title:
The Trigonometric Rosen-Morse Potential in the Supersymmetric Quantum
  Mechanics and its Exact Solutions

abstract:
  The analytic solutions of the one-dimensional Schroedinger equation for the
trigonometric Rosen-Morse potential reported in the literature rely upon the
Jacobi polynomials with complex indices and complex arguments. We first draw
attention to the fact that the complex Jacobi polynomials have non-trivial
orthogonality properties which make them uncomfortable for physics
applications. Instead we here solve above equation in terms of real orthogonal
polynomials. The new solutions are used in the construction of the
quantum-mechanic superpotential.


title:
Local Invariants and Pairwise Entanglement in Symmetric Multi-qubit
  System

abstract:
  Pairwise entanglement properties of a symmetric multi-qubit system are
analyzed through a complete set of two-qubit local invariants. Collective
features of entanglement, such as spin squeezing, are expressed in terms of
invariants and a classifcation scheme for pairwise entanglement is proposed.
The invariant criteria given here are shown to be related to the recently
proposed (Phys. Rev. Lett. 95, 120502 (2005)) generalized spin squeezing
inequalities for pairwise entanglement in symmetric multi-qubit states.


title: Remote Implementation of Quantum Operations

abstract:
  Shared entanglement allows, under certain conditions, the remote
implementation of quantum operations. We revise and extend recent theoretical
results on the remote control of quantum systems as well as experimental
results on the remote manipulation of photonic qubits via linear optical
elements.


title: Fluctuations and Noise: A General Model with Applications

abstract:
  A wide variety of dissipative and fluctuation problems involving a quantum
system in a heat bath can be described by the independent-oscillator (IO) model
Hamiltonian. Using Heisenberg equations of motion, this leads to a generalized
quantum Langevin equation (QLE) for the quantum system involving two quantities
which encapsulate the properties of the heat bath. Applications include: atomic
energy shifts in a blackbody radiation heat bath; solution of the problem of
runaway solutions in QED; electrical circuits (resistively shunted Josephson
barrier, microscopic tunnel junction, etc.); conductivity calculations (since
the QLE gives a natural separation between dissipative and fluctuation forces);
dissipative quantum tunneling; noise effects in gravitational wave detectors;
anomalous diffusion; strongly driven quantum systems; decoherence phenomena;
analysis of Unruh radiation and entropy for a dissipative system.


title: Mixing of Quantum Walk on Circulant Bunkbeds

abstract:
  We give new observations on the mixing dynamics of a continuous-time quantum
walk on circulants and their bunkbed extensions. These bunkbeds are defined
through two standard graph operators: the join G + H and the Cartesian product
of graphs G and H.Our results include the following:
  1. The quantum walk is average uniform mixing on circulants with bounded
eigenvalue multiplicity. This extends a known fact about the cycles. 2.
Explicit analysis of the probability distribution of the quantum walk on the
join of circulants. This explains why complete partite graphs are not average
uniform mixing, using the fact the complete n-vertex graph is the join of a
1-vertex graph and the (n-1)-vertex complete graph, and that the complete
m-partite graph, where each partition has size n, is the m-fold join of the
empty n-vertex graph. 3. The quantum walk on the Cartesian product of a
m-vertex path P and a circulant G, is average uniform mixing if G is. This
highlights a difference between circulants and the hypercubes. Our proofs
employ purely elementary arguments based on the spectra of the graphs.


title: Noise thresholds for optical quantum computers

abstract:
  In this paper we numerically investigate the fault-tolerant threshold for
optical cluster-state quantum computing. We allow both photon loss noise and
depolarizing noise (as a general proxy for all local noise), and obtain a
threshold region of allowed pairs of values for the two types of noise. Roughly
speaking, our results show that scalable optical quantum computing is possible
for photon loss probabilities less than 0.003, and for depolarization
probabilities less than 0.0001.


title:
From Einstein's Theorem to Bell's Theorem: A History of Quantum
  Nonlocality

abstract:
  In this Einstein Year of Physics it seems appropriate to look at an important
aspect of Einstein's work that is often down-played: his contribution to the
debate on the interpretation of quantum mechanics. Contrary to popular opinion,
Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the
claimed completeness of orthodox quantum mechanics. I suggest that Einstein's
argument, as stated most clearly in 1946, could justly be called Einstein's
reality-locality-completeness theorem, since it proves that one of these three
must be false. Einstein's instinct was that completeness of orthodox quantum
mechanics was the falsehood, but he failed in his quest to find a more complete
theory that respected reality and locality. Einstein's theorem, and possibly
Einstein's failure, inspired John Bell in 1964 to prove his reality-locality
theorem. This strengthened Einstein's theorem (but showed the futility of his
quest) by demonstrating that either reality or locality is a falsehood. This
revealed the full nonlocality of the quantum world for the first time.


title:
Local copying and local discrimination as a study for non-locality of a
  set

abstract:
  We focus on the non-locality concerning local copying and local
discrimination, especially for a set of orthogonal maximally entangled states
in prime dimensional systems, as a study of non-locality of a set of states. As
a result, for such a set, we completely characterize deterministic local
copiability and show that local copying is more difficult than local
discrimination. From these result, we can conclude that lack algebraic symmetry
causes extra non-locality of a set.


title: Aspects of Cosmic Inflation in Expanding Bose-Einstein Condensates

abstract:
  Phonons in expanding Bose-Einstein condensates with wavelengths much larger
than the healing length behave in the same way as quantum fields within a
universe undergoing an accelerated expansion. This analogy facilitates the
application of many tools and concepts known from general relativity (such as
horizons) and the prediction of the corresponding effects such as the freezing
of modes after horizon crossing and the associated amplification of quantum
fluctuations. Basically the same amplification mechanism is (according to our
standard model of cosmology) supposed to be responsible for the generation of
the initial inhomogeneities -- and hence the seeds for the formation of
structures such as our galaxy -- during cosmic inflation (i.e., a very early
epoch in the evolution of our universe). After a general discussion of the
analogy (\emph{analogue cosmology}), we calculate the frozen and amplified
density-density fluctuations for quasi-two dimensional (Q2D) and three
dimensional (3D) condensates which undergo a free expansion after switching off
the (longitudinal) trap. PACS: 03.75.Kk, 04.62.+v.


title:
A Software Package to Construct Polynomial Sets over Z_2 for Determining
  the Output of Quantum Computations

abstract:
  A C# package is presented that allows a user for an input quantum circuit to
generate a set of multivariate polynomials over the finite field Z_2 whose
total number of solutions in Z_2 determines the output of the quantum
computation defined by the circuit. The generated polynomial system can further
be converted to the canonical Groebner basis form which provides a universal
algorithmic tool for counting the number of common roots of the polynomials.


title: Perfect State Transfer: Beyond Nearest-Neighbor Couplings

abstract:
  In this paper we build on the ideas presented in previous works for perfectly
transferring a quantum state between opposite ends of a spin chain using a
fixed Hamiltonian. While all previous studies have concentrated on
nearest-neighbor couplings, we demonstrate how to incorporate additional terms
in the Hamiltonian by solving an Inverse Eigenvalue Problem. We also explore
issues relating to the choice of the eigenvalue spectrum of the Hamiltonian,
such as the tolerance to errors and the rate of information transfer.


title: Hybrid cluster state proposal for a quantum game

abstract:
  We propose an experimental implementation of a quantum game algorithm in a
hybrid scheme combining the quantum circuit approach and the cluster state
model. An economical cluster configuration is suggested to embody a quantum
version of the Prisoners' Dilemma. Our proposal is shown to be within the
experimental state-of-art and can be realized with existing technology. The
effects of relevant experimental imperfections are also carefully examined.


title: Tight adversary bounds for composite functions

abstract:
  The quantum adversary method is a versatile method for proving lower bounds
on quantum algorithms. It yields tight bounds for many computational problems,
is robust in having many equivalent formulations, and has natural connections
to classical lower bounds. A further nice property of the adversary method is
that it behaves very well with respect to composition of functions. We
generalize the adversary method to include costs--each bit of the input can be
given an arbitrary positive cost representing the difficulty of querying that
bit. We use this generalization to exactly capture the adversary bound of a
composite function in terms of the adversary bounds of its component functions.
Our results generalize and unify previously known composition properties of
adversary methods, and yield as a simple corollary the Omega(sqrt{n}) bound of
Barnum and Saks on the quantum query complexity of read-once functions.


title:
Subwavelength atom localization via amplitude and phase control of the
  absorption spectrum-II

abstract:
  Interaction of the internal states of an atom with spatially dependent
standing-wave cavity field can impart position information of the atom passing
through it leading to subwavelength atom localization. We recently demonstrated
a new regime of atom localization [Sahrai {\it et al.}, Phys. Rev. A {\bf 72},
013820 (2005)], namely sub-half-wavelength localization through phase control
of electromagnetically induced transparency. This regime corresponds to extreme
localization of atoms within a chosen half-wavelength region of the
standing-wave cavity field. Here we present further investigation of the
simplified model considered earlier and show interesting features of the
proposal. We show how the model can be used to simulate variety of energy level
schemes. Furthermore, the dressed-state analysis is employed to explain the
emergence and suppression of the localization peaks, and the peak positions and
widths. The range of parameters for obtaining clean sub-half-wavelength
localization is identified.


title:
Generation of GHZ-type and \emph{W}-type entangled coherent states of
  three-cavity fields

abstract:
  We present experimental schemes to prepare the three-cavity GHZ-type and
\emph{W}-type entangled coherent states in the context of dispersive cavity
quantum electrodynamics. The schemes can be easily generalized to prepare the
GHZ-type and \emph{W}-type entangled coherent states of $n$-cavity fields. The
discussion of our schemes indicates that it can be realized by current
technologies.


title: Local Entanglement and quantum phase transition in spin models

abstract:
  Due to the phase interference of electromagnetic wave, one can recover the
total image of one object from a small piece of holograph, which records the
interference pattern of two laser light reflected from it. Similarly, the
quantum superposition principle allows us to derive the global phase diagram of
quantum spin models by investigating a proper local measurement. In the present
paper, we study the two-site entanglement in the antifferomagnetic spin models
with both spin-1/2 and 1. We show that its behaviors reveal some important
information on the global properties and the quantum phase transition of these
systems.


title: Attractive Casimir Forces in a Closed Geometry

abstract:
  We study the Casimir force acting on a conducting piston with arbitrary cross
section. We find the exact solution for a rectangular cross section and the
first three terms in the asymptotic expansion for small height to width ratio
when the cross section is arbitrary. Though weakened by the presence of the
walls, the Casimir force turns out to be always attractive. Claims of repulsive
Casimir forces for related configurations, like the cube, are invalidated by
cutoff dependence.


title:
Note on the Zero-Energy-Limit Solution for the Modified Gross-Pitaevskii
  Equation

abstract:
  The modified Gross-Pitaevskii equation was derived and solved to obtain the
1D solution in the zero-energy limit. This stationary solution could account
for the dominated contributions due to the kinetic effect as well as the
chemical potential in inhomogeneous Bose gases.


title:
Quantitative conditions do not guarantee the validity of the adiabatic
  approximation

abstract:
  In this letter, we point out that the widely used quantitative conditions in
the adiabatic theorem are insufficient in that they do not guarantee the
validity of the adiabatic approximation. We also reexamine the inconsistency
issue raised by Marzlin and Sanders (Phys. Rev. Lett. 93, 160408, 2004) and
elucidate the underlying cause.


title:
On the connection between the Schrodinger and the Heisenberg pictures
  for unbounded operators

abstract:
  It is well known that the unboundedness of operators in Hilbert space entails
domain troubles. It is also well known that most domain troubles can be
surmounted by extending the Hilbert space to a rigged Hilbert space. In this
note, we point out another of such troubles, namely the correspondence between
the Schrodinger and the Heisenberg pictures for unbounded operators, and sketch
the solution of this problem within the rigged Hilbert space.


title: Feed-forward and its role in conditional linear optical quantum dynamics

abstract:
  Nonlinear optical quantum gates can be created probabilistically using only
single photon sources, linear optical elements and photon-number resolving
detectors. These gates are heralded but operate with probabilities much less
than one. There is currently a large gap between the performance of the known
circuits and the established upper bounds on their success probabilities. One
possibility for increasing the probability of success of such gates is
feed-forward, where one attempts to correct certain failure events that
occurred in the gate's operation. In this brief report we examine the role of
feed-forward in improving the success probability. In particular, for the
non-linear sign shift gate, we find that in a three-mode implementation with a
single round of feed-forward the optimal average probability of success is
approximately given by p= 0.272. This value is only slightly larger than the
general optimal success probability without feed-forward, P= 0.25.


title: Quantum Key Distribution with Vacua or Dim Pulses as Decoy States

abstract:
  Recently, Hwang has proposed a decoy state method in quantum key distribution
(QKD). In Hwang's proposal, the average photon number of the decoy state is
about two. Here, we propose a new decoy state scheme using vacua or very weak
coherent states as decoy states and discuss its advantages.


title: Nonorthogonal decoy-state Quantum Key Distribution

abstract:
  In practical quantum key distribution (QKD), weak coherent states as the
photon sources have a limit in secure key rate and transmission distance
because of the existence of multiphoton pulses and heavy loss in transmission
line. Decoy states method and nonorthogonal encoding protocol are two important
weapons to combat these effects. Here, we combine these two methods and propose
a efficient method that can substantially improve the performance of QKD. We
find a 79 km increase in transmission distance over the prior record using
decoy states method.


title: Non-Unitary Quantum Walks on Hyper-Cycles

abstract:
  We present analytical treatment of quantum walks on multidimensional
hyper-cycle graphs. We derive the analytical expression of the probability
distribution for strong and weak decoherence regimes. Upper bound to mixing
time is obtained.


title:
Construction of $3\otimes 3$ entangled edge states with positive partial
  transposes

abstract:
  We construct a class of $3\otimes 3$ entangled edge states with positive
partial transposes using indecomposable positive linear maps. This class
contains several new types of entangled edge states with respect to the range
dimensions of themselves and their partial transposes.


title: Squeezing in Multivariate Spin Systems

abstract:
  In contrast to the canonically conjugate variates $q$,$p$ representing the
position and momentum of a particle in the phase space distributions, the three
Cartesian components, $J_{x}$,$J_{y}$, $J_{z}$ of a spin-$j$ system constitute
the mutually non-commuting variates in the quasi-probabilistic spin
distributions. It can be shown that a univariate spin distribution is never
squeezed and one needs to look into either bivariate or trivariate
distributions for signatures of squeezing. Several such distributions result if
one considers different characteristic functions or moments based on various
correspondence rules. As an example, discrete probability distribution for an
arbitrary spin-1 assembly is constructed using Wigner-Weyl and Margenau-Hill
correspondence rules. It is also shown that a trivariate spin-1 assembly
resulting from the exposure of nucleus with non-zero quadrupole moment to
combined electric quadrupole field and dipole magnetic field exhibits squeezing
in cerain cases.


title: Radiation of the blackbody in the external field

abstract:
  The blackbody is considered in the external general field. The additional
coefficients of stimulated emission and absorption are introduced into the
Einstein mechanism. Then, the generalized Planck formula is derived. The
Einstein and Debye formula for the specific heat is possible to generalize. The
application of the theory to the sonoluminescence, the relic radiation and
solar spectrum is discussed.


title: Angular spectrum of quantized light beams

abstract:
  We introduce a generalized angular spectrum representation for quantized
light beams. By using our formalism, we are able to derive simple expressions
for the electromagnetic vector potential operator in the case of: {a)}
time-independent paraxial fields, {b)} time-dependent paraxial fields, and {c)}
non-paraxial fields. For the first case, the well known paraxial results are
fully recovered.


title: Condition for the adiabatic approximation

abstract:
  We give a sufficient condition for the quantum adiabatic approximation, which
is quantitative and can be used to estimate error caused by this approximation.
We also discuss when the traditional condition is sufficient.


title:
A review on the decoy-state method for practical quantum key
  distribution

abstract:
  We present a review on the historic development of the decoy state method,
including the background, principles, methods, results and development. We also
clarify some delicate concepts. Given an imperfect source and a very lossy
channel, the photon-number-splitting (PNS) attack can make the quantum key
distribution (QKD) in practice totally insecure. Given the result of ILM-GLLP,
one knows how to distill the secure final key if he knows the fraction of
tagged bits. The purpose of decoy state method is to do a tight verification of
the the fraction of tagged bits. The main idea of decoy-state method is
changing the intensities of source light and one can verify the fraction of
tagged bits of certain intensity by watching the the counting rates of pulses
of different intensities. Since the counting rates are small quantities, the
effect of statistical fluctuation is very important. It has been shown that
3-state decoy-state method in practice can work even with the fluctuations and
other errors.


title: Improving the purity of one- and two-qubit gates by AC fields

abstract:
  We investigate the influence of AC driving fields on the coherence properties
of one- and two-qubit gate operations. In both cases, we find that for suitable
driving parameters, the gate purity improves significantly. A mapping of the
time-dependent system-bath model to an effective static model provides
analytical results. The resulting purity loss compares favorably with numerical
results.


title: Structure of high-order quantum adiabatic approximation

abstract:
  The paper studies the structure of high-order adiabatic approximation of a
wave function for slowly changing Hamiltonians. A constructive technique for
explicit separation of fast and slow components of the wave function is
developed. The fast components are determined by dynamic phases, while the slow
components are given by asymptotic series evaluated by means of an explicit
recurrent procedure. It is shown that the slow components represent
quasiadiabatic states, which play conceptually the same role as energy levels
in stationary systems or Floquet states in time-periodic systems. As an
application, we derive high-order asymptotic expressions for quasienergies of
periodic Hamiltonians. As examples, a two-state (spin-1/2) system in
periodically changing magnetic filed, and a particle in moving square potential
well are studied.


title: Purity estimation with separable measurements

abstract:
  Given a large number N of copies of a qubit state of which we wish to
estimate its purity, we prove that separable-measurement protocols can be as
efficient as the optimal joint-measurement one if classical communication is
used. This shows that the optimal estimation of the entanglement of a two-qubit
state can also be achieved asymptotically with fully separable measurements.
Thus, quantum memories provide no advantage in this situation. The relationship
between our global Bayesian approach and the quantum Cramer-Rao bound is
discussed.


title: Conclusive Entangling Probe

abstract:
  A design is given for an optimized entangling probe attacking the BB84
(Bennett-Brassard 1984) protocol of quantum key distribution and yielding
maximum information to the probe for a full range of induced error rates. Probe
photon polarization states become optimally entangled with the signal states on
their way between the legitimate transmitter and receiver. Although standard
von-Neumann projective measurements of the probe yield maximum information on
the pre-privacy amplified key, if instead the probe measurements are performed
with a certain positive operator valued measure, then the measurement results
are conclusive, at least some of the time, for a full range of inconclusive
rates.


title: Copenhagen Interpretation of Quantum Mechanics Is Incorrect

abstract:
  (A point-by-point response to a comment (quant-ph/0509130) on our paper
(quant-ph/0509089) is added as Appendix C. We find the comment incorrect.)
  Einstein's criticism of the Copenhagen interpretation of quantum mechanics is
an important part of his legacy. Although most physicists consider Einstein's
criticism technically unfounded, we show that the Copenhagen interpretation is
actually incorrect, since Born's probability explanation of the wave function
is incorrect due to a false assumption on "continuous probabilities" in modern
probability theory. "Continuous probability" means a "probability measure" that
can take every value in a subinterval of the unit interval (0, 1). We prove
that such "continuous probabilities" are invalid. Since Bell's inequality also
assumes "continuous probabilities", the result of the experimental test of
Bell's inequality is not evidence supporting the Copenhagen interpretation.
Although successful applications of quantum mechanics and explanation of
quantum phenomena do not necessarily rely on the Copenhagen interpretation, the
question asked by Einstein 70 years ago, i.e., whether a complete description
of reality exists, still remains open.


title: The Symmetric Stable L\'{e}vy Flights and the Feynman Path Integral

abstract:
  We determine the solution of the fractional spatial diffusion equation in
n-dimensional Euclidean space for a "free" particle by computing the
corresponding propagator. We employ both the Hamiltonian and Lagrangian
approaches which produce exact results for the case of jumps governed by
symmetric stable L\'{e}vy flights.


title:
On the security of AlphaEta: Response to `Some attacks on quantum-based
  cryptographic protocols'

abstract:
  Lo and Ko in [1] have developed some attacks on the cryptosystem called
AlphaEta [2], claiming that these attacks undermine the security of AlphaEta
for both direct encryption and key generation. In this paper, we show that
their arguments fail in many different ways. In particular, the first attack in
[1] requires channel loss or length of known-plaintext that is exponential in
the key length and is unrealistic even for moderate key lengths. The second
attack is a Grover search attack based on `asymptotic orthogonality' and was
not analyzed quantitatively in [1]. We explain why it is not logically possible
to ``pull back'' an argument valid only at n=infinity into a limit statement,
let alone one valid for a finite number of transmissions n. We illustrate this
by a `proof' using a similar asymptotic orthogonality argument that
coherent-state BB84 is insecure for any value of loss. Even if a limit
statement is true, this attack is a priori irrelevant as it requires an
indefinitely large amount of known-plaintext, resources and processing. We also
explain why the attacks in [1] on AlphaEta as a key-generation system are based
on misinterpretations of [2]. Some misunderstandings in [1] regarding certain
issues in cryptography and optical communications are also pointed out. Short
of providing a security proof for AlphaEta, we provide a description of
relevant results in standard cryptography and in the design of AlphaEta to put
the above issues in the proper framework and to elucidate some security
features of this new approach to quantum cryptography.


title:
Reply to: 'Reply to: "Comment on: `How much security does Y-00 protocol
  provide us?` " '

abstract:
  Nishioka et al claim in [1], elaborating on their earlier paper [2], that the
direct encryption scheme called Y-00 [3,4] is equivalent to a classical
non-random additive stream cipher, and thus offers no more security than the
latter. In this paper, we show that this claim is false and that Y-00 may be
considered equivalent to a \emph{random} cipher. We explain why a random cipher
provides additional security compared to its nonrandom counterpart. Some
criticisms in [1] on the use of Y-00 for key generation are also briefly
responded to.


title: Conditional quantum distinguishability and pure quantum communication

abstract:
  I design a simple way of distinguishing non-orthogonal quantum states with
perfect reliability using only quantum control-not gates in one condition. In
this way, we can implement pure quantum communication in directly sending
classical information, Ekert quantum cryptography and quantum teleportation
without the help of classical communications channel.


title: Single-cell atomic quantum memory for light

abstract:
  Recent experiments demonstrating atomic quantum memory for light [B.
Julsgaard et al., Nature 432, 482 (2004)] involve two macroscopic samples of
atoms, each with opposite spin polarization. It is shown here that a single
atomic cell is enough for the memory function if the atoms are optically pumped
with suitable linearly polarized light, and quadratic Zeeman shift and/or ac
Stark shift are used to manipulate rotations of the quadratures. This should
enhance the performance of our quantum memory devices since less resources are
needed and losses of light in crossing different media boundaries are avoided.


title: Entanglement reciprocation between qubits and continuous variables

abstract:
  We investigate how entanglement can be transferred between qubits and
continuous variable (CV) systems. We find that one ebit borne in maximally
entangled qubits can be fully transferred to two CV systems which are initially
prepared in pure separable Gaussian field with high excitation. We show that it
is possible, though not straightforward, to retrieve the entanglement back to
qubits from the entangled CV systems. The possibility of deposition of multiple
ebits from qubits to the initially unentangled CV systems is also pointed out.


title: Potential Errors in a Scheme of Universal Quantum Gates in Kane's Model

abstract:
  We re--investigate a plausible proposal for universal quantum gates in Kane's
model, in which the authors assumed that electron spin is always downward under
a background magnetic field and the value of controlling parameters is varied
instantaneously. We demonstrate that a considerable error appears, for example,
in the X rotation. As result, the controlled operations don't work. Such a
failure is caused by improper choice of the computational bases; actually, the
electron spin is not always downward over time during quantum operations.


title:
An absolutely secure QKD scheme with no detection noise, entanglement
  and classical communication

abstract:
  A new quantum communication scheme is introduced which is the quantum
realization of the classical Kish-Sethuraman (KS) cipher. First the message is
bounced back with additional encryption by the Receiver and the original
encryption is removed and the message is resent by the Sender. The mechanical
analogy of this operation is using two padlocks; one by the Sender and one by
the Receiver. We show that the rotation of the polarization is an operator
which satisfies the conditions required for the KS encryption operators
provided single photons are communicated. The new method is not only simple but
has several advantages. The Evasdropper extracts zero information even if she
executes a quantum measurement on the state. The communication can be done by
two publicly agreed orthogonal states. Therefore, there is no inherent
detection noise. No classical channel and no entangled states are required for
the communication.


title:
Comment on "Impossibility of distant indirect measurement of the quantum
  Zeno effect"

abstract:
  In the paper by M. Hotta and M. Morikawa [Phys. Rev. A 69, 052114 (2004)] the
non-existence of the quantum Zeno effect caused by indirect measurements has
been claimed. It is shown here that the pertinent proof is incorrect, and the
claim unfounded.


title: Experimental Tailoring of a Three-Level Lambda System in Tm3+:YAG

abstract:
  Quantum information transfer from light to atom ensembles and vice versa has
both basic and practical importance. Among the relevant topics let us mention
entanglement and decoherence of macroscopic systems, together with applications
to quantum memory for long distance quantum cryptography. Although the first
experimental demonstrations have been performed in atomic vapors and clouds,
rare earth ion doped crystals are also interesting media for such processes. In
this paper we address Tm3+ ions capability to behave as three-level lambda
systems, a key ingredient to convert optical excitation into a spontaneous-
emission-free spin wave. Indeed Tm3+ falls within reach of light sources that
can be stabilized easily to the required degree. In the absence of zero-field
hyperfine structure we apply an external magnetic field to lift the nuclear
spin degeneracy in Tm3+:YAG. We experimentally determine the gyromagnetic
tensor components with the help of spectral hole-burning techniques. Then
appropriate orientation of the applied field enables us to optimize the
transition probability ratio along the two legs of the lambda. The resulting
three-level lambda system should suit quantum information processing
requirements.


title: Physical Purification of Quantum States

abstract:
  We introduce the concept of a physical process that purifies a mixed quantum
state, taken from a set of states, and investigate the conditions under which
such a purification map exists. Here, a purification of a mixed quantum state
is a pure state in a higher-dimensional Hilbert space, the reduced density
matrix of which is identical to the original state. We characterize all sets of
mixed quantum states, for which perfect purification is possible. Surprisingly,
some sets of two non-commuting states are among them. Furthermore, we
investigate the possibility of performing an imperfect purification.


title: On complementary channels and the additivity problem

abstract:
  We explore complementarity between output and environment of a quantum
channel (or, more generally, CP map), making an observation that the output
purity characteristics for complementary CP maps coincide. Hence, validity of
the mutiplicativity/additivity conjecture for a class of CP maps implies its
validity for complementary maps. The class of CP maps complementary to
entanglement-breaking ones is described and is shown to contain diagonal CP
maps as a proper subclass, resulting in new class of CP maps (channels) for
which the multiplicativity/additivity holds. Covariant and Gaussian channels
are discussed briefly in this context.


title: Orientation of molecules via laser-induced anti-alignment

abstract:
  We show that field-free molecular orientation induced by a half-cycle pulse
may be considerably enhanced by an additional laser pulse inducing molecular
anti-alignment. Two qualitatively different enhancement mechanisms are
identified depending on the pulse order, and their effects are optimized with
the help of quasi-classical as well as fully quantum models.


title: Robust "trapping states" in the motion of a trapped ion

abstract:
  A novel robust mechanism for the generation of "trapping states" is shown to
exist in the coupling of a two-level system with an oscillator, which is based
on nonlinearities in the laser-induced vibronic coupling. This mechanism is
exemplified with an ion confined in the potential well of a trap, where the
nonlinearities are due to Franck--Condon type overlap integrals of the laser
waves with the ionic centre-of-mass wavefunction. In contrast to the coherent
trapping mechanism known from micro-maser theory, this mechanism works also in
an incoherent regime operated by noisy lasers and is therefore much more robust
against external decoherence effects. These features favour the incoherent
regime, in particular for the preparation of highly excited trapping states.


title: On the notion of reconstruction of quantum theory

abstract:
  What belongs to quantum theory is no more than what is needed for its
derivation. We argue for an approach focusing on reconstruction rather than
interpretation of quantum mechanics and analyze several examples of
reconstruction. We submit that reconstruction advances our understanding of
quantum theory irrespective of one's ontological stance.


title:
Return operator, cross Bell bases and protocol of teleportation of
  arbitrary multipartite qubit entanglement

abstract:
  In this paper, we define the return operator, the cross product operator and
the cross Bell bases. Using the cross Bell bases, we give a protocol of
teleportation of arbitrary multipartite qubit entanglement, this scheme is a
quite natural generalization of the BBCJPW scheme. We find that this
teleportation, in fact, is essentially determined by the teleportation of every
single unknown qubit state as in the original scheme of BBCJPW. The calculation
in detail is given for the case of tripartite qubit.


title: Information-theoretic principle entails orthomodularity of a lattice

abstract:
  Quantum logical axiomatic systems for quantum theory usually include a
postulate that a lattice under consideration is orthomodular. We propose a
derivation of orthomodularity from an information-theoretic axiom. This
provides conceptual clarity and removes a long-standing puzzle about the
meaning of orthomodularity.


title: Quantum nature of laser light

abstract:
  All compositions of a mixed-state density operator are equivalent for the
prediction of the probabilities of future outcomes of measurements. For
retrodiction, however, this is not the case. The retrodictive formalism of
quantum mechanics provides a criterion for deciding that some compositions are
fictional. Fictional compositions do not contain preparation device operators,
that is operators corresponding to states that could have been prepared. We
apply this to Molmer's controversial conjecture that optical coherences in
laser light are a fiction and find agreement with his conjecture. We generalise
Molmer's derivation of the interference between two lasers to avoid the use of
any fictional states. We also examine another possible method for
discriminating between conerent states and photon number states in laser light
and find that it does not work, with the equivalence for prediction saved by
entanglement.


title: Coherent states of a charged particle in a uniform magnetic field

abstract:
  The coherent states are constructed for a charged particle in a uniform
magnetic field based on coherent states for the circular motion which have
recently been introduced by the authors.


title:
Quantum Lubrication: Suppression of Friction in a First Principle Four
  Stroke Heat Engine

abstract:
  A quantum model of a heat engine resembling the Otto cycle is employed to
explore strategies to suppress frictional losses. These losses are caused by
the inability of the engine's working medium to follow adiabatically the change
in the Hamiltonian during the expansion and compression stages. By adding
external noise to the engine, frictional losses can be suppressed.


title: Emergence of thermodynamic behavior within composite quantum systems

abstract:
  Entanglement within a given device provides a potential resource for quantum
information processing. Entanglement between system and environment leads to
decoherence (thus suppressing non-classical features within the system) but
also opens up a route to robust and universal control. The latter is related to
thermodynamic equilibrium, a generic behavior of bi-partite quantum systems.
Fingerprints of this equilibrium behavior (including relaxation and stability)
show up already far from the thermodynamic limit, where a complete solution of
the underlying Schroedinger dynamics of the total system is still feasible.


title: Replacing Two Controlled-U's with Two CNOTs

abstract:
  We give a simple, closed-form formula, what we call the Deflation Identity,
for converting any 2-qubit circuit with exactly two controlled-U's (and some
1-qubit rotations) into an equivalent circuit with just two CNOTs (and some
1-qubit rotations). We also give two interesting applications of the Deflation
Identity; one to "opening and closing a breach" in a quantum circuit, the other
to the CS decomposition of a 2-qubit operator.


title:
Non-adiabatic quantum molecular dynamics: Ionization of many electron
  systems

abstract:
  We propose a novel method to describe realistically ionization processes with
absorbing boundary conditions in basis expansion within the formalism of the
so-called Non-Adiabatic Quantum Molecular Dynamics. This theory couples
self-consistently a classical description of the nuclei with a quantum
mechanical treatment of the electrons in atomic many-body systems. In this
paper we extend the formalism by introducing absorbing boundary conditions via
an imaginary potential. It is shown how this potential can be constructed in
time-dependent density functional theory in basis expansion. The approach is
first tested on the hydrogen atom and the pre-aligned hydrogen molecular ion
H2+ in intense laser fields where reference calculations are available. It is
then applied to study the ionization of non-aligned H2+ and H2. Striking
differences in the orientation dependence between both molecules are found.
Surprisingly, enhanced ionization is predicted for perpendicularly aligned
molecules.


title:
Array of planar Penning traps as a nuclear magnetic resonance molecule
  for quantum computation

abstract:
  An array of planar Penning traps, holding single electrons, can realize an
artificial molecule suitable for NMR-like quantum information processing. The
effective spin-spin coupling is accomplished by applying a magnetic field
gradient, combined to the Coulomb interaction acting between the charged
particles. The system lends itself to scalability, since the same substrate can
easily accommodate an arbitrary number of traps. Moreover, the coupling
strength is tunable and under experimental control. Our theoretical predictions
take into account a realistic setting, within the reach of current technology.


title: Coherent Backscattering of Light with Nonlinear Atomic Scatterers

abstract:
  We study coherent backscattering of a monochromatic laser by a dilute gas of
cold two-level atoms in the weakly nonlinear regime. The nonlinear response of
the atoms results in a modification of both the average field propagation
(nonlinear refractive index) and the scattering events. Using a perturbative
approach, the nonlinear effects arise from inelastic two-photon scattering
processes. We present a detailed diagrammatic derivation of the elastic and
inelastic components of the backscattering signal both for scalar and vectorial
photons. Especially, we show that the coherent backscattering phenomenon
originates in some cases from the interference between three different
scattering amplitudes. This is in marked contrast with the linear regime where
it is due to the interference between two different scattering amplitudes. In
particular we show that, if elastically scattered photons are filtered out from
the photo-detection signal, the nonlinear backscattering enhancement factor
exceeds the linear barrier two, consistently with a three-amplitude
interference effect.


title:
On the general equation of motion of quantum thermodynamics and the
  distinction between quantal and nonquantal uncertainties

abstract:
  A general quantum theory encompassing Mechanics, Thermodynamics and
irreversible dynamics is presented in two parts. The first part is concerned
exclusively with the description of the states of any individual physical
system. It is based on a new nonlinear quantum equation of motion, which
reduces to the Schroedinger equation of motion of motion of conventional
quantum dynamics only under special conditions. It accounts for the
implications of the laws of Thermodynamics as well as for irreversible
phenomena, such as the natural tendency of an isolated system to transit from
any non-equilibrium state to an equilibrium state of higher entropy.
Conversely, the laws of Thermodynamics and irreversibility emerge as
manifestations of the fundamental quantum dynamical behaviour of the elementary
constituents of any material system. We call this part Quantum Thermodynamics.
The second part of the theory, which contains the first as a special case, is
concerned with the description of stochastic distributions of states in an
ensemble of identical physical systems each of which individually obeys the
laws of Quantum Thermodynamics. It is based on a new measure-theoretic
description of ensembles. It accounts unambiguously for the essential
distinction between two types of uncertainties that are generally present in an
ensemble, namely, quantal uncertainties due to the inherent quantal nature of
the states of each individual member system and nonquantal uncertainties due to
the stochastic distribution of states. We call this part Quantum Statistical
Thermodynamics.


title:
Cavity-QED tests of representations of canonical commutation relations
  employed in field quantization

abstract:
  Various aspects of dissipative and nondissipative decoherence of Rabi
oscillations are discussed in the context of field quantization in alternative
representations of CCR. Theory is confronted with experiment, and a possibility
of more conclusive tests is analyzed.

categories: quant-ph hep-th math-ph math.MP physics.atom-ph


title: Quantum computing (Kwantumberekening)

abstract:
  There has been no lack of coverage in the past few years in scientific
journals of the topic of quantum computation. Rightly so, as this is a novel
idea with--so far--at least one very important practical application (prime
factorisation) as soon as the technology can accommodate reasonably sized
computations. Interest in quantum computing has been sparked by both the
realization that increasing miniaturisation will eventually bring computer
scientists face-to-face with quantum effects, and by the grasping of the
potential for massive parallelism inherent in the Hilbert space representation
of quantum systems and in the special effects of quantum entanglement.


title: Macroscopic Entanglement by Entanglement Swapping

abstract:
  We present a scheme for entangling two micromechanical oscillators. The
scheme exploits the quantum effects of radiation pressure and it is based on a
novel application of entanglement swapping, where standard optical measurements
are used to generate purely mechanical entanglement. The scheme is presented by
first solving the general problem of entanglement swapping between arbitrary
bipartite Gaussian states, for which simple input-output formulas are provided.


title:
The ultra-sensitive electrical detection of spin Rabi oscillation at
  paramagnetic defects

abstract:
  A short review of the pulsed electrically detected magnetic resonance (pEDMR)
experiment is presented. PEDMR allows the highly sensitive observation of
coherent electron spin motion of charge carriers and defects in semiconductors
by means of transient current measurements. The theoretical foundations, the
experimental implementation, its sensitivity and its potential with regard to
the investigation of electronic transitions in semiconductors are discussed.
For the example of the P_b center at the crystalline silicon (111) to silicon
dioxide interface it is shown experimentally how one can detect spin
Rabi-oscillation, its dephasing, coherence decays and spin-coupling effects.


title: Continuous variable tripartite entanglement from twin nonlinearities

abstract:
  In this work we analyse and compare the continuous variable tripartite
entanglement available from the use of two concurrent or cascaded $\chi^{(2)}$
nonlinearities. We examine both idealised travelling-wave models and more
experimentally realistic intracavity models, showing that tripartite entangled
outputs are readily producible. These may be a useful resource for such
applications as quantum cryptography and teleportation.


title: Symmetric measurements attaining the accessible information

abstract:
  A theorem of Davies states that for symmetric quantum states there exists a
symmetric POVM maximizing the mutual information. To apply this theorem the
representation of the symmetry group has to be irreducible. We obtain a similar
yet weaker result for reducible representations. We apply our results to the
double trines ensemble and show numerically that for this ensemble the pretty
good measurement is optimal.


title: Entanglement-assisted Orientation in Space

abstract:
  We demonstrate that quantum entanglement can help separated individuals in
making decisions if their goal is to find each other in the absence of any
communication between them. We derive a Bell-like inequality that the
efficiency of every classical solution for our problem has to obey, and
demonstrate its violation by the quantum efficiency. This proves that no
classical strategy can be more efficient than the quantum one.


title: Another dual formulation of the separability problem

abstract:
  We show how the separability problem is dual to that of decomposing any given
matrix into a conic combination of rank-one partial isometries, thus offering a
duality approach different to the positive maps characterization problem.
Several inmediate consequences are analyzed: (i) a sufficient criterion for
separability for bipartite quantum systems, (ii) a complete solution to the
separability problem for pure states also of bipartite systems independent of
the classical Schmidt decomposition method and (iii) a natural generalization
of these results to multipartite systems.


title: Feedback cooling of a single trapped ion

abstract:
  Based on a real-time measurement of the motion of a single ion in a Paul
trap, we demonstrate its electro-mechanical cooling below the Doppler limit by
homodyne feedback control (cold damping). The feedback cooling results are well
described by a model based on a quantum mechanical Master Equation.


title:
Properties of Conjugate Channels with Applications to Additivity and
  Multiplicativity

abstract:
  Quantum channels can be described via a unitary coupling of system and
environment, followed by a trace over the environment state space. Taking the
trace instead over the system state space produces a different mapping which we
call the conjugate channel. We explore the properties of conjugate channels and
describe several different methods of construction. In general, conjugate
channels map M_d to M_d' with d < d', and different constructions may differ by
conjugation with a partial isometry.
  We show that a channel and its conjugate have the same minimal output entropy
and maximal output p-norm. It then follows that the additivity and
multiplicativity conjectures for these measures of optimal output purity hold
for a product of channels if and only if they also hold for the product of
their conjugates. This allows us to reduce these conjectures to the special
case of maps taking M_d to M_d' with a minimal representation of dimension at
most d.
  We find explicit expressions for the conjugates for a number of well-known
examples, including entanglement-breaking channels, unital qubit channels, the
depolarizing channel, and a subclass of random unitary channels. For the
entanglement-breaking channels, channels this yields a new class of channels
for which additivity and multiplicativity of optimal output purity can be
established. For random unitary channels using the generalized Pauli matrices,
we obtain a new formulation of the multiplicativity conjecture. The conjugate
of the completely noisy channel plays a special role and suggests a mechanism
for using noise to transmit information.


title: Time Reversal Communication in Multi-Path Fading Channels with Pinholes

abstract:
  The paper presents an analysis of the time reversal in multi-path
Rayleigh-fading channels with $N$ inputs (transmitters) and $M$ outputs
(receivers).
  The main issues addressed are the condition of statistical stability, the
rate of information transfer and the effect of pinholes. The stability
condition is proved to be $MC\ll N_{\rm eff}B$ for broadband channels and $M\ll
N_{\rm eff}$ for narrowband channels where $C$ is the symbol rate, $B$ is the
bandwidth and $N_{\rm eff}$ is the {\em effective} number of transmitters. It
is shown that when the number of layers, $n-1$, is relatively low compared to
the logarithm of numbers of pinholes $N_{\rm eff}$ is given by $n^{-1}$ times
the harmonic mean of the number of transmitters and the numbers of pinholes at
all layers. On the other hand, when the number of layers is relatively large
the effective number of pinholes diminishes exponentially. The energy
efficiency is shown to be optimal when the power supply is set to the noise
level times $BN_{\rm eff}$ and that the maximal information rate is roughly
$BN_{\rm eff}$ when the stability condition is violated.


title: Homodyne measurement of average photon number

abstract:
  We describe a new scheme for the measurement of mean photon flux at an
arbitrary optical sideband frequency using homodyne detection. Experimental
implementation of the technique requires an AOM in addition to the homodyne
detector, and does not require phase locking. The technique exhibits
polarisation, frequency and spatial mode selectivity, as well as much improved
speed, resolution and dynamic range when compared to linear photodetectors and
avalanche photo diodes (APDs), with potential application to quantum state
tomography and information encoding using an optical frequency basis.
Experimental data also directly confirms the Quantum Mechanical description of
vacuum noise.


title: Quantum Signature Protocol without the Trusted Third Party

abstract:
  An authentic digital signature scheme based on the correlation of
Greenberger-Horne-Zeilinger (GHZ) states was presented. In this scheme, by
performing a local unitary operation on the third particles of each GHZ
triplet, Alice can encode message M and get its signature S. Bob performs CNOT
operation on the combined GHZ triplets can recovery the message M and directly
authenticates Alice's signature S. Our scheme was designed to use quantum
secret key to guaranteed unconditional security, as well as use quantum
fingerprinting to avoid trick attacks and reduce communication complexity.


title:
Comment on ''Copenhagen Interpretation of Quantum Mechanics Is
  Incorrect''

abstract:
  It is shown that ''Theorem 1'' of the article ''Copenhagen Interpretation of
Quantum Mechanics Is Incorrect'' by G.-L. Li and V.O.K. Li (see
quant-ph/0509089) is false. Therefore the assertion expressed in the title of
that article is untenable.


title: Direct experimental evidence of free fermion antibunching

abstract:
  Fermion antibunching was observed on a beam of free noninteracting neutrons.
A monochromatic beam of thermal neutrons was first split by a graphite single
crystal, then fed to two detectors, displaying a reduced coincidence rate. The
result is a fermionic complement to the Hanbury Brown and Twiss effect for
photons.


title: N-fold Supersymmetry in Quantum Systems with Position-dependent Mass

abstract:
  We formulate the framework of N-fold supersymmetry in one-body quantum
mechanical systems with position-dependent mass (PDM). We show that some of the
significant properties in the constant-mass case such as the equivalence to
weak quasi-solvability also hold in the PDM case. We develop a systematic
algorithm for constructing an N-fold supersymmetric PDM system. We apply it to
obtain type A N-fold supersymmetry in the case of PDM, which is characterized
by the so-called type A monomial space. The complete classification and general
form of effective potentials for type A N-fold supersymmetry in the PDM case
are given.


title: Joint measurements and Bell inequalities

abstract:
  Joint quantum measurements of non-commuting observables are possible, if one
accepts an increase in the measured variances. A necessary condition for a
joint measurement to be possible is that a joint probability distribution
exists for the measurement. This fact suggests that there may be a link with
Bell inequalities, as these will be satisfied if and only if a joint
probability distribution for all involved observables exists. We investigate
the connections between Bell inequalities and conditions for joint quantum
measurements to be possible. Mermin's inequality for the three-particle
Greenberger-Horne-Zeilinger state turns out to be equivalent to the condition
for a joint measurement on two out of the three quantum systems to exist.
Gisin's Bell inequality for three co-planar measurement directions, meanwhile,
is shown to be less strict than the condition for the corresponding joint
measurement.


title: Interacting classical and quantum ensembles

abstract:
  A consistent description of interactions between classical and quantum
systems is relevant to quantum measurement theory, and to calculations in
quantum chemistry and quantum gravity. A solution is offered here to this
longstanding problem, based on a universally-applicable formalism for ensembles
on configuration space. This approach overcomes difficulties arising in
previous attempts, and in particular allows for backreaction on the classical
ensemble, conservation of probability and energy, and the correct classical
equations of motion in the limit of no interaction. Applications include
automatic decoherence for quantum ensembles interacting with classical
measurement apparatuses; a generalisation of coherent states to hybrid harmonic
oscillators; and an equation for describing the interaction of quantum matter
fields with classical gravity, that implies the radius of a Robertson-Walker
universe with a quantum massive scalar field can be sharply defined only for
particular `quantized' values.


title:
Exact Solution for a Two-Level Atom in Radiation Fields and the Freeman
  Resonances

abstract:
  Using techniques of complex analysis in an algebraic approach, we solve the
wave equation for a two-level atom interacting with a monochromatic light field
exactly. A closed-form expression for the quasi-energies is obtained, which
shows that the Bloch-Siegert shift is always finite, regardless of whether the
original or the shifted level spacing is an integral multiple of the driving
frequency, $\omega$. We also find that the wave functions, though finite when
the original level spacing is an integral multiple of $\omega$, become
divergent when the intensity-dependent shifted energy spacing is an integral
multiple of the photon energy. This result provides, for the first time in the
literature, an ab-initio theoretical explanation for the occurrence of the
Freeman resonances observed in above-threshold ionization experiments.


title: q-deformed Fermions

abstract:
  This is a study of $q$-Fermions arising from a q-deformed algebra of harmonic
oscillators. Two distinct algebras will be investigated. Employing the first
algebra, the Fock states are constructed for the generalized Fermions obeying
Pauli exclusion principle. The distribution function and other thermodynamic
properties such as the internal energy and entropy are derived. Another
generalization of fermions from a different q-deformed algebra is investigated
which deals with q-fermions not obeying the exclusion principle. Fock states
are constructed for this system. The basic numbers appropriate for this system
are determined as a direct consequence of the algebra. We also establish the
Jackson Derivative, which is required for the q-calculus needed to describe
these generalized Fermions.


title: Schrodinger Cat States for Quantum Information Processing

abstract:
  We extensively discuss how Schrodinger cat states (superpositions of
well-separated coherent states) in optical systems can be used for quantum
information processing.


title:
Generation of entangled photons by trapped ions in microcavities under a
  magnetic field gradient

abstract:
  We propose a potential scheme to generate entangled photons by manipulating
trapped ions embedded in two-mode microcavities, respectively, assisted by a
magnetic field gradient. By means of the spin-spin coupling due to the magnetic
field gradient and the Coulomb repulsion between the ions, we show how to
efficiently generate entangled photons by detecting the internal states of the
trapped ions. We emphasize that our scheme is advantageous to create complete
sets of entangled multi-photon states. The requirement and the experimental
feasibility of our proposal are discussed in detail.


title:
Experimental Measurement of Mixed State Geometric Phase by Quantum
  Interferometry using NMR

abstract:
  Geometric phase has been proposed as one of the promising methodologies to
perform fault tolerant quantum computations. However, since decoherence plays a
crucial role in such studies, understanding of mixed state geometric phase has
become important. While mixed state geometric phase was first introduced
mathematically by Uhlmann, recently Sjoqvist et al. [Phys. Rev. Lett. 85(14),
2845 (2000)] have described the mixed state geometric phase in the context of
quantum interference and shown theoretically that the visibility as well as the
shift of the interference pattern are functions of geometric phase and the
purity of the mixed state. Here we report the first experimental study of the
dependence of interference visibility and shift of the interference pattern on
the mixed state geometric phase by Nuclear Magnetic Resonance.


title: Universal entanglement concentration

abstract:
  We propose a new protocol of \textit{universal} entanglement concentration,
which converts many copies of an \textit{unknown} pure state to an \textit{%
exact} maximally entangled state. The yield of the protocol, which is outputted
as a classical information, is probabilistic, and achives the entropy rate with
high probability, just as non-universal entanglement concentration protocols
do.
  Our protocol is optimal among all similar protocols in terms of wide
varieties of measures either up to higher orders or non-asymptotically,
depending on the choice of the measure. The key of the proof of optimality is
the following fact, which is a consequence of the symmetry-based construction
of the protocol: For any invariant measures, optimal protocols are found out in
modifications of the protocol only in its classical output, or the claim on the
product.
  We also observe that the classical part of the output of the protocol gives a
natural estimate of the entropy of entanglement, and prove that that estimate
achieves the better asymptotic performance than any other (potentially global)
measurements.


title: Continuous time quantum walks in phase space

abstract:
  We formulate continuous time quantum walks (CTQW) in a discrete quantum
mechanical phase space. We define and calculate the Wigner function (WF) and
its marginal distributions for CTQWs on circles of arbitrary length $N$. The WF
of the CTQW shows characteristic features in phase space. Revivals of the
probability distributions found for continuous and for discrete quantum carpets
do manifest themselves as characteristic patterns in phase space.


title: Field tuned atom-atom entanglement via diople-dipole interaction

abstract:
  We propose a simple scheme, in which only one atom couples to a cavity field,
to entangle two two-level atoms. We connect two atoms with dipole-dipole
interaction since one of them can move around the cavity. The results show that
the peak entanglment does not depend on dipole-dipole interaction strength but
on field density at a certain controlling time. So the field density can act as
a switch for maximum entanglement (ME) generation.


title: Local field modulated entanglment among three distant atoms

abstract:
  We extend the scheme for that proposed by S. Mancini and S. Bose (Phys. Rev.
A \QTR{bf}{70}, 022307(2004)) to the case of triple-atom. Under mean field
approximation, we obtain an effective Hamiltonian of triple-body Ising-model
interaction. Furthermore, we stress on discussing the influence of the
existence of a third-atom on the two-atom entanglement and testing the
modulation effects of locally applied optical fields and fiber on the
entanglement properties of our system.


title:
Entangling Two-Atom Through Cooperative Interaction Under Stimulated
  Emission

abstract:
  We discuss the generation of two-atom entanglement inside a resonant
microcavity under stimulated emission (STE) interaction. The amount of
entanglement is shown based on different atomic initial state. For each kind of
intial state, we obtain the entanglement period and the entanglement critical
point, which are found to deeply depend on driving field density. In case of
atomic state $| ee >$, the entanglement can be induced due to STE. In case of
atomic state $| eg >$, there is a competition between driving field indued
entanglement and STE induced entanglement. When two atoms are initially in $|
gg >$, we can find a lumbar region where STE increases the amount and period of
entanglement.


title:
The dissipation of the system and the atom in two-photon Jaynes-Cummings
  model with degenerate atomic levels

abstract:
  The method of perturbative expansion of master equation is employed to study
the dissipative properties of system and of atom in the two-photon
Jaynes-Cummings model (JCM) with degenerate atomic levels. The numerical
results show that the degeneracy of atomic levels prolongs the period of
entanglement between the atom and the field. The asymptotic value of atomic
linear entropy is apparently increased by the degeneration. The amplitude of
local entanglement and disentanglement is suppressed. The better the initial
coherence property of the degenerate atom, the larger the coherence loss.


title: Engineering atom-atom thermal entanglement via two-photon process

abstract:
  We study the system that two atoms simultaneously interact with a single-mode
thermal field via different couplings and different spontaneous emission rates
when two-photon process is involved. It is found that we indeed can employ the
different couplings to produce the atom-atom thermal entanglement in two-photon
process. The different atomic spontaneous emission rates are also utilizable in
generating thermal entanglement. We also investigate the effect of the cavity
leakage. To the initial atomic state $|ee> ,$a slight leakage can relieve the
restriction of interaction time and we can obtain a large and steady
entanglement.


title:
Photon Frequency Mode Matching using Acousto-Optic Frequency Beam
  Splitters

abstract:
  It is a difficult engineering task to create distinct solid state single
photon sources which nonetheless emit photons at the same frequency. It is also
hard to create entangled photon pairs from quantum dots. In the spirit of
quantum engineering we propose a simple optical circuit which can, in the right
circumstances, make frequency distinguishable photons frequency
indistinguishable. Our circuit can supply a downstream solution to both
problems, opening up a large window of allowed frequency mismatches between
physical mechanisms. The only components used are spectrum analysers/prisms and
an Acousto-Optic Modulator. We also note that an Acousto-Optic Modulator can be
used to obtain Hong-Ou-Mandel two photon interference effects from the
frequency distinguishable photons generated by distinct sources.


title: Two-level quantum dynamics, integrability and unitary NOT gates

abstract:
  We study the dynamics of a two-level quantum system interacting with an
external electromagnetic field periodic and quasiperiodic in time. The quantum
evolution is described exactly by the classical equations of motion of a
gyromagnet in a time-dependent magnetic field. We prove that this classical
system is integrable as a consequence of the underlying unitary quantum
dynamics. As a consequence, for the periodic case: i) rigorous assessment of
the validity of the rotating-wave approximation (RWA) becomes possible even
beyond the assumptions of resonance and weak coupling (the latter conditions
are also shown to follow from the method of averaging); ii) we determine
conditions for the realization of the quantum NOT operation beyond the RWA, by
means of classical stroboscopic maps. The results bear upon areas as diverse as
quantum optics, nuclear magnetic resonance, and quantum computation.


title: A Bayesian Account of Quantum Histories

abstract:
  We investigate whether quantum history theories can be consistent with
Bayesian reasoning and whether such an analysis helps clarify the
interpretation of such theories. First, we summarise and extend recent work
categorising two different approaches to formalising multi-time measurements in
quantum theory. The standard approach consists of describing an ordered series
of measurements in terms of history propositions with non-additive
`probabilities'. The non-standard approach consists of defining multi-time
measurements to consist of sets of exclusive and exhaustive history
propositions and recovering the single-time exclusivity of results when
discussing single-time history propositions. We analyse whether such history
propositions can be consistent with Bayes' rule. We show that certain class of
histories are given a natural Bayesian interpretation, namely the linearly
positive histories originally introduced by Goldstein and Page. Thus we argue
that this gives a certain amount of interpretational clarity to the
non-standard approach. We also attempt a justification of our analysis using
Cox's axioms of probability theory.


title: Geometric nature in adiabatic evolution of dark eigenstates

abstract:
  In a recent Letter [Phys. Rev. Lett. {\bf 95}, 080502 (2005)], an interesting
scheme was proposed to implement a type of conditional quantum phase gates with
built-in fault-tolerant feature via adiabatic evolution of dark eigenstates. In
this comment we elaborate the geometric nature of the gate scheme and clarify
that it still belongs to a class of conventional geometric quantum computation.


title: Is there Unruh radiation?

abstract:
  It is generally accepted that a system undergoing uniform acceleration with
respect to zero-temperature vacuum will thermalize at a finite temperature (the
so-called Unruh temperature) that is proportional to the acceleration. However,
the question of whether or not the system actually radiates is highly
controversial. Thus, we are motivated to present an exact calculation using a
generalized quantum Langevin equation to describe an oscillator (the detector)
moving under a constant force and coupled to a one-dimensional scalar field
(scalar electrodynamics). Moreover, our analysis is simplified by using the
oscillator as a detector. We show that this system does not radiate despite the
fact that it does in fact thermalize at the Unruh temperature. We remark upon a
differing opinion expressed regarding a system coupled to the electromagnetic
field.


title: Joint measurements of spin, operational locality and uncertainty

abstract:
  Joint, or simultaneous, measurements of non-commuting observables are
possible within quantum mechanics, if one accepts an increase in the variances
of the jointly measured observables. In this paper, we discuss joint
measurements of a spin 1/2 particle along any two directions. Starting from an
operational locality principle, it is shown how to obtain a bound on how sharp
the joint measurement can be. We give a direct interpretation of this bound in
terms of an uncertainty relation.


title: Lower Bounds on Quantum Query Complexity

abstract:
  Shor's and Grover's famous quantum algorithms for factoring and searching
show that quantum computers can solve certain computational problems
significantly faster than any classical computer. We discuss here what quantum
computers_cannot_ do, and specifically how to prove limits on their
computational power. We cover the main known techniques for proving lower
bounds, and exemplify and compare the methods.


title: Extremality of Gaussian quantum states

abstract:
  We investigate Gaussian quantum states in view of their exceptional role
within the space of all continuous variables states. A general method for
deriving extremality results is provided and applied to entanglement measures,
secret key distillation and the classical capacity of Bosonic quantum channels.
We prove that for every given covariance matrix the distillable secret key rate
and the entanglement, if measured appropriately, are minimized by Gaussian
states. This result leads to a clearer picture of the validity of frequently
made Gaussian approximations. Moreover, it implies that Gaussian encodings are
optimal for the transmission of classical information through Bosonic channels,
if the capacity is additive.


title: Quantum optics of ultra-cold molecules

abstract:
  Quantum optics has been a major driving force behind the rapid experimental
developments that have led from the first laser cooling schemes to the
Bose-Einstein condensation (BEC) of dilute atomic and molecular gases. Not only
has it provided experimentalists with the necessary tools to create ultra-cold
atomic systems, but it has also provided theorists with a formalism and
framework to describe them: many effects now being studied in
quantum-degenerate atomic and molecular systems find a very natural explanation
in a quantum optics picture. This article briefly reviews three such examples
that find their direct inspiration in the trailblazing work carried out over
the years by Herbert Walther, one of the true giants of that field.
Specifically, we use an analogy with the micromaser to analyze ultra-cold
molecules in a double-well potential; study the formation and dissociation
dynamics of molecules using the passage time statistics familiar from
superradiance and superfluorescence studies; and show how molecules can be used
to probe higher-order correlations in ultra-cold atomic gases, in particular
bunching and antibunching.


title: An Atom Trap Relying on Optical Pumping

abstract:
  We have investigated a new radiation pressure trap which relies on optical
pumping and does not require any magnetic field. It employs six circularly
polarized divergent beams and works on the red of a $J_{g} \longrightarrow
J_{e} = J_{g} + 1$ atomic transition with $J_{g} \geq 1/2$. We have
demonstrated this trap with cesium atoms from a vapour cell using the 852 nm
$J_{g} = 4 \longrightarrow J_{e} = 5$ resonance transition. The trap contained
up to $3 \cdot 10^{7}$ atoms in a cloud of $1/\sqrt{e}$ radius of 330 $\mu$m.


title: Identifying a Two-State Hamiltonian in the Presence of Decoherence

abstract:
  Mapping the system evolution of a two-state system allows the determination
of the effective system Hamiltonian directly. We show how this can be achieved
even if the system is decohering appreciably over the observation time. A
method to include various decoherence models is given and the limits of this
technique are explored. This technique is applicable both to the problem of
calibrating a control Hamiltonian for quantum computing applications and for
precision experiments in two-state quantum systems. For simple models of
decoherence, this method can be applied even when the decoherence time is
comparable to the oscillation period of the system.


title:
Comprehensive proof of the Greenberger-Horne-Zeilinger Theorem for the
  four-qubit system

abstract:
  Greenberger-Horne-Zeilinger (GHZ) theorem asserts that there is a set of
mutually commuting nonlocal observables with a common eigenstate on which those
observables assume values that refute the attempt to assign values only
required to have them by the local realism of Einstein, Podolsky, and Rosen
(EPR). It is known that for a three-qubit system there is only one form of the
GHZ-Mermin-like argument with equivalence up to a local unitary transformation,
which is exactly Mermin's version of the GHZ theorem. In this paper, however,
for a four-qubit system which was originally studied by GHZ, we show that there
are nine distinct forms of the GHZ-Mermin-like argument. The proof is obtained
by using some geometric invariants to characterize the sets of mutually
commuting nonlocal spin observables on the four-qubit system. It is proved that
there are at most nine elements (except for a different sign) in a set of
mutually commuting nonlocal spin observables in the four-qubit system, and each
GHZ-Mermin-like argument involves a set of at least five mutually commuting
four-qubit nonlocal spin observables with a GHZ state as a common eigenstate in
GHZ's theorem. Therefore, we present a complete construction of the GHZ theorem
for the four-qubit system.


title:
Semiclassical quantization of non-Hamiltonian dynamical systems without
  memory

abstract:
  We propose a new method of quantization of a wide class of dynamical systems
that originates directly from the equations of motion. The method is based on
the correspondence between the classical and the quantum Poisson brackets,
postulated by Dirac. This correspondence applied to open (non-Hamiltonian)
systems allows one to point out the way of transition from the quantum
description based on the Lindblad equation to the dynamical description of
their classical analogs by the equations of motion and vice versa. As the
examples of using of the method we describe the procedure of the quantization
of three widely considered dynamical systems: 1) the harmonic oscillator with
friction, 2) the oscillator with a nonlinear damping that simulates the process
of the emergence of the limit cycle, and 3) the system of two periodic rotators
with a weak interaction that synchronizes their oscillations. We discuss a
possible application of the method for a description of quantum fluctuations in
Josephson junctions with a strong damping and for the quantization of open
magnetic systems with a dissipation and a pumping.


title:
Exact solution of quantum dynamics of a cantilever coupling to a single
  trapped ultracold ion

abstract:
  The quantum behavior of a precooled cantilever can be probed highly
efficiently by coupling to a trapped ultracold ion, in which a fast cooling of
the cantilever down to the ground vibrational state is possible. We solve the
dynamics of the coupling system by a squeezed-state expansion technique, and
can in principle obtain the exact solution of the time-evolution of the
coupling system. Compared to the treatment under rotating-wave approximation,
we can present a more accurate description of the quantum behavior of the
cantilever.


title: Efficient Circuits for Exact-Universal Computations with Qudits

abstract:
  This paper concerns the efficient implementation of quantum circuits for
qudits. We show that controlled two-qudit gates can be implemented without
ancillas and prove that the gate library containing arbitrary local unitaries
and one two-qudit gate, CINC, is exact-universal. A recent paper (PRL 94
230502) describes quantum circuits for qudits which require O(d^n) two-qudit
gates for state synthesis and O(d^{2n}) two-qudit gates for unitary synthesis,
matching the respective lower bound complexities. In this work, we present the
state synthesis circuit in much greater detail and prove that it is correct.
Also, the (n-2)/(d-2) ancillas required in the original algorithm may be
removed without changing the asymptotics. Further, we present a new algorithm
for unitary synthesis, inspired by the QR matrix decomposition, which is also
asymptotically optimal.


title:
Exponential complexity of an adiabatic algorithm for an NP-complete
  problem

abstract:
  We prove an analytical expression for the size of the gap between the ground
and the first excited state of quantum adiabatic algorithm for the
3-satisfiability, where the initial Hamiltonian is a projector on the subspace
complementary to the ground state. For large problem sizes the gap decreases
exponentially and as a consequence the required running time is also
exponential.


title: Mixing and Decoherence in Continuous-Time Quantum Walks on Cycles

abstract:
  We prove analytical results showing that decoherence can be useful for mixing
time in a continuous-time quantum walk on finite cycles. This complements the
numerical observations by Kendon and Tregenna (Physical Review A 67 (2003),
042315) of a similar phenomenon for discrete-time quantum walks. Our analytical
treatment of continuous-time quantum walks includes a continuous monitoring of
all vertices that induces the decoherence process. We identify the dynamics of
the probability distribution and observe how mixing times undergo the
transition from quantum to classical behavior as our decoherence parameter
grows from zero to infinity. Our results show that, for small rates of
decoherence, the mixing time improves linearly with decoherence, whereas for
large rates of decoherence, the mixing time deteriorates linearly towards the
classical limit. In the middle region of decoherence rates, our numerical data
confirms the existence of a unique optimal rate for which the mixing time is
minimized.


title:
Teleportation of an arbitrary mixture of diagonal states of multiqubits
  via classical correlation and classical communication

abstract:
  We propose a protocol in which the faithful and deterministic teleportation
of an arbitrary mixture of diagonal states is completed $via$ classical
correlation and classical communication. Our scheme can be generalized
straightforwardly to the case of $N$-qubits by using $N$ copies of classical
correlated pairs and classical communication. Moreover, a varying scheme by
using the generalized classical correlated state within a multiqubit space is
also presented. In addition, the arbitrary mixed state whose set of
eigenvectors is known are a direct application of our protocol.


title: Generating entangled photon pairs from a cavity-QED system

abstract:
  We propose a scheme for the controlled generation of Einstein-Podosky-Rosen
(EPR) entangled photon pairs from an atom coupled to a high Q optical cavity,
extending the prototype system as a source for deterministic single photons. A
thorough theoretical analysis confirms the promising operating conditions of
our scheme as afforded by currently available experimental setups. Our result
demonstrates the cavity QED system as an efficient and effective source for
entangled photon pairs, and shines new light on its important role in quantum
information science.


title: Quantum states on Harmonic lattices

abstract:
  We investigate bosonic Gaussian quantum states on an infinite cubic lattice
in arbitrary spatial dimensions. We derive general properties of such states as
ground states of quadratic Hamiltonians for both critical and non-critical
cases. Tight analytic relations between the decay of the interaction and the
correlation functions are proven and the dependence of the correlation length
on band gap and effective mass is derived. We show that properties of critical
ground states depend on the gap of the point-symmetrized rather than on that of
the original Hamiltonian. For critical systems with polynomially decaying
interactions logarithmic deviations from polynomially decaying correlation
functions are found. Moreover, we provide a generalization of the matrix
product state representation for Gaussian states and show that properties hold
analogously to the case of finite dimensional spin systems.


title:
Correlations, spectral gap, and entanglement in harmonic quantum systems
  on generic lattices

abstract:
  We investigate the relationship between the gap between the energy of the
ground state and the first excited state and the decay of correlation functions
in harmonic lattice systems. We prove that in gapped systems, the exponential
decay of correlations follows for both the ground state and thermal states.
Considering the converse direction, we show that an energy gap can follow from
algebraic decay and always does for exponential decay. The underlying lattices
are described as general graphs of not necessarily integer dimension, including
translationally invariant instances of cubic lattices as special cases. Any
local quadratic couplings in position and momentum coordinates are allowed for,
leading to quasi-free (Gaussian) ground states. We make use of methods of
deriving bounds to matrix functions of banded matrices corresponding to local
interactions on general graphs. Finally, we give an explicit entanglement-area
relationship in terms of the energy gap for arbitrary, not necessarily
contiguous regions on lattices characterized by general graphs.

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


title: Quantum Information Processing with Single Photons

abstract:
  Photons are natural carriers of quantum information due to their ease of
distribution and long lifetime. This thesis concerns various related aspects of
quantum information processing with single photons. Firstly, we demonstrate
N-photon entanglement generation through a generalised N X N symmetric beam
splitter known as the Bell multiport. A wide variety of 4-photon entangled
states as well as the N-photon W-state can be generated with an unexpected
non-monotonic decreasing probability of success with N. We also show how the
same setup can be used to generate multiatom entanglement. A further study of
multiports also leads us to a multiparticle generalisation of the
Hong-Ou-Mandel dip which holds for all Bell multiports of even number of input
ports. Next, we demonstrate a generalised linear optics based photon filter
that has a constant success probability regardless of the number of photons
involved. This filter has the highest reported success probability and is
interferometrically robust. Finally, we demonstrate how repeat-until-success
quantum computing can be performed with two distant nodes with unit success
probability using only linear optics resource. We further show that using
non-identical photon sources, robustness can still be achieved, an illustration
of the nature and advantages of measurement-based quantum computation. A direct
application to the same setup leads naturally to arbitrary multiphoton state
generation on demand. Finally, we demonstrate how polarisation entanglement of
photons can be detected from the emission of two atoms in a Young's double-slit
type experiment without linear optics, resulting in both atoms being also
maximally entangled.


title: On the Optimality of Quantum Encryption Schemes

abstract:
  It is well known that n bits of entropy are necessary and sufficient to
perfectly encrypt n bits (one-time pad). Even if we allow the encryption to be
approximate, the amount of entropy needed doesn't asymptotically change.
However, this is not the case when we are encrypting quantum bits. For the
perfect encryption of n quantum bits, 2n bits of entropy are necessary and
sufficient (quantum one-time pad), but for approximate encryption one
asymptotically needs only n bits of entropy. In this paper, we provide the
optimal trade-off between the approximation measure epsilon and the amount of
classical entropy used in the encryption of single quantum bits. Then, we
consider n-qubit encryption schemes which are a composition of independent
single-qubit ones and provide the optimal schemes both in the 2- and the
operator-norm. Moreover, we provide a counterexample to show that the
encryption scheme of Ambainis-Smith based on small-bias sets does not work in
the operator-norm.


title: Cloning of observables

abstract:
  We introduce the concept of cloning for classes of observables and classify
cloning machines for qubit systems according to the number of parameters needed
to describe the class under investigation. A no-cloning theorem for observables
is derived and the connections between cloning of observables and joint
measurements of noncommuting observables are elucidated. Relationships with
cloning of states and non-demolition measurements are also analyzed.


title: The ubiquitous XP commutator

abstract:
  Position and momentum of a particle can take any value in a continuous
spectrum; these values are independent but their indeterminacies are
correlated; momentum and position are mutually the generators of the
transformations in each other. It is shown in a concise way, how all these
features arise solely from their commutation relation $[X,P]=i\hbar$. The
article is complete and self contained, adequate for didactic use.


title: Elliptical torii in a constant magnetic field

abstract:
  The Schrodinger equation for an electron on the surface of an elliptical
torus in the presence of a constant azimuthally symmetric magnetic field is
developed. The single particle spectrum and eigenfunctions as a function of
magnetic flux through the torus are determined and it is shown that inclusion
of the geometric potential is necessary to recover the limiting cases of
vertical strip and flat ring structures.


title: Measurement driven quantum evolution

abstract:
  We study the problem of mapping an unknown mixed quantum state onto a known
pure state without the use of unitary transformations. This is achieved with
the help of sequential measurements of two non-commuting observables only. We
show that the overall success probability is maximized in the case of measuring
two observables whose eigenstates define mutually unbiased bases. We find that
for this optimal case the success probability quickly converges to unity as the
number of measurement processes increases and that it is almost independent of
the initial state. In particular, we show that to guarantee a success
probability close to one the number of consecutive measurements must be larger
than the dimension of the Hilbert space. We connect these results to quantum
copying, quantum deleting and entanglement generation.


title:
Predictability sieve, pointer states, and the classicality of quantum
  trajectories

abstract:
  We study various measures of classicality of the states of open quantum
systems subject to decoherence. Classical states are expected to be stable in
spite of decoherence, and are thought to leave conspicuous imprints on the
environment. Here these expected features of environment-induced superselection
(einselection) are quantified using four different criteria: predictability
sieve (which selects states that produce least entropy), purification time
(which looks for states that are the easiest to find out from the imprint they
leave on the environment), efficiency threshold (which finds states that can be
deduced from measurements on a smallest fraction of the environment), and
purity loss time (that looks for states for which it takes the longest to lose
a set fraction of their initial purity). We show that when pointer states --
the most predictable states of an open quantum system selected by the
predictability sieve -- are well defined, all four criteria agree that they are
indeed the most classical states. We illustrate this with two examples: an
underdamped harmonic oscillator, for which coherent states are unanimously
chosen by all criteria, and a free particle undergoing quantum Brownian motion,
for which most criteria select almost identical Gaussian states (although, in
this case, predictability sieve does not select well defined pointer states.)


title: Topological Quantum Computing with Only One Mobile Quasiparticle

abstract:
  In a topological quantum computer, universal quantum computation is performed
by dragging quasiparticle excitations of certain two dimensional systems around
each other to form braids of their world lines in 2+1 dimensional space-time.
In this paper we show that any such quantum computation that can be done by
braiding $n$ identical quasiparticles can also be done by moving a single
quasiparticle around n-1 other identical quasiparticles whose positions remain
fixed.


title:
Fast Ground State Manipulation of Neutral Atoms in Microscopic Optical
  Traps

abstract:
  We demonstrate Rabi flopping at MHz rates between ground hyperfine states of
neutral $^{87}$Rb atoms that are trapped in two micron sized optical traps.
Using tightly focused laser beams we demonstrate high fidelity, site specific
Rabi rotations with crosstalk on neighboring sites separated by $8 \mu\rm m$ at
the level of $10^{-3}$. Ramsey spectroscopy is used to measure a dephasing time
of $870 \mu\rm s$ which is $\approx$ 5000 times longer than the time for a
$\pi/2$ pulse.


title: On Superselection Rules in Bohm-Bell Theories

abstract:
  The meaning of superselection rules in Bohm-Bell theories (i.e., quantum
theories with particle trajectories) is different from that in orthodox quantum
theory. More precisely, there are two concepts of superselection rule, a weak
and a strong one. Weak superselection rules exist both in orthodox quantum
theory and in Bohm-Bell theories and represent the conventional understanding
of superselection rules. We introduce the concept of strong superselection
rule, which does not exist in orthodox quantum theory. It relies on the clear
ontology of Bohm-Bell theories and is a sharper and, in the Bohm-Bell context,
more fundamental notion. A strong superselection rule for the observable G
asserts that one can replace every state vector by a suitable statistical
mixture of eigenvectors of G without changing the particle trajectories or
their probabilities. A weak superselection rule asserts that every state vector
is empirically indistinguishable from a suitable statistical mixture of
eigenvectors of G. We establish conditions on G for both kinds of
superselection. For comparison, we also consider both kinds of superselection
in theories of spontaneous wave function collapse.


title: Spacetime algebra and electron physics

abstract:
  This paper surveys the application of geometric algebra to the physics of
electrons. It first appeared in 1996 and is reproduced here with only minor
modifications. Subjects covered include non-relativistic and relativistic
spinors, the Dirac equation, operators and monogenics, the Hydrogen atom,
propagators and scattering theory, spin precession, tunnelling times, spin
measurement, multiparticle quantum mechanics, relativistic multiparticle wave
equations, and semiclassical mechanics.


title: Quantum metrology

abstract:
  We point out a general framework that encompasses most cases in which quantum
effects enable an increase in precision when estimating a parameter (quantum
metrology). The typical quantum precision-enhancement is of the order of the
square root of the number of times the system is sampled. We prove that this is
optimal and we point out the different strategies (classical and quantum) that
permit to attain this bound.


title: Characterization of bipartite states using a single homodyne detector

abstract:
  We suggest a scheme to reconstruct the covariance matrix of a two-mode state
using a single homodyne detector plus a polarizing beam splitter and a
polarization rotator. It can be used to fully characterize bipartite Gaussian
states and to extract relevant informations on generic states.


title: The Communication Complexity of the Hamming Distance Problem

abstract:
  We investigate the randomized and quantum communication complexity of the
Hamming Distance problem, which is to determine if the Hamming distance between
two n-bit strings is no less than a threshold d. We prove a quantum lower bound
of \Omega(d) qubits in the general interactive model with shared prior
entanglement. We also construct a classical protocol of O(d \log d) bits in the
restricted Simultaneous Message Passing model, improving previous protocols of
O(d^2) bits (A. C.-C. Yao, Proceedings of the Thirty-Fifth Annual ACM Symposium
on Theory of Computing, pp. 77-81, 2003), and O(d\log n) bits (D. Gavinsky, J.
Kempe, and R. de Wolf, quant-ph/0411051, 2004).


title: Spacetime path formalism: localized states

abstract:
  This note is an addendum to quant-ph/0507115. In that paper, I present a
formalism for relativistic quantum mechanics in which the spacetime paths of
particles are considered fundamental, reproducing the standard results of the
traditional formulation of relativistic quantum mechanics and quantum field
theory. Now, it is well known that there are issues with the ability to
localize the position of particles in the usual formulation of relativistic
quantum mechanics. The present note shows how, in the spacetime path formalism,
the natural representation of on-shell 3-momentum states is effectively a
Foldy-Wouthuysen transformation of the traditional representation, addressing
the localization issues of position states and, further, providing a
straightforward non-relativistic limit.


title:
On the most efficient unitary transformation for programming quantum
  channels

abstract:
  We address the problem of finding the optimal joint unitary transformation on
system + ancilla which is the most efficient in programming any desired channel
on the system by changing the state of the ancilla. We present a solution to
the problem for dim(H)=2 for both system and ancilla.


title:
Correlation in superradiance: A closed-form approach to cooperative
  effects

abstract:
  We have developed a novel method to describe superradiance and related
cooperative and collective effects in a closed form. Using the method we derive
a two-atom master equation in which any complexity of atomic levels,
semiclassical coupling fields and quantum fluctuations in the fields can be
included, at least in principle. As an example, we consider the dynamics of an
initially inverted two-level system and show how even such in a simple system
phenomena such as the initial radiation burst or broadening due to
dipole-dipole interactions occur, but it is also possible to estimate the
population of the subradiant state during the radiative decay. Finally, we find
that correlation only, not entanglement is responsible for superradiance.


title: Spin Decoherence in a Gravitational Field

abstract:
  We discuss a mechanism of spin decoherence in gravitation within the
framework of general relativity. The spin state of a particle moving in a
gravitational field is shown to decohere due to the curvature of spacetime. As
an example, we analyze a particle going around a static spherically-symmetric
object.


title:
On the distribution of 1550-nm photon pairs efficiently generated using
  a periodically poled lithium niobate waveguide

abstract:
  We report on the generation of photon pairs in the 1550-nm band suitable for
long-distance fiber-optic quantum key distribution. The photon pairs were
generated in a periodically poled lithium niobate waveguide with a high
conversion-efficiency. Using a pulsed semiconductor laser with a pulse rate of
800 kHz and a maximum average pump power of 50 muW, we obtained a coincidence
rate of 600 s^-1. Our measurements are in agreement with a Poissonian
photon-pair distribution, as is expected from a comparison of the coherence
time of the pump and of the detected photons. An average of 0.9 photon pairs
per pulse was obtained.


title: CNOT gate by adiabatic passage with an optical cavity

abstract:
  We propose a scheme for the construction of a CNOT gate by adiabatic passage
in an optical cavity. In opposition to a previously proposed method, the
technique is not based on fractional adiabatic passage, which requires the
control of the ratio of two pulse amplitudes. Moreover, the technique
constitutes a decoherence-free method in the sense that spontaneous emission
and cavity damping are avoided since the dynamics follows dark states.


title: Efficient Implementation of Controlled-Rotations by Using Entanglement

abstract:
  Implementation of controlled-rotations using entanglement is considered. We
show that the successful probability is closely related to the entanglement and
the rotation angle. The successful probability will increase if we increase the
entanglement we use or decrease the controlled-rotation angle and the
probability will trend to unit when the entangled state trends to a Bell state
or the controlled-rotation angle trends to zero.