption that the input signal states are Gaussian states. As a direct
consequence, we also show the additivity of the minimal output entropy and that
of the energy-constrained Holevo capacity for those Gaussian channels under
Gaussian inputs. To the best of our knowledge, newly discovered majorization
relation on symplectic eigenvalues, which is also of independent interest,
plays a central role in the proof.


title: Gaussian operator bases for correlated fermions

abstract:
  We formulate a general multi-mode Gaussian operator basis for fermions, to
enable a positive phase-space representation of correlated Fermi states. The
Gaussian basis extends existing bosonic phase-space methods to Fermi systems
and thus enables first-principles dynamical or equilibrium calculations in
quantum many-body Fermi systems. We prove the completeness and positivity of
the basis, and derive differential forms for products with one- and two-body
operators. Because the basis satisfies fermionic superselection rules, the
resulting phase space involves only c-numbers, without requiring anti-commuting
Grassmann variables.


title:
Comparison of the Cost Metrics for Reversible and Quantum Logic
  Synthesis

abstract:
  A breadth-first search method for determining optimal 3-line circuits
composed of quantum NOT, CNOT, controlled-V and controlled-V+ (NCV) gates is
introduced. Results are presented for simple gate count and for technology
motivated cost metrics. The optimal NCV circuits are also compared to NCV
circuits derived from optimal NOT, CNOT and Toffoli (NCT) gate circuits. The
work presented here provides basic results and motivation for continued study
of the direct synthesis of NCV circuits, and establishes relations between
function realizations in different circuit cost metrics.


title: Non-Locality and Classical Communication of the Hidden Variable Theories

abstract:
  In all local realistic theories worked out till now, locality is considered
as a basic assumption. Most people in the field consider the inconsistency
between local realistic theories and quantum mechanics to be a result of
non-local nature of quantum mechanics. In this paper, we derive Bell's
inequality for particles with instantaneous interactions, and show that the
aforementioned contradiction still exists between quantum mechanics and
non-local hidden variable models. Then, we use this non-locality to obtain the
GHZ theorem. In what follows, we show that Bacon and Toner's protocol, for the
simulation of Bell correlation, by using local hidden variables augmented by
classical communication, have some inconsistency with quantum mechanics. Our
approach can answer to Brassard questions from another viewpoint, we show that
if we accept that our nature obeys quantum mechanical laws, then all of quantum
mechanic results cannot be simulated by realistic theories augmented by
classical communication or a single instance use of non-local box.


title: Dissipative decoherence in the Grover algorithm

abstract:
  Using the methods of quantum trajectories we study effects of dissipative
decoherence on the accuracy of the Grover quantum search algorithm. The
dependence on the number of qubits and dissipation rate are determined and
tested numerically with up to 16 qubits. As a result, our numerical and
analytical studies give the universal law for decay of fidelity and probability
of searched state which are induced by dissipative decoherence effects. This
law is in agreement with the results obtained previously for quantum chaos
algorithms.


title:
Beams of electromagnetic radiation carrying angular momentum: The
  Riemann-Silberstein vector and the classical-quantum correspondence

abstract:
  All beams of electromagnetic radiation are made of photons. Therefore, it is
important to find a precise relationship between the classical properties of
the beam and the quantum characteristics of the photons that make a particular
beam. It is shown that this relationship is best expressed in terms of the
Riemann-Silberstein vector -- a complex combination of the electric and
magnetic field vectors -- that plays the role of the photon wave function. The
Whittaker representation of this vector in terms of a single complex function
satisfying the wave equation greatly simplifies the analysis. Bessel beams,
exact Laguerre-Gauss beams, and other related beams of electromagnetic
radiation can be described in a unified fashion. The appropriate photon quantum
numbers for these beams are identified. Special emphasis is put on the angular
momentum of a single photon and its connection with the angular momentum of the
beam.


title: Entanglement of remote atomic qubits

abstract:
  We report observations of entanglement of two remote atomic qubits, achieved
by generating an entangled state of an atomic qubit and a single photon at Site
A, transmitting the photon to Site B in an adjacent laboratory through an
optical fiber, and converting the photon into an atomic qubit. Entanglement of
the two remote atomic qubits is inferred by performing, locally, quantum state
transfer of each of the atomic qubits onto a photonic qubit and subsequent
measurement of polarization correlations in violation of the Bell inequality
|S| <2. We experimentally determine S =2.16 +/- 0.03. Entanglement of two
remote atomic qubits, each qubit consisting of two independent spin wave
excitations, and reversible, coherent transfer of entanglement between matter
and light, represent important advances in quantum information science.


title:
Bounded-Error Quantum State Identification and Exponential Separations
  in Communication Complexity

abstract:
  We consider the problem of bounded-error quantum state identification: given
either state \alpha_0 or state \alpha_1, we are required to output `0', `1' or
`?' ("don't know"), such that conditioned on outputting `0' or `1', our guess
is correct with high probability. The goal is to maximize the probability of
not outputting `?'. We prove a direct product theorem: if we're given two such
problems, with optimal probabilities a and b, respectively, and the states in
the first problem are pure, then the optimal probability for the joint
bounded-error state identification problem is O(ab). Our proof is based on
semidefinite programming duality and may be of wider interest.
  Using this result, we present two exponential separations in the simultaneous
message passing model of communication complexity. Both are shown in the
strongest possible sense. First, we describe a relation that can be computed
with O(log n) classical bits of communication in the presence of shared
randomness, but needs Omega(n^{1/3}) communication if the parties don't share
randomness, even if communication is quantum. This shows the optimality of
Yao's recent exponential simulation of shared-randomness protocols by quantum
protocols without shared randomness. Second, we describe a relation that can be
computed with O(log n) classical bits of communication in the presence of
shared entanglement, but needs Omega((n/log n)^{1/3}) communication if the
parties share randomness but no entanglement, even if communication is quantum.
This is the first example in communication complexity of a situation where
entanglement buys you much more than quantum communication does.


title:
Storage and retrieval of single photons transmitted between remote
  quantum memories

abstract:
  An elementary quantum network operation involves storing a qubit state in an
atomic quantum memory node, and then retrieving and transporting the
information through a single photon excitation to a remote quantum memory node
for further storage or analysis. Implementations of quantum network operations
are thus conditioned on the ability to realize such matter-to-light and/or
light-to-matter quantum state mappings. Here, we report generation,
transmission, storage and retrieval of single quanta using two remote atomic
ensembles. A single photon is generated from a cold atomic ensemble at Site A
via the protocol of Duan, Lukin, Cirac, and Zoller (DLCZ) [Nature v.414, 413
(2001)] and is directed to Site B through a 100 meter long optical fiber. The
photon is converted into a single collective excitation via the dark-state
polariton approach of Fleischhauer and Lukin [Phys. Rev. Lett. v.84, 5094
(2000)]. After a programmable storage time the atomic excitation is converted
back into a single photon. This is demonstrated experimentally, for a storage
time of 500 nanoseconds, by measurement of an anticorrelation parameter a.
Storage times exceeding ten microseconds are observed by intensity
cross-correlation measurements. The length of the storage period is two orders
of magnitude longer than the time to achieve conversion between photonic and
atomic quanta. The controlled transfer of single quanta between remote quantum
memories constitutes an important step towards distributed quantum networks.


title: Observation of dark state polariton collapses and revivals

abstract:
  By time-dependent variation of a control field, both coherent and single
photon states of light are stored in, and retrieved from, a cold atomic gas.
The efficiency of retrieval is studied as a function of the storage time in an
applied magnetic field. A series of collapses and revivals is observed, in very
good agreement with theoretical predictions. The observations are interpreted
in terms of the time evolution of the collective excitation of atomic spin wave
and light wave, known as the dark-state polariton.


title: Convolutional and tail-biting quantum error-correcting codes

abstract:
  Rate-(n-2)/n unrestricted and CSS-type quantum convolutional codes with up to
4096 states and minimum distances up to 10 are constructed as stabilizer codes
from classical self-orthogonal rate-1/n F_4-linear and binary linear
convolutional codes, respectively. These codes generally have higher rate and
less decoding complexity than comparable quantum block codes or previous
quantum convolutional codes. Rate-(n-2)/n block stabilizer codes with the same
rate and error-correction capability and essentially the same decoding
algorithms are derived from these convolutional codes via tail-biting.


title: Theory of dark-state polariton collapses and revivals

abstract:
  We investigate the dynamics of dark-state polaritons in an atomic ensemble
with ground-state degeneracy. A signal light pulse may be stored and retrieved
from the atomic sample by adiabatic variation of the amplitude of a control
field. During the storage process, a magnetic field causes rotation of the
atomic hyperfine coherences, leading to collapses and revivals of the
dark-state polariton number. These collapses and revivals should be observable
in measurements of the retrieved signal field, as a function of storage time
and magnetic field orientation.


title: Experimental investigation of planar ion traps

abstract:
  Chiaverini et al. [Quant. Inf. Comput. 5, 419 (2005)] recently suggested a
linear Paul trap geometry for ion trap quantum computation that places all of
the electrodes in a plane. Such planar ion traps are compatible with modern
semiconductor fabrication techniques and can be scaled to make compact, many
zone traps. In this paper we present an experimental realization of planar ion
traps using electrodes on a printed circuit board to trap linear chains of tens
of 0.44 micron diameter charged particles in a vacuum of 15 Pa (0.1 torr). With
these traps we address concerns about the low trap depth of planar ion traps
and develop control electrode layouts for moving ions between trap zones
without facing some of the technical difficulties involved in an atomic ion
trap experiment. Specifically, we use a trap with 36 zones (77 electrodes)
arranged in a cross to demonstrate loading from a traditional four rod linear
Paul trap, linear ion movement, splitting and joining of ion chains, and
movement of ions through intersections. We further propose an additional DC
biased electrode above the trap which increases the trap depth dramatically,
and a novel planar ion trap geometry that generates a two dimensional lattice
of point Paul traps.


title:
Synthesis of multi-qudit Hybrid and d-valued Quantum Logic Circuits by
  Decomposition

abstract:
  Recent research in generalizing quantum computation from 2-valued qudits to
d-valued qudits has shown practical advantages for scaling up a quantum
computer. A further generalization leads to quantum computing with hybrid
qudits where two or more qudits have different finite dimensions. Advantages of
hybrid and d-valued gates (circuits) and their physical realizations have been
studied in detail by Muthukrishnan and Stroud (Physical Review A, 052309,
2000), Daboul et al. (J. Phys. A: Math. Gen. 36 2525-2536, 2003), and Bartlett
et al (Physical Review A, Vol.65, 052316, 2002). In both cases, a quantum
computation is performed when a unitary evolution operator, acting as a quantum
logic gate, transforms the state of qudits in a quantum system. Unitary
operators can be represented by square unitary matrices. If the system consists
of a single qudit, then Tilma et al (J.Phys. A: Math. Gen. 35 (2002)
10467-10501) have shown that the unitary evolution matrix (gate) can be
synthesized in terms of its Euler angle parameterization. However, if the
quantum system consists of multiple qudits, then a gate may be synthesized by
matrix decomposition techniques such as QR factorization and the Cosine-sine
Decomposition (CSD). In this article, we present a CSD based synthesis method
for n qudit hybrid quantum gates, and as a consequence, derive a CSD based
synthesis method for n qudit gates where all the qudits have the same
dimension.


title: Zero-knowledge against quantum attacks

abstract:
  This paper proves that several interactive proof systems are zero-knowledge
against quantum attacks. This includes a few well-known classical
zero-knowledge proof systems as well as quantum interactive proof systems for
the complexity class HVQSZK, which comprises all problems having "honest
verifier" quantum statistical zero-knowledge proofs. It is also proved that
zero-knowledge proofs for every language in NP exist that are secure against
quantum attacks, assuming the existence of quantum computationally concealing
commitment schemes. Previously no non-trivial proof systems were known to be
zero-knowledge against quantum attacks, except in restricted settings such as
the honest-verifier and common reference string models. This paper therefore
establishes for the first time that true zero-knowledge is indeed possible in
the presence of quantum information and computation.


title: Exact solution of qubit decoherence models by a transfer matrix method

abstract:
  We present a new method for the solution of the behavior of an ensemble of
qubits in a random time-dependent external field. The forward evolution in time
is governed by a transfer matrix. The elements of this matrix determine the
various decoherence times. The method provides an exact solution in cases where
the noise is piecewise constant in time. We show that it applies, for example,
to a realistic model of decoherence of electron spins in semiconductors.
Results are obtained for the non-perturbative regimes of the models, and we see
a transition from weak relaxation to overdamped behavior as a function of noise
anisotropy.


title:
Theory of 'which path' dephasing in single electron interference due to
  trace in conductive environment

abstract:
  A single-electron two-path interference (Young) experiment is considered
theoretically. The decoherence of an electron wave packet due to the 'which
path' trace left in the conducting (metallic) plate placed under the electron
trajectories is calculated using the many-body quantum description of the
electron gas reservoir.


title: Thermalization of quantum systems by finite baths

abstract:
  We consider a discrete quantum system coupled to a finite bath, which may
consist of only one particle, in contrast to the standard baths which usually
consist of continua of oscillators, spins, etc. We find that such finite baths
may nevertheless equilibrate the system though not necessarily in the way
predicted by standard open system techniques. This behavior results regardless
of the initial state being correlated or not.


title:
Temporal aspects of one-dimensional completed scattering: An alternative
  view

abstract:
  A {\it completed} scattering of a particle on a static one-dimensional (1D)
potential barrier is a combined quantum process to consist from two elementary
sub-processes (transmission and reflection) evolved coherently at all stages of
scattering and macroscopically distinct at the final stage. The existing model
of the process is clearly inadequate to its nature: all one-particle
"observables" and "tunneling times", introduced as quantities to be common for
the sub-processes, cannot be experimentally measured and, consequently, have no
physical meaning; on the contrary, quantities introduced for either sub-process
have no basis, for the time evolution of either sub-process is unknown in this
model. We show that the wave function to describe a completed scattering can be
uniquely presented as the sum of two solutions to the Schr\"odinger equation,
which describe separately the sub-processes at all stages of scattering. For
symmetric potential barriers such solutions are found explicitly. For either
sub-process we define the time spent, on the average, by a particle in the
barrier region. We define it as the Larmor time. As it turned out, this time is
just Buttiker's dwell time averaged over the corresponding localized state.
Thus, firstly, we justify the known definition of the local dwell time
introduced by Hauge and co-workers as well by Leavens and Aers, for now this
time can be measured; secondly, we confirm that namely Buttiker's dwell time
gives the energy-distribution for the tunneling time; thirdly, we state that
all the definitions are valid only if they are based on the wave functions for
transmission and reflection found in our paper. Besides, we define the exact
and asymptotic group times to be auxiliary in timing the scattering process.


title: Quantum Weakly Nondeterministic Communication Complexity

abstract:
  We study the weakest model of quantum nondeterminism in which a classical
proof has to be checked with probability one by a quantum protocol. We show the
first separation between classical nondeterministic communication complexity
and this model of quantum nondeterministic communication complexity for a total
function. This separation is quadratic.


title:
Entanglement induced in spin-1/2 particles by a spin chain near its
  critical points

abstract:
  A relation between entanglement and criticality of spin chains is
established. The entanglement we exploit is shared between auxiliary particles,
which are isolated from each other, but are coupled to the same critical
spin-1/2 chain. We analytically evaluate the reduced density matrix, and
numerically show the entanglement of the auxiliary particles in the proximity
of the critical points of the spin chain. We find that the entanglement induced
by the spin-chain may reach one, and it can signal very well the critical
points of the chain. A physical understanding and experimental realization with
trapped ions are presented.


title: Controllable Entanglement of Lights in a Five-Level System

abstract:
  We analyze the nonlinear optical response of a five-level system under a
novel configuration of electro-magnetically induced transparency. We show that
a giant Kerr nonlinearity with a relatively large cross-phase modulation
coefficient that occurs in such system may be used to produce an efficient
photon-photon entanglement. We demonstrate that such photon-photon entanglement
is practically controllable and hence facilitates promising applications in
quantum information and computation.


title: An R||C_{max} Quantum Scheduling Algorithm

abstract:
  Grover's search algorithm can be applied to a wide range of problems; even
problems not generally regarded as searching problems, can be reformulated to
take advantage of quantum parallelism and entanglement, and lead to algorithms
which show a square root speedup over their classical counterparts.
  In this paper, we discuss a systematic way to formulate such problems and
give as an example a quantum scheduling algorithm for an $R||C_{max}$ problem.
$R||C_{max}$ is representative for a class of scheduling problems whose goal is
to find a schedule with the shortest completion time in an unrelated parallel
machine environment.
  Given a deadline, or a range of deadlines, the algorithm presented in this
paper allows us to determine if a solution to an $R||C_{max}$ problem with $N$
jobs and $M$ machines exists, and if so, it provides the schedule. The time
complexity of the quantum scheduling algorithm is $\mathcal{O}(\sqrt{M^N})$
while the complexity of its classical counterpart is $\mathcal{O}(M^N)$.


title: On Nonzero Kronecker Coefficients and their Consequences for Spectra

abstract:
  A triple of spectra (r^A, r^B, r^{AB}) is said to be admissible if there is a
density operator rho^{AB} with (Spec rho^A, Spec rho^B, Spec rho^{AB})=(r^A,
r^B, r^{AB}). How can we characterise such triples? It turns out that the
admissible spectral triples correspond to Young diagrams (mu, nu, lambda) with
nonzero Kronecker coefficient [M. Christandl and G. Mitchison, to appear in
Comm. Math. Phys., quant-ph/0409016; A. Klyachko, quant-ph/0409113]. This means
that the irreducible representation V_lambda is contained in the tensor product
of V_mu and V_nu. Here, we show that such triples form a finitely generated
semigroup, thereby resolving a conjecture of Klyachko. As a consequence we are
able to obtain stronger results than in [M. Ch. and G. M. op. cit.] and give a
complete information-theoretic proof of the correspondence between triples of
spectra and representations. Finally, we show that spectral triples form a
convex polytope.


title:
Single photon source characterization with a superconducting single
  photon detector

abstract:
  Superconducting single photon detectors (SSPD) based on nanopatterned niobium
nitride wires offer single photon counting at fast rates, low jitter, and low
dark counts, from visible wavelengths well into the infrared. We demonstrate
the first use of an SSPD, packaged in a commercial cryocooler, for single
photon source characterization. The source is an optically pumped,
microcavity-coupled InGaAs quantum dot, emitting single photons on demand at
902 nm. The SSPD replaces the second silicon Avalanche Photodiode (APD) in a
Hanbury-Brown Twiss interferometer measurement of the source second-order
correlation function, g (2) (tau). The detection efficiency of the
superconducting detector system is >2 % (coupling losses included). The SSPD
system electronics jitter is 170 ps, versus 550 ps for the APD unit, allowing
the source spontaneous emission lifetime to be measured with improved
resolution.


title: Delayed commutation in quantum computer networks

abstract:
  In the same way that classical computer networks connect and enhance the
capabilities of classical computers, quantum networks can combine the
advantages of quantum information and communications. We propose a
non-classical network element, a delayed commutation switch, that can solve the
problem of switching time in packet switching networks. With the help of some
local ancillary qubits and superdense codes we can route the information after
part of it has left the network node.


title:
Effects of detector efficiency mismatch on security of quantum
  cryptosystems

abstract:
  We suggest a type of attack on quantum cryptosystems that exploits variations
in detector efficiency as a function of a control parameter accessible to an
eavesdropper. With gated single-photon detectors, this control parameter can be
the timing of the incoming pulse. When the eavesdropper sends short pulses
using the appropriate timing so that the two gated detectors in Bob's setup
have different efficiencies, the security of quantum key distribution can be
compromised. Specifically, we show for the Bennett-Brassard 1984 (BB84)
protocol that if the efficiency mismatch between 0 and 1 detectors for some
value of the control parameter gets large enough (roughly 15:1 or larger), Eve
can construct a successful faked-states attack causing a quantum bit error rate
lower than 11%. We also derive a general security bound as a function of the
detector sensitivity mismatch for the BB84 protocol. Experimental data for two
different detectors are presented, and protection measures against this attack
are discussed.


title:
Dephasing due to Intermode Coupling in Superconducting Stripline
  Resonators

abstract:
  The nonlinearity exhibited by the kinetic inductance of a superconducting
stripline couples stripline resonator modes together in a manner suitable for
quantum non-demolition measurement of the number of photons in a given
resonator mode. Quantum non-demolition measurement is accomplished by
coherently driving another resonator mode, referred to as the detector mode,
and measuring its response. We show that the sensitivity of such a detection
scheme is directly related to the dephasing rate induced by such an intermode
coupling. We show that high sensitivity is expected when the detector mode is
driven into the nonlinear regime and operated close to a point where critical
slowing down occurs.


title:
Topological phase for entangled two-qubit states and the representation
  of the SO(3)group

abstract:
  We discuss the representation of the $SO(3)$ group by two-qubit maximally
entangled states (MES). We analyze the correspondence between $SO(3)$ and the
set of two-qubit MES which are experimentally realizable. As a result, we offer
a new interpretation of some recently proposed experiments based on MES.
Employing the tools of quantum optics we treat in terms of two-qubit MES some
classical experiments in neutron interferometry, which showed the $\pi $-phase
accrued by a spin-$1/2$ particle precessing in a magnetic field. By so doing,
we can analyze the extent to which the recently proposed experiments - and
future ones of the same sort - would involve essentially new physical aspects
as compared with those performed in the past. We argue that the proposed
experiments do extend the possibilities for displaying the double connectedness
of $SO(3)$, although for that to be the case it results necessary to map
elements of $SU(2)$ onto physical operations acting on two-level systems.


title: Dephasing in matter-wave interferometry

abstract:
  We review different attempts to show the decoherence process in
double-slit-like experiments both for charged particles (electrons) and neutral
particles with permanent dipole moments. Interference is studied when electrons
or atomic systems are coupled to classical or quantum electromagnetic fields.
The interaction between the particles and time-dependent fields induces a
time-varying Aharonov phase. Averaging over the phase generates a suppression
of fringe visibility in the interference pattern. We show that, for suitable
experimental conditions, the loss of contrast for dipoles can be almost as
large as the corresponding one for coherent electrons and therefore, be
observed. We analyze different trajectories in order to show the dependence of
the decoherence factor with the velocity of the particles.


title: Evolving Quantum Circuits using Genetic Algorithms

abstract: The article is taken out.


title: Temperature Dependence of the Casimir Effect

abstract:
  In view of the increasing accuracy of Casimir experiments, there is a need
for performing accurate theoretical calculations. Using accurate experimental
data for the permittivities we present, via the Lifshitz formula applied to the
standard Casimir setup with two parallel plates, accurate theoretical results
in case of the metals Au, Cu and Al. Both similar and dissimilar cases are
considered. Concentrating in particular on the finite temperature effect, we
show how the Casimir pressure varies with separation for three different
temperatures, T={1, 300, 350}K. The metal surfaces are taken to be perfectly
plane. The experimental data for the permittivities are generally yielding
results that are in good agreement with those calculated from the Drude
relation with finite relaxation frequency. We give the results in tabular form,
in order to facilitate the assessment of the temperature correction which is on
the 1% level. We emphasize two points: (i) The most promising route for a
definite experimental verification of the finite temperature correction appears
to be to concentrate on the case of large separations (optimum around 2
micrometres); and (ii) there is no conflict between the present kind of theory
and the Nernst theorem in thermodynamics.


title:
Generation of two-color polarization-entangled optical beams with a
  self-phase-locked two-crystal Optical Parametric Oscillator

abstract:
  A new device to generate polarization-entangled light in the continuous
variable regime is introduced. It consists of an Optical Parametric Oscillator
with two type-II phase-matched non-linear crystals orthogonally oriented,
associated with birefringent elements for adjustable linear coupling. We give
in this paper a theoretical study of its classical and quantum properties. It
is shown that two optical beams with adjustable frequencies and well-defined
polarization can be emitted. The Stokes parameters of the two beams are
entangled. The principal advantage of this setup is the possibility to directly
generate polarization entangled light without the need of mixing four modes on
beam splitters as required in current experimental setups. This device opens
new directions for the study of light-matter interfaces and generation of
multimode non-classical light and higher dimensional phase space.


title: Quantum Brachistochrone

abstract:
  We present a general framework for finding the time-optimal evolution and the
optimal Hamiltonian for a quantum system with a given set of initial and final
states. Our formulation is based on the variational principle and is analogous
to that for the brachistochrone in classical mechanics. We reduce the problem
to a formal equation for the Hamiltonian which depends on certain constraint
functions specifying the range of available Hamiltonians. For some simple
examples of the constraints, we explicitly find the optimal solutions.


title:
Impossibility of Exact Flipping of Three Arbitrary Quantum States Via
  Incomparability

abstract:
  We present here a scheme that relates seemingly two different kinds of
physical impossibilities of quantum information processing. We derive, exact
flipping of three arbitrary states not lying in one great circle is not
possible with certainty, by using the existence of incomparable states which
are not interconvertible deterministically by local operations and classical
communications. In contrast, considering the non-existence of exact universal
flipper, the incomparability of a pair of bipartite pure entangled states can
be established.


title: Synthesis of Ternary Quantum Logic Circuits by Decomposition

abstract:
  Recent research in multi-valued logic for quantum computing has shown
practical advantages for scaling up a quantum computer. Multivalued quantum
systems have also been used in the framework of quantum cryptography, and the
concept of a qudit cluster state has been proposed by generalizing the qubit
cluster state. An evolutionary algorithm based synthesizer for ternary quantum
circuits has recently been presented, as well as a synthesis method based on
matrix factorization.In this paper, a recursive synthesis method for ternary
quantum circuits based on the Cosine-Sine unitary matrix decomposition is
presented.


title:
Optimization of Quantum Information Processing Maximizing Mutual
  Information

abstract:
  A model of quantum noisy channel with input encoding by a classical random
vector is described. An equation of optimality is derived to determine a
complete set of wave functions describing quantum decodings based on
quasi-measurements maximizing the classical amount of transmitted information.
A solution of this equation is found for the Gaussian multimode case with input
Gaussian distribution. It is described by the overcomplete family of coherent
vectors describing an optimal quasimeasurement of the canonical annihilation
amplitudes in the output Hilbert space. It is found that the optimal decoding
in this case realizes the maximum amount I=Spln[1+S/(N+1)] of the classical
information as transmitted via the classical Gaussian channel with the
effective noise covariance matrix N+I. A physical realization of optimal
quasi-measurement based on an indirect (heterodyne) observation of the
canonical operators is suggested.


title:
On the Sufficient Optimality Condition for Quantum Information
  Processing

abstract:
  The necessary and sufficient conditions of optimality of the decoding of
quantum signals minimizing the Bayesian risk are generalized for the Shannon
mutual information criteria. It is shown that for a linear channel with
Gaussian boson noise these conditions are satisfied by coherent
quasi-measurement of the canonical annihilation amplitudes in the received
superposition.


title: Continuous-variable optical quantum state tomography

abstract:
  This review covers latest developments in continuous-variable quantum-state
tomography of optical fields and photons, placing a special accent on its
practical aspects and applications in quantum information technology. Optical
homodyne tomography is reviewed as a method of reconstructing the state of
light in a given optical mode. A range of relevant practical topics are
discussed, such as state-reconstruction algorithms (with emphasis on the
maximum-likelihood technique), the technology of time-domain homodyne
detection, mode matching issues, and engineering of complex quantum states of
light. The paper also surveys quantum-state tomography for the transverse
spatial state (spatial mode) of the field in the special case of fields
containing precisely one photon.


title: Scheme for generating the cluster states via atomic ensembles

abstract:
  A scheme for generating the cluster states via atomic ensembles is proposed.
The scheme has inherent fault tolerance function and is robust to realistic
noise and imperfections. All the facilities used in our scheme are well within
the current technology.


title:
Exactly solvable quantum state reduction models with time-dependent
  coupling

abstract:
  A closed-form solution to the energy-based stochastic Schrodinger equation
with a time-dependent coupling is obtained. The solution is algebraic in
character, and is expressed directly in terms of independent random data. The
data consist of (i) a random variable H which has the distribution P(H=E_i) =
pi_i, where pi_i is the transition probability from the initial state to the
Luders state with energy E_i; and (ii) an independent P-Brownian motion, where
P is the physical probability measure associated with the dynamics of the
reduction process. When the coupling is time-independent, it is known that
state reduction occurs asymptotically--that is to say, over an infinite time
horizon. In the case of a time-dependent coupling, we show that if the
magnitude of the coupling decreases sufficiently rapidly, then the energy
variance will be reduced under the dynamics, but the state need not reach an
energy eigenstate. This situation corresponds to the case of a ``partial'' or
``incomplete'' measurement of the energy. We also construct an example of a
model where the opposite situation prevails, in which complete state reduction
is achieved after the passage of a finite period of time.


title: Entanglement swapping, light cones and elements of reality

abstract:
  Recently, a number of two-participant all-versus-nothing Bell experiments
have been proposed. Here, we give local realistic explanations for these
experiments. More precisely, we examine the scenario where a participant swaps
his entanglement with two other participants and then is removed from the
experiment; we also examine the scenario where two particles are in the same
light cone, i.e. belong to a single participant. Our conclusion is that, in
both cases, the proposed experiments are not convincing proofs against local
realism.


title:
Correlated observables in single-particle systems and field theoretic
  interpretations

abstract:
  Bell-type experiments that test correlated observables typically involve
measurements of spin or polarization on multi-particle systems in singlet
states. These observables are all non-commuting and satisfy an uncertainty
relation. Theoretically, the non-commuting nature should be independent of
whether the singlet state consists of multiple particles or a single particle.
Recent experiments in single neutron interferometry have in fact demonstrated
this. In addition, if Bell-type inequalities can be found for experiments
involving spin and polarization, the same should be true for experiments
involving other non-commuting observables such as position and momentum as in
the original EPR paper. As such, an experiment is proposed to measure (quantum
mechanically) position and momentum for a single oscillator as a means for
deriving a Bell-type inequality for these correlated observables. The
experiment, if realizable, would shed light on the basic nature of matter,
perhaps pointing to some form of self-entanglement, and would also help to
further elucidate a possible mechanism behind the Heisenberg uncertainty
principle. Violation of these inequalities would, in fact, offer yet another
confirmation of the principle.


title:
Quantum efficiency of single-photon sources in the cavity-QED
  strong-coupling regime

abstract:
  We calculate the integrated-pulse quantum efficiency of single-photon sources
in the cavity quantum electrodynamics (QED) strong-coupling regime. An
analytical expression for the quantum efficiency is obtained in the
Weisskopf-Wigner approximation. Optimal conditions for a high quantum
efficiency and a temporally localized photon emission rate are examined. We
show the condition under which the earlier result of Law and Kimble [J. Mod.
Opt. 44, 2067 (1997)] can be used as the first approximation to our result.


title: Scheme for sharing classical information via tripartite entangled states

abstract:
  We investigate schemes for quantum secret sharing and quantum dense coding
via tripartite entangled states. We present a scheme for sharing classical
information via entanglement swapping using two tripartite entangled GHZ
states. In order to throw light upon the security affairs of the quantum dense
coding protocol, we also suggest a secure quantum dense coding scheme via W
state in analogy with the theory of sharing information among involved users.


title:
Secure quantum dense coding via tripartite entangled GHZ state in cavity
  QED

abstract:
  We investigate economic protocol to securely encoding classical information
among three users via entangled GHZ states. We implement the scheme in cavity
QED with atomic qubits where the atoms interact simultaneously with a highly
detuned cavity mode with the assistance of a classical field. The scheme is
insensitive to the cavity decay and the thermal field, thus based on cavity QED
techniques presently it might be realizable.


title: Tunneling in a magnetic field

abstract:
  Quantum tunneling between two potential wells in a magnetic field can be
strongly increased when the potential barrier varies in the direction
perpendicular to the line connecting the two wells and remains constant along
this line. An oscillatory structure of the wave function is formed in the
direction joining the wells. The resulting motion can be coherent like motion
in a conventional narrow band periodic structure. A particle penetrates the
barrier over a long distance which strongly contrasts to WKB-like tunneling.
The whole problem is stationary. A not very small tunneling transparency can be
set between two quantum wires with real physical parameters and separated by a
long potential barrier. The phenomenon is connected to Euclidean resonance.


title: An Optimal Photon Counting Polarimeter

abstract:
  We present experimental results on a method to perform polarimetry on
ensembles of single photons. Our setup is based on a measurement method known
to be optimal for estimating the state of two level systems. The setup has no
moving parts and is sensitive to weak sources (emitting single photons) of
light as it relies on photon counting and has potential applications in both
classical polarization measurements and quantum communication scenarios. In our
implementation, we are able to reconstruct the Stokes parameters of pure
polarization states with an average fidelity of 99.9%.


title: Strong Fourier Sampling Fails over $G^n$

abstract:
  We present a negative result regarding the hidden subgroup problem on the
powers $G^n$ of a fixed group $G$. Under a condition on the base group $G$, we
prove that strong Fourier sampling cannot distinguish some subgroups of $G^n$.
Since strong sampling is in fact the optimal measurement on a coset state, this
shows that we have no hope of efficiently solving the hidden subgroup problem
over these groups with separable measurements on coset states (that is, using
any polynomial number of single-register coset state experiments). Base groups
satisfying our condition include all nonabelian simple groups. We apply our
results to show that there exist uniform families of nilpotent groups whose
normal series factors have constant size and yet are immune to strong Fourier
sampling.


title: Towards quantum mechanics from a theory of experiments

abstract:
  Essential elements of quantum theory are derived from an epistemic point of
view, i.e., the viewpoint that thetheory has to do with what can be said about
nature. This gives a relationship to statistical reasoning and to other areas
of modelling and decision making. In particular, a quantum state can be defined
from an epistemic point of view to consist of two elements: A (maximal)
question about the value of some parameter together with the answer to that
question. Quantization itself can be approached from the point of view of model
reduction under symmetry.


title: Robust implementations of Quantum Repeaters

abstract:
  We show how to efficiently exploit decoherence free subspaces (DFSs), which
are immune to collective noise, for realizing quantum repeaters with long lived
quantum memories. Our setup consists of an assembly of simple modules and we
show how to implement them in systems of cold, neutral atoms in arrays of
dipole traps. We develop methods for realizing robust gate operations on qubits
encoded in a DFS using collisional interactions between the atoms. We also give
a detailed analysis of the performance and stability of all required gate
operations and emphasize that all modules can be realized with current or near
future experimental technology.


title: Casimir interaction between normal or superfluid grains in the Fermi sea

abstract:
  We report on a new force that acts on cavities (literally empty regions of
space) when they are immersed in a background of non-interacting fermionic
matter fields. The interaction follows from the obstructions to the (quantum
mechanical) motions of the fermions caused by the presence of bubbles or other
(heavy) particles in the Fermi sea, as, for example, nuclei in the neutron sea
in the inner crust of a neutron star or superfluid grains in a normal Fermi
liquid. The effect resembles the traditional Casimir interaction between
metallic mirrors in the vacuum. However, the fluctuating electromagnetic fields
are replaced by fermionic matter fields. We show that the fermionic Casimir
problem for a system of spherical cavities can be solved exactly, since the
calculation can be mapped onto a quantum mechanical billiard problem of a
point-particle scattered off a finite number of non-overlapping spheres or
disks. Finally we generalize the map method to other Casimir systems,
especially to the case of a fluctuating scalar field between two spheres or a
sphere and a plate under Dirichlet boundary conditions.

categories: quant-ph cond-mat.stat-mech nlin.CD nucl-th


title: Novel cloning machine with supplementary information

abstract:
  Probabilistic cloning was first proposed by Duan and Guo. Then Pati
established a novel cloning machine (NCM) for copying superposition of multiple
clones simultaneously. In this paper, we deal with the novel cloning machine
with supplementary information (NCMSI). For the case of cloning two states, we
demonstrate that the optimal efficiency of the NCMSI in which the original
party and the supplementary party can perform quantum communication equals that
achieved by a two-step cloning protocol wherein classical communication is only
allowed between the original and the supplementary parties. From this
equivalence it follows that NCMSI may increase the success probabilities for
copying. Also, an upper bound on the unambiguous discrimination of two
nonorthogonal pure product states is derived. Our investigation generalizes and
completes the results in the literature.


title: Phase Sensitivity of a Mach-Zehnder Interferometer

abstract:
  The best performance of a Mach-Zehnder interferometer is achieved with the
input state |N_T/2 + 1>|N_T/2-1 > + |N_T/2 - 1>|N_T/2+1>, being N_T the total
number of atoms/photons. This gives: i) a phase-shift error confidence
C_{68%}=2.67/N_T with ii) a single interferometric measurement. Different input
quantum states can achieve the Heisenberg scaling ~ 1/N_T but with higher
prefactors and at the price of a statistical analysis of two or more
independent measurements.


title:
A Dual Observer Information Exchange Theory of Measurement of Quantum
  Mechanics

abstract: The article is taken out.


title: A Study on the basics of Quantum Computing

abstract: The article is taken out.


title: Quantum Gauss Jordan Elimination

abstract:
  In this paper we construct the Quantum Gau\ss Jordan Elimination (QGJE)
Algorithm and estimate the complexity time of computation of Reduced Row
Echelon Form (RREF) of an $N\times N$ matrix using QGJE procedure. The main
theorem asserts that QGJE has computation time of order $2^{N/2}$.


title: Accounting Principles are Simulated on Quantum Computers

abstract:
  The paper is devoted to a new idea of simulation of accounting by quantum
computing. We expose the actual accounting principles in a pure mathematics
language. After that we simulated the accounting principles on quantum
computers. We show that all arbitrary accounting actions are exhausted by the
described basic actions. The main problem of accounting are reduced to some
system of linear equations in the economic model of Leontief. In this
simulation we use our constructed quantum Gau\ss-Jordan Elimination to solve
the problem and the time of quantum computing is some square root order faster
than the time in classical computing.


title: Casimir torque

abstract:
  We develop a formalism for the calculation of the flow of angular momentum
carried by the fluctuating electromagnetic field within a cavity bounded by two
flat anisotropic materials. By generalizing a procedure employed recently for
the calculation of the Casimir force between arbitrary materials, we obtain an
expression for the torque between anisotropic plates in terms of their
reflection amplitude matrices. We evaluate the torque in 1D for ideal and
realistic model materials.


title: Fault-Tolerant Quantum Computation for Local Leakage Faults

abstract:
  We provide a rigorous analysis of fault-tolerant quantum computation in the
presence of local leakage faults. We show that one can systematically deal with
leakage by using appropriate leakage-reduction units such as quantum
teleportation. The leakage noise is described by a Hamiltonian and the noise is
treated coherently, similar to general non-Markovian noise analyzed in Refs.
quant-ph/0402104 and quant-ph/0504218. We describe ways to limit the use of
leakage-reduction units while keeping the quantum circuits fault-tolerant and
we also discuss how leakage reduction by teleportation is naturally achieved in
measurement-based computation.


title: Casimir-like tunneling-induced electronic forces

abstract:
  We study the quantum forces that act between two nearby conductors due to
electronic tunneling. We derive an expression for these forces by calculating
the flux of momentum arising from the overlap of evanescent electronic fields.
Our result is written in terms of the electronic reflection amplitudes of the
conductors and it has the same structure as Lifshitz's formula for the
electromagnetically mediated Casimir forces. We evaluate the tunneling force
between two semiinfinite conductors and between two thin films separated by an
insulating gap. We discuss some applications of our results.


title: Maps for Lorentz transformations of spin

abstract:
  Lorentz transformations of spin density matrices for a particle with positive
mass and spin 1/2 are described by maps of the kind used in open quantum
dynamics. They show how the Lorentz transformations of the spin depend on the
momentum. Since the spin and momentum generally are entangled, the maps
generally are not completely positive and act in limited domains. States with
two momentum values are considered, so the maps are for the spin qubit
entangled with the qubit made from the two momentum values, and results from
the open quantum dynamics of two coupled qubits can be applied. Inverse maps
are used to show that every Lorentz transformation completely removes the spin
polarization, and so completely removes the information, from a number of spin
density matrices. The size of the spin polarization that is removed is
calculated for particular cases.


title: Variational approach to dequantization

abstract:
  We present a dequantization procedure based on a variational approach whereby
quantum fluctuations latent in the quantum momentum are suppressed. This is
done by adding generic local deformations to the quantum momentum operator
which give rise to a deformed kinetic term quantifying the amount of
``fuzzyness'' caused by such fluctuations. Considered as a functional of such
deformations, the deformed kinetic term is shown to possess a unique minimum
which is seen to be the classical kinetic energy. Furthermore, we show that
extremization of the associated deformed action functional introduces an
essential nonlinearity to the resulting field equations which are seen to be
the classical Hamilton-Jacobi and continuity equations. Thus, a variational
procedure determines the particular deformation that has the effect of
suppressing the quantum fluctuations, resulting in dequantization of the
system.


title: Simulating quantum computation by contracting tensor networks

abstract:
  The treewidth of a graph is a useful combinatorial measure of how close the
graph is to a tree. We prove that a quantum circuit with $T$ gates whose
underlying graph has treewidth $d$ can be simulated deterministically in
$T^{O(1)}\exp[O(d)]$ time, which, in particular, is polynomial in $T$ if
$d=O(\log T)$. Among many implications, we show efficient simulations for
log-depth circuits whose gates apply to nearby qubits only, a natural
constraint satisfied by most physical implementations. We also show that
one-way quantum computation of Raussendorf and Briegel (Physical Review
Letters, 86:5188--5191, 2001), a universal quantum computation scheme with
promising physical implementations, can be efficiently simulated by a
randomized algorithm if its quantum resource is derived from a small-treewidth
graph.


title:
Classical simulation of quantum many-body systems with a tree tensor
  network

abstract:
  We show how to efficiently simulate a quantum many-body system with tree
structure when its entanglement is bounded for any bipartite split along an
edge of the tree. This is achieved by expanding the {\em time-evolving block
decimation} simulation algorithm for time evolution from a one dimensional
lattice to a tree graph, while replacing a {\em matrix product state} with a
{\em tree tensor network}. As an application, we show that any one-way quantum
computation on a tree graph can be efficiently simulated with a classical
computer.


title:
Tensor Norms and the Classical Communication Complexity of Nonlocal
  Quantum Measurement

abstract:
  We initiate the study of quantifying nonlocalness of a bipartite measurement
by the minimum amount of classical communication required to simulate the
measurement. We derive general upper bounds, which are expressed in terms of
certain tensor norms of the measurement operator. As applications, we show that
(a) If the amount of communication is constant, quantum and classical
communication protocols with unlimited amount of shared entanglement or shared
randomness compute the same set of functions; (b) A local hidden variable model
needs only a constant amount of communication to create, within an arbitrarily
small statistical distance, a distribution resulted from local measurements of
an entangled quantum state, as long as the number of measurement outcomes is
constant.


title:
Eavesdropping on Blind Quantum Key Distribution through a Labeling
  Attack

abstract:
  I present an eavesdropping on the protocol proposed by W.-H. Kye, et al.
[Phys. Rev. Lett. 95, 040501 (2005)]. I show how an undetectable Eve can steal
the whole information by labeling and then measuring the photons prepared by
the user Alice.


title:
Coherent-Squeezed State Representation of Travelling General Gaussian
  Wave Packets

abstract:
  Using the time-dependent annihilation and creation operators, the invariant
operators, for a free mass and an oscillator, we find the coherent-squeezed
state representation of a travelling general Gaussian wave packet with initial
expectation values, $x_0$ and $p_0$, of the position and momentum and
variances, $\Delta x_0$ and $\Delta p_0$. The initial general Gaussian wave
packet takes, up to a normalization factor, the form $e^{i p_0 x/\hbar} e^{- (1
\mp i \delta) (x - x_0)^2 / 4 (\Delta x_0)^2}$, where $\delta = \sqrt{(2\Delta
x_0 \Delta p_0/\hbar)^2 -1}$ denotes a measure of deviation from the minimum
uncertainty or the initial position-momentum correlation $\delta = 2\Delta
(xp)_0 / \hbar$. The travelling Gaussian wave packet takes, up to a
time-dependent phase and normalization factor, the form $e^{i p_c x/\hbar} e^{-
(1 - 2 i \Delta (xp)_t/\hbar) (x - x_c)^2 / 4 (\Delta x_t)^2}$ and the centroid
follows the the classical trajectory with $x_c(t)$ and $p_c(t)$. The position
variance is found to have additionally a linearly time-dependent term
proportional to $\delta$ with both positive and negative signs.


title:
Quantum mechanics as an asymptotic projection of statistical mechanics
  of classical fields: derivation of Schr\"{o}dinger's, Heisenberg's and von
  Neumann's equations

abstract:
  We show that QM can be represented as a natural projection of a classical
statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real
Hilbert space. Statistical states are given by Gaussian measures on $\Omega$
having zero mean value and dispersion of very small magnitude $\alpha$ (which
is considered as a small parameter of the model). Such statistical states can
be interpreted as fluctuations of the background field, cf. with SED and
Nelson's mechanics. Physical variables (e.g., energy) are given by maps $f:
\Omega \to {\bf R}$ (functions of classical fields). The conventional quantum
representation of our prequantum classical statistical model is constructed on
the basis of the Taylor expansion (up to the terms of the second order at the
vacuum field point $\psi\_{\rm{vacuum}}\equiv 0)$ of variables $f: \Omega \to
{\bf R}$ with respect to the small parameter $\sqrt{\alpha}.$ The complex
structure of QM is induced by the symplectic structure on the
infinite-dimensional phase space $\Omega.$ A Gaussian measure (statistical
state) is represented in QM by its covariation operator. Equations of
Schr\"{o}dinger, Heisenberg and von Neumann are images of Hamiltonian dynamics
on $\Omega.$ The main experimental prediction of our prequantum model is that
experimental statistical averages can deviate from ones given by QM.


title:
Self-interference of a single Bose-Einstein condensate due to boundary
  effects

abstract:
  A simple model wavefunction, consisting of a linear combination of two
free-particle Gaussians, describes many of the observed features seen in the
interactions of two isolated Bose-Einstein condensates as they expand, overlap,
and interfere. We show that a simple extension of this idea can be used to
predict the qualitative time-development of a single expanding BEC condensate
produced near an infinite wall boundary, giving similar interference phenomena.
We also briefly discuss other possible time-dependent behaviors of single BEC
condensates in restricted geometries,such as wave packet revivals.


title: Non-Hamiltonian Commutators in Quantum Mechanics

abstract:
  The symplectic structure of quantum commutators is first unveiled and then
exploited to introduce generalized non-Hamiltonian brackets in quantum
mechanics. It is easily recognized that quantum-classical systems are described
by a particular realization of such a bracket. In light of previous work, this
introduces a unified approach to classical and quantum-classical
non-Hamiltonian dynamics. In order to illustrate the use of non-Hamiltonian
commutators, it is shown how to define thermodynamic constraints in
quantum-classical systems. In particular, quantum-classical Nos\'e-Hoover
equations of motion and the associated stationary density matrix are derived.
The non-Hamiltonian commutators for both Nos\'e-Hoover chains and
Nos\'e-Andersen (constant-pressure constant temperature) dynamics are also
given. Perspectives of the formalism are discussed.


title: Generalized Teleportation Protocol

abstract:
  A generalized teleportation protocol (GTP) for N qubits is presented, where
the teleportation channels are non-maximally entangled and all the free
parameters of the protocol are considered: Alice's measurement basis, her sets
of acceptable results, and Bob's unitary operations. The full range of Fidelity
(F) of the teleported state and the Probability of Success (P_{suc}) to obtain
a given fidelity are achieved by changing these free parameters. A channel
efficiency bound is found, where one can determine how to divide it between F
and P_{suc}. A one qubit formulation is presented and then expanded to N
qubits. A proposed experimental setup that implements the GTP is given using
linear optics.


title: Bound states for one-electron atoms in higher dimensions

abstract:
  We study the Schrodinger equation for one-electron atoms in space-times with
d >= 4 spatial dimensions where the Gauss law is assumed to be valid. It is
shown that there are no normalizable wave functions corresponding to bound
states. The consistency with the classical limit is discussed.


title:
Memory Efficient Quantum Circuit Simulator Based on Linked List
  Architecture

abstract:
  In this paper, we will introduce the quantum circuit simulator we developed
in C++ environment. We devise a novel method for efficient memory handling
using linked list structures that enables us to simulate a quantum circuit of
up to 20 qubits in a reasonable time. Our package can simulate the activity of
any quantum circuit constructed by the user; it will also be used to understand
the robustness of certain quantum algorithms such as Simons and Shors.


title:
Entanglement Degree of Parasupersymmetric Coherent States of Harmonic
  Oscillator

abstract:
  We study the boson-parafermion entanglement of the parasupersymmetric
coherent states of the harmonic oscillator and derive the degree of
entanglement in terms of the concurrence. The conditions for obtaining the
maximal entanglement is also examined, and it is shown that in the usual
supersymmetry situation we can obtain maximally entangled Bell states.


title: Environment induced incoherent controllability

abstract:
  We prove that the environment induced entanglement between two non
interacting, two-dimensional quantum systems S and P can be used to control the
dynamics of S by means of the initial state of P. Using a simple, exactly
solvable model, we show that both accessibility and controllability of S can be
achieved under suitable conditions on the interaction of S and P with the
environment.


title: Uncommon information (the cost of exchanging a quantum state)

abstract:
  If two parties share an unknown quantum state, one can ask how much quantum
communication is needed for party A to send her share to party B. Recently, it
was found that the number of qubits which should be sent is given by the
conditional entropy. This quantifies the notion of partial information, and it
can even be negative. Here, we not only demand that A send her state to B, but
additionally, B should send his state to A. Paradoxically, we find that
requiring that the parties perform this additional task can lower the amount of
quantum communication required. This primitive, which we call quantum state
exchange, can be used to quantify the notion of uncommon information, since the
two parties only need to send each other the parts of their state they don't
hold in common. In the classical case, the concept of uncommon information
follows trivially from the concept of partial information. We find that for
quantum states, this is not so. We prove upper and lower bounds for the
uncommon information and find optimal protocols for several classes of states.


title:
Optical generation of hybrid entangled state via entangling
  single-photon-added coherent state

abstract:
  We propose a feasible scheme to realize the optical entanglement of
single-photon-added coherent state (SPACS) and show that, besides the Sanders
entangled coherent state, the entangled SPACS also leads to new forms of hybrid
entanglement of quantum Fock state and classical coherent state. We probe the
essential difference of two types of hybrid entangled state (HES). This HES
provides a novel link between the discrete- and the continuous-variable
entanglement in a natural way.


title: Information free quantum bus for generating stabiliser states

abstract:
  Efficient generation of spatially delocalised entangled states is at the
heart of quantum information science. Generally flying qubits are proposed for
long range entangling interactions, however here we introduce a bus-mediated
alternative for this task. Our scheme permits efficient and flexible generation
of deterministic two-qubit operator measurements and has links to the important
concepts of mode-entanglement and repeat-until-success protocols. Importantly,
unlike flying qubit protocols, our bus particle never contains information
about the individual quantum states of the particles, hence is
information-free.


title: Coupled-channel version of PT-symmetric square well

abstract:
  Coupled pair of PT-symmetric square wells is studied as a prototype of a
quantum system characterized by two manifestly non-Hermitian commuting
observables. We demonstrate that there exists a domain of couplings where both
the respective sets of eigenvalues (viz., energies and spin projections) remain
real and where the model acquires a consistent probabilistic interpretation
mediated by an `ad hoc' scalar product.


title:
Relation between Dimension and Angular Momentum for Radially Symmetric
  Potential in $N$-dimensional Space

abstract:
  It is proved that when solving Schroedinger equations for radially symmetric
potentials the effect of higher dimensions on the radial wave function is
equivalent to the effect of higher angular momenta in lower dimensional cases.
This result is applied to giving solutions for several radially symmetric
potentials in N-dimension.


title: Effective magnetic fields induced by EIT in ultra-cold atomic gases

abstract:
  We study the influence of two resonant laser beams (to be referred to as the
control and probe beams) on the centre of mass motion of ultra-cold atoms
characterised by three energy levels of the Lambda-type. The laser beams being
in the Electromagnetically Induced Transparency (EIT) configuration drive the
atoms to their dark states. We impose the adiabatic approximation and obtain an
effective equation of motion for the dark state atoms. The equation contains a
vector potential type interaction as well as an effective trapping potential.
We concentrate on the situation where the control and probe beams are
co-propagating and have Orbital Angular Momenta (OAM). The effective magnetic
field is then oriented along the propagation direction of the control and probe
beams. Its spatial profile can be shaped by choosing proper laser beams. We
analyse several situations where the effective magnetic field exhibits a radial
dependence. In particular we study effective magnetic fields induced by Bessel
beams, and demonstrate how to generate a constant effective magnetic field for
a ring geometry of the atomic trap. We also discuss a possibility to create an
effective field of a magnetic monopole.


title: Quantum cloning

abstract:
  The impossibility of perfectly copying (or cloning) an arbitrary quantum
state is one of the basic rules governing the physics of quantum systems. The
processes that perform the optimal approximate cloning have been found in many
cases. These "quantum cloning machines" are important tools for studying a wide
variety of tasks, e.g. state estimation and eavesdropping on quantum
cryptography. This paper provides a comprehensive review of quantum cloning
machines (both for discrete-dimensional and for continuous-variable quantum
systems); in addition, it presents the role of cloning in quantum cryptography,
the link between optimal cloning and light amplification via stimulated
emission, and the experimental demonstrations of optimal quantum cloning.


title: Phase time for a tunneling particle

abstract:
  We study the nature of tunneling phase time for various quantum mechanical
structures such as networks and rings having potential barriers in their arms.
We find the generic presence of Hartman effect, with superluminal velocities as
a consequence, in these systems. In quantum networks it is possible to control
the `super arrival' time in one of the arms by changing the parameters on
another arm which is spatially separated from it. This is yet another quantum
nonlocal effect. Negative time delays (time advancement) and `ultra Hartman
effect' with negative saturation times have been observed in some parameter
regimes. In presence and absence of Aharonov-Bohm (AB) flux quantum rings show
Hartman effect. We obtain the analytical expression for the saturated phase
time. In the opaque barrier regime this is independent of even the AB flux
thereby generalizing the Hartman effect. We also briefly discuss the concept of
"space collapse or space destroyer" by introducing a free space in between two
barriers covering the ring. Further we show in presence of absorption the
reflection phase time exhibits Hartman effect in contrast to the transmission
phase time.


title: Entropic bounds and continual measurements

abstract:
  Some bounds on the entropic informational quantities related to a quantum
continual measurement are obtained and the time dependencies of these
quantities are studied.


title:
Time-energy and time-entropy uncertainty relations in dissipative
  quantum dynamics

abstract:
  We derive exact relations and general inequalities that extend the usual
time-energy uncertainty relations from the domain of unitary Hamiltonian
dynamics to that of dissipative dynamics as described by a broad class of
linear and nonlinear evolution equations for the density operator. For
non-dissipative dynamics, by using the Schroedinger inequality instead of the
Heisenberg-Robertson inequality, we obtain a general exact time-energy
uncertainty relation which is sharper than the usual Mandelstam-Tamm-Messiah
relation $\tau_F\Delta_H\ge \hbar/2$. For simultaneous unitary/dissipative
dynamics, the usual time-energy uncertainty relation is replaced by a less
restrictive relation that depends on the characteristic time of dissipation,
$\tau$, and the uncertainty associated with the generalized nonequilibrium
Massieu-function operator which defines the structure of the dissipative part
of the assumed class of evolution equations. Within the steepest-entropy-ascent
dissipative quantum dynamics of an isolated system introduced earlier by this
author, we obtain the interesting time-energy and time-entropy uncertainty
relation $(2\tau_F\Delta_H/ \hbar)^2+ (\tau_F\Delta_S/k_B\tau)^2 \ge 1$. We
illustrate this result and various other inequalities by means of numerical
simulations.


title:
Quantum secure direct communication without using perfect quantum
  channel

abstract:
  Most of the quantum secure direct communication protocol needs a
pre-established secure quantum channel. Only after insuring the security of
quantum channel, could the sender encode the secret message and send them to
the receiver through the secure channel. In this paper, we present a quantum
secure direct communication protocol using Einstein-Podolsky-Rosen pairs. It is
not necessary for the present protocol to insure the security of quantum
channel before transmitting the secret message. In the present protocol, all
Einstein-Podolsky-Rosen pairs are used to transmit the secret message except
those chosen for eavesdropping check.


title:
The possibility of absolute calibration of analog detectors by using
  parametric down-conversion: a systematical study

abstract:
  Accurate calibration of photodetectors both in analog and in photon-counting
regime is fundamental for various scientific applications, which range from
"traditional" quantum optics to the studies on foundations of quantum
mechanics, quantum cryptography, quantum computation, etc. In this paper we
systematically study the possibility of the absolute calibration of analog
photo-detectors based on the properties of parametric amplifiers. Our results
show that such a method can be effectively developed with interesting possible
metrological applications.


title: Qubit rotation and Berry Phase

abstract:
  A quantized fermion can be represented by a scalar particle encircling a
magnetic flux line. It has the spinor structure which can be constructed from
quantum gates and qubits. We have studied here the role of Berry phase in
removing dynamical phase during one qubit rotation of a quantized fermion. The
entanglement of two qubit inserting spin-echo to one of them results the change
of Berry phase that can be considered as a measure of entanglement. Some effort
is given to study the effect of noise on the Berry phase of spinor and their
entangled states.


title: A Simple Path Integration For the Time Dependent Oscillator

abstract:
  Feynman propagator is calculated for the time dependent harmonic oscillator
by converting the problem into a free particle motion


title: A Polynomial Quantum Algorithm for Approximating the Jones Polynomial

abstract:
  The Jones polynomial, discovered in 1984, is an important knot invariant in
topology. Among its many connections to various mathematical and physical
areas, it is known (due to Witten) to be intimately connected to Topological
Quantum Field Theory (TQFT). The works of Freedman, Kitaev, Larsen and Wang
provide an efficient simulation of TQFT by a quantum computer, and vice versa.
These results implicitly imply the existence of an efficient quantum algorithm
that provides a certain additive approximation of the Jones polynomial at the
fifth root of unity, e^{2\pi i/5}, and moreover, that this problem is
BQP-complete. Unfortunately, this important algorithm was never explicitly
formulated. Moreover, the results mentioned are heavily based on TQFT, which
makes the algorithm essentially inaccessible to computer scientists.
  We provide an explicit and simple polynomial quantum algorithm to approximate
the Jones polynomial of an n-strands braid with m crossings at any primitive
root of unity e^{2\pi i/k}, where the running time of the algorithm is
polynomial in m,n and k. Our algorithm is based, rather than on TQFT, on well
known mathematical results. By the results of Freedman et. al., our algorithm
solves a BQP complete problem.
  The algorithm we provide exhibits a structure which we hope is generalizable
to other quantum algorithmic problems. Candidates of particular interest are
the approximations of other #P-hard problems, most notably, the partition
function of the Potts model, a model which is known to be tightly connected to
the Jones polynomial.


title: Quantum Solution to the Extended Newcomb's Paradox

abstract:
  We regard the Newcomb's Paradox as a reduction of the Prisoner's Dilemma and
search for the considerable quantum solution. The all known classical solutions
to the Newcomb's problem always imply that human has freewill and is due to the
unfair set-up(including strategies)of the Newcomb's Problem. In this reason, we
here substitute the asymmetric payoff matrix to the general form of the payoff
matrix M and consider both of them use the same quantum strategy. As a result
we obtained the fair Nash equilibrium, which is better than the case using
classical strategies. This means that whether the supernatural being has the
precognition or not depends only on the choice of strategy.


title: Quantum error correction via robust probe modes

abstract:
  We propose a new scheme for quantum error correction using robust continuous
variable probe modes, rather than fragile ancilla qubits, to detect errors
without destroying data qubits. The use of such probe modes reduces the
required number of expensive qubits in error correction and allows efficient
encoding, error detection and error correction. Moreover, the elimination of
the need for direct qubit interactions significantly simplifies the
construction of quantum circuits. We will illustrate how the approach
implements three existing quantum error correcting codes: the 3-qubit bit-flip
(phase-flip) code, the Shor code, and an erasure code.


title: Modeling photo-detectors in quantum optics

abstract:
  Photo-detection plays a fundamental role in experimental quantum optics and
is of particular importance in the emerging field of linear optics quantum
computing. Present theoretical treatment of photo-detectors is highly idealized
and fails to consider many important physical effects. We present a physically
motivated model for photo-detectors which accommodates for the effects of
finite resolution, bandwidth and efficiency, as well as dark-counts and
dead-time. We apply our model to two simple well known applications, which
illustrates the significance of these characteristics.


title: Robust Logic Gates and Realistic Quantum Computation

abstract:
  The composite rotation approach has been used to develop a range of robust
quantum logic gates, including single qubit gates and two qubit gates, which
are resistant to systematic errors in their implementation. Single qubit gates
based on the BB1 family of composite rotations have been experimentally
demonstrated in a variety of systems, but little study has been made of their
application in extended computations, and there has been no experimental study
of the corresponding robust two qubit gates to date. Here we describe an
application of robust gates to Nuclear Magnetic Resonance (NMR) studies of
approximate quantum counting. We find that the BB1 family of robust gates is
indeed useful, but that the related NB1, PB1, B4 and P4 families of tailored
logic gates are less useful than initially expected.


title: Quantum Error Correcting Codes From The Compression Formalism

abstract:
  We solve the fundamental quantum error correction problem for bi-unitary
channels on two-qubit Hilbert space. By solving an algebraic compression
problem, we construct qubit codes for such channels on arbitrary dimension
Hilbert space, and identify correctable codes for Pauli-error models not
obtained by the stabilizer formalism. This is accomplished through an
application of a new tool for error correction in quantum computing called the
``higher-rank numerical range''. We describe its basic properties and discuss
possible further applications.


title: Quantum marginal problem and N-representability

abstract:
  A variant of the quantum marginal problem was known from early sixties as
N-representability problem. In 1995 it was designated by National Research
Council of USA as one of ten most prominent research challenges in quantum
chemistry. In spite of this recognition the progress was very slow, until a
couple of years ago the problem came into focus again, now in framework of
quantum information theory. In the paper I give an account of the recent
development.


title:
Block-block entanglement and quantum phase transitions in
  one-dimensional extended Hubbard model

abstract:
  In this paper, we study block-block entanglement in the ground state of
one-dimensional extended Hubbard model. Our results show that the phase diagram
derived from the block-block entanglement manifests richer structure than that
of the local (single site) entanglement because it comprises nonlocal
correlation. Besides phases characterized by the charge-density-wave, the
spin-density-wave, and phase-separation, which can be sketched out by the local
entanglement, singlet superconductivity phase could be identified on the
contour map of the block-block entanglement. Scaling analysis shows that ${\rm
log}_2(l)$ behavior of the block-block entanglement may exist in both
non-critical and the critical regions, while some local extremum are induced by
the finite-size effect. We also study the block-block entanglement defined in
the momentum space and discuss its relation to the phase transition from
singlet superconducting state to the charge-density-wave state.


title:
Controlling excess noise in fiber optics continuous variables quantum
  key distribution

abstract:
  We describe a continuous variables coherent states quantum key distribution
system working at 1550 nm, and entirely made of standard fiber optics and
telecom components, such as integrated-optics modulators, couplers and fast
InGaAs photodiodes. The setup is composed of an emitter randomly modulating a
coherent state in the complex plane with a doubly Gaussian distribution, and a
receiver based on a shot noise limited time-resolved homodyne detector. By
using a reverse reconciliation protocol, the device can transfer a raw key rate
up to 1 Mb/s, with a proven security against Gaussian or non-Gaussian attacks.
The dependence of the secret information rate of the present fiber set-up is
studied as a function of the line transmission and excess noise.