title: Constrainted Coherent States

abstract:
  Coherent states possess a regularized path integral and gives a natural
relation between classical variables and quantum operators. Recent work by
Klauder and Whiting has included extended variables, that can be thought of as
gauge fields, into this formalism. In this paper, I consider the next step, and
look at the roll of first class constraints.


title: Multi-mode density matrices of light via amplitude and phase control

abstract:
  A new method is described for determining the quantum state of correlated
multimode radiation by interfering the modes and measuring the statistics of
the superimposed fields in four-port balanced homodyne detection. The full
information on the $N$-mode quantum state is obtained by controlling both the
relative amplitudes and the phases of the modes, which simplifies the
reconstruction of density matrices to only $N+1$ Fourier transforms. In
particular, this method yields time-correlated multimode density matrices of
optical pulses by superimposing the signal by a sequence of short
local-oscillator pulses.


title: Quantum Cryptographic Network based on Quantum Memories

abstract:
  Quantum correlations between two particles show non-classical properties
which can be used for providing secure transmission of information. We present
a quantum cryptographic system, in which users store particles in quantum
memories kept in a transmission center. Correlations between the particles
stored by two users are created upon request by projecting their product state
onto a fully entangled state. Our system allows for secure communication
between any pair of users who have particles in the same center. Unlike other
quantum cryptographic systems, it can work without quantum channels and is
suitable for building a quantum cryptographic network. We also present a
modified system with many centers.


title: Quantum data processing and error correction

abstract:
  This paper investigates properties of noisy quantum information channels. We
define a new quantity called {\em coherent information} which measures the
amount of quantum information conveyed in the noisy channel. This quantity can
never be increased by quantum information processing, and it yields a simple
necessary and sufficient condition for the existence of perfect quantum error
correction.


title: Sending quantum entanglement through noisy channels

abstract:
  This paper addresses some general questions of quantum information theory
arising from the transmission of quantum entanglement through (possibly noisy)
quantum channels. A pure entangled state is prepared of a pair of systems $R$
and $Q$, after which $Q$ is subjected to a dynamical evolution given by the
superoperator $\superop^{Q}$. Two interesting quantities can be defined for
this process: the entanglement fidelity $F_{e}$ and the entropy production
$S_{e}$. It turns out that neither of these quantities depends in any way on
the system $R$, but only on the initial state and dynamical evolution of $Q$.
$F_{e}$ and $S_{e}$ are related to various other fidelities and entropies, and
are connected by an inequality reminiscent of the Fano inequality of classical
information theory. Some insight can be gained from these techniques into the
security of quantum cryptographic protocols and the nature of quantum
error-correcting codes.


title: Mixed State Entanglement and Quantum Error Correction

abstract:
  Entanglement purification protocols (EPP) and quantum error-correcting codes
(QECC) provide two ways of protecting quantum states from interaction with the
environment. In an EPP, perfectly entangled pure states are extracted, with
some yield D, from a mixed state M shared by two parties; with a QECC, an arbi-
trary quantum state $|\xi\rangle$ can be transmitted at some rate Q through a
noisy channel $\chi$ without degradation. We prove that an EPP involving one-
way classical communication and acting on mixed state $\hat{M}(\chi)$ (obtained
by sharing halves of EPR pairs through a channel $\chi$) yields a QECC on
$\chi$ with rate $Q=D$, and vice versa. We compare the amount of entanglement
E(M) required to prepare a mixed state M by local actions with the amounts
$D_1(M)$ and $D_2(M)$ that can be locally distilled from it by EPPs using one-
and two-way classical communication respectively, and give an exact expression
for $E(M)$ when $M$ is Bell-diagonal. While EPPs require classical communica-
tion, QECCs do not, and we prove Q is not increased by adding one-way classical
communication. However, both D and Q can be increased by adding two-way com-
munication. We show that certain noisy quantum channels, for example a 50%
depolarizing channel, can be used for reliable transmission of quantum states
if two-way communication is available, but cannot be used if only one-way com-
munication is available. We exhibit a family of codes based on universal hash-
ing able toachieve an asymptotic $Q$ (or $D$) of 1-S for simple noise models,
where S is the error entropy. We also obtain a specific, simple 5-bit single-
error-correcting quantum block code. We prove that {\em iff} a QECC results in
high fidelity for the case of no error the QECC can be recast into a form where
the encoder is the matrix inverse of the decoder.


title:
Coherent States for Kronecker Products of Non-Compact Groups:
  Formulation and Applications

abstract:
  We introduce and study the properties of a class of coherent states for the
group SU(1,1) X SU(1,1) and derive explicit expressions for these using the
Clebsch-Gordan algebra for the SU(1,1) group. We restrict ourselves to the
discrete series representations of SU(1,1). These are the generalization of the
`Barut Girardello' coherent states to the Kronecker Product of two non-compact
groups.The resolution of the identity and the analytic phase space
representation of these states is presented. This phase space representation is
based on the basis of products of `pair coherent states' rather than the
standard number state canonical basis. We discuss the utility of the resulting
`bi-pair coherent states' in the context of four-mode interactions in quantum
optics.


title: Decoherence Bounds on Quantum Computation with Trapped Ions

abstract:
  Using simple physical arguments we investigate the capabilities of a quantum
computer based on cold trapped ions. From the limitations imposed on such a
device by spontaneous decay, laser phase coherence, ion heating and other
sources of error, we derive a bound between the number of laser interactions
and the number of ions that may be used. The largest number which may be
factored using a variety of species of ion is determined.


title: Einstein-Podolsky-Rosen Correlations in Deuteron Photodisintegration

abstract:
  Einstein-Podolsky-Rosen correlations have so far been measured only between
pairs of photons and between pairs of protons. It is proposed to measure these
correlations between the proton and the neutron emerging from breakup of the
deuteron induced by gamma rays near threshold. The feasibility of the
experiment is discussed. Polarimeters with substantially higher overall
efficiency than the presently reported value of $10^{-4}$ are needed in order
to get enough events.


title: Stabilisation of Quantum Computations by Symmetrisation

abstract:
  We propose a method for the stabilisation of quantum computations (including
quantum state storage). The method is based on the operation of projection into
$\cal SYM$, the symmetric subspace of the full state space of $R$ redundant
copies of the computer. We describe an efficient algorithm and quantum network
effecting $\cal SYM$--projection and discuss the stabilising effect of the
proposed method in the context of unitary errors generated by hardware
imprecision, and nonunitary errors arising from external environmental
interaction. Finally, limitations of the method are discussed.


title: Reply to Comment: Quantum Cryptography Based on Orthogonal States?

abstract:
  This is our Reply to Peres' Comment [quant-ph/9509003] to "Quantum
Cryptography Based on Orthogonal States" [Phys. Rev. Lett. 75, 1239 (1995)].


title: The Persistent Quantum Bit

abstract:
  The construction of large, coherent quantum systems necessary for quantum
computation remains an entreating but elusive goal, due to the ubiquitous
nature of decoherence. Recent progress in quantum error correction schemes have
given new hope to this field, but thus far, the codes presented in the
literature assume a restricted number of errors and error free encoding,
decoding, and measurement. We investigate a specific scenario without these
assumptions; in particular, we evaluate a scheme to preserve a single quantum
bit against phase damping using a three-qubit encoding based on Shor. By
applying a new formalism which gives simple operators for decoherence and noisy
logic gates, we find the fidelity of the stored qubit as a function of time,
including decoherence which occurs not only during storage but also during
processing. We generalize our results to include any source of error, and
derive an upper limit on the allowable decoherence per timestep. Physically,
our results suggest the feasibility of engineering artificial metastable states
through repeated error correction.


title: Quantum Bit Regeneration

abstract:
  Decoherence and loss will limit the practicality of quantum cryptography and
computing unless successful error correction techniques are developed. To this
end, we have discovered a new scheme for perfectly detecting and rejecting the
error caused by loss (amplitude damping to a reservoir at T=0), based on using
a dual-rail representation of a quantum bit. This is possible because (1)
balanced loss does not perform a ``which-path'' measurement in an
interferometer, and (2) balanced quantum nondemolition measurement of the
``total'' photon number can be used to detect loss-induced quantum jumps
without disturbing the quantum coherence essential to the quantum bit. Our
results are immediately applicable to optical quantum computers using single
photonics devices.


title: Is Quantization Geometry?

abstract:
  The metric known to be relevant for standard quantization procedures receives
a natural interpretation and its explicit use simultaneously gives both
physical and mathematical meaning to a (coherent-state) phase-space path
integral, and at the same time establishes a fully satisfactory, geometric
procedure of quantization.


title: Coherent State Quantization of Constraint Systems

abstract:
  A careful reexamination of the quantization of systems with first- and
second-class constraints from the point of view of coherent-state phase-space
path integration reveals several significant distinctions from more
conventional treatments. Most significantly, we emphasize the importance of
using path-integral measures for Lagrange multipliers which ensure that the
quantum system satisfies the quantum constraint conditions. Our procedures
involve no delta-functionals of the classical constraints, no need for gauge
fixing of first-class constraints, no need to eliminate second-class
constraints, no potentially ambiguous determinants, and have the virtue of
resolving differences between canonical and path-integral approaches. Several
examples are considered in detail.


title: A Theory of Quantum Error-Correcting Codes

abstract:
  Quantum Error Correction will be necessary for preserving coherent states
against noise and other unwanted interactions in quantum computation and
communication. We develop a general theory of quantum error correction based on
encoding states into larger Hilbert spaces subject to known interactions. We
obtain necessary and sufficient conditions for the perfect recovery of an
encoded state after its degradation by an interaction. The conditions depend
only on the behavior of the logical states. We use them to give a recovery
operator independent definition of error-correcting codes. We relate this
definition to four others: The existence of a left inverse of the interaction,
an explicit representation of the error syndrome using tensor products, perfect
recovery of the completely entangled state, and an information theoretic
identity. Two notions of fidelity and error for imperfect recovery are
introduced, one for pure and the other for entangled states. The latter is more
appropriate when using codes in a quantum memory or in applications of quantum
teleportation to communication. We show that the error for entangled states is
bounded linearly by the error for pure states. A formal definition of
independent interactions for qubits is given. This leads to lower bounds on the
number of qubits required to correct $e$ errors and a formal proof that the
classical bounds on the probability of error of $e$-error-correcting codes
applies to $e$-error-correcting quantum codes, provided that the interaction is
dominated by an identity component.


title: A Quantum Lattice-Gas Model for the Many-Particle Schroedinger Equation

abstract:
  We consider a general class of discrete unitary dynamical models on the
lattice. We show that generically such models give rise to a wavefunction
satisfying a Schroedinger equation in the continuum limit, in any number of
dimensions. There is a simple mathematical relationship between the mass of the
Schroedinger particle and the eigenvalues of a unitary matrix describing the
local evolution of the model. Second quantized versions of these unitary models
can be defined, describing in the continuum limit the evolution of a
nonrelativistic quantum many-body theory. An arbitrary potential is easily
incorporated into these systems. The models we describe fall in the class of
quantum lattice gas automata, and can be implemented on a quantum computer with
a speedup exponential in the number of particles in the system. This gives an
efficient algorithm for simulating general nonrelativistic interacting quantum
many-body systems on a quantum computer.


title: Perfect quantum error correction coding in 24 laser pulses

abstract:
  An efficient coding circuit is given for the perfect quantum error correction
of a single qubit against arbitrary 1-qubit errors within a 5 qubit code. The
circuit presented employs a double `classical' code, i.e., one for bit flips
and one for phase shifts. An implementation of this coding circuit on an
ion-trap quantum computer is described that requires 26 laser pulses. A further
circuit is presented requiring only 24 laser pulses, making it an efficient
protection scheme against arbitrary 1-qubit errors. In addition, the
performance of two error correction schemes, one based on the quantum Zeno
effect and the other using standard methods, is compared. The quantum Zeno
error correction scheme is found to fail completely for a model of noise based
on phase-diffusion.


title:
Radiation Decohernce, State Vector Collapse and QED Nonequivalent
  Representations

abstract:
  The state vector evolution in the interaction of initial measured pure state
with collective quantum system or the field with a very large number of degrees
of freedom N is analysed in a nonperturbative QED formalism. As the example the
measurement of the electron final state scattered on nucleus or neutrino is
considered.In the nonperturbative field theory the complete manifold of the
system states is nonseparable i.e. is described by tensor product of infinitely
many independent Hilbert spaces. The interaction of this system with the
measured state can result in the final states which belong to different Hilbert
spaces which corresponds to different values of some classical observables,i.e.
spontaneous symmetry breaking occurs. Interference terms (IT) between such
states in the measurement of any Hermitian observable are infinitely small and
due to it the final pure states can't be distinguished from the mixed ones,
characteristic for the state collapse. The evolution from initial to final
system state is nonunitary and become formally irreversible in the limit of
infinite time. The electromagnetic (e-m) bremmstrahlung produced in the
electron scattering process contain the unrestricted number of soft photons
which radiation flux become classic observable. Analoguous processes which
occurs in the second kind phase transitions in ferromagnetic and phonon
excitations in cristall lattice are considered briefly.


title:
A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming
  Bound

abstract:
  I develop methods for analyzing quantum error-correcting codes, and use these
methods to construct an infinite class of codes saturating the quantum Hamming
bound. These codes encode $k=n-j-2$ qubits in $n=2^j$ qubits and correct $t=1$
error.


title:
Quantum privacy amplification and the security of quantum cryptography
  over noisy channels

abstract:
  Existing quantum cryptographic schemes are not, as they stand, operable in
the presence of noise on the quantum communication channel. Although they
become operable if they are supplemented by classical privacy-amplification
techniques, the resulting schemes are difficult to analyse and have not been
proved secure. We introduce the concept of quantum privacy amplification and a
cryptographic scheme incorporating it which is provably secure over a noisy
channel. The scheme uses an `entanglement purification' procedure which,
because it requires only a few quantum Controlled-Not and single-qubit
operations, could be implemented using technology that is currently being
developed. The scheme allows an arbitrarily small bound to be placed on the
information that any eavesdropper may extract from the encrypted message.


title: The Parity Bit in Quantum Cryptography

abstract:
  An $n$-bit string is encoded as a sequence of non-orthogonal quantum states.
The parity bit of that $n$-bit string is described by one of two density
matrices, $\rho_0^{(n)}$ and $\rho_1^{(n)}$, both in a Hilbert space of
dimension $2^n$. In order to derive the parity bit the receiver must
distinguish between the two density matrices, e.g., in terms of optimal mutual
information. In this paper we find the measurement which provides the optimal
mutual information about the parity bit and calculate that information. We
prove that this information decreases exponentially with the length of the
string in the case where the single bit states are almost fully overlapping. We
believe this result will be useful in proving the ultimate security of quantum
crytography in the presence of noise.


title:
Quantum Electronic Devices Based on Metal-Dielectric Transition in
  Low-Dimensional Quantum Structures

abstract:
  Two types of optically manipulated quantum electronic devices are considered:
a quantum dot and a finite periodic molecular chain, with the period doubled
under resonance optical excitation. The stability of the working regimes of the
devices in large scale of temperatures is discussed. Some motivation in favor
of the molecular chain is suggested. A class of materials, which can be used
for producing this device is discussed.


title: Quantum Mechanics of Measurement

abstract:
  An analysis of quantum measurement is presented that relies on an
information-theoretic description of quantum entanglement. In a consistent
quantum information theory of entanglement, entropies (uncertainties)
conditional on measurement outcomes can be negative, implying that measurement
can be described via unitary, entropy-conserving, interactions, while still
producing randomness in a measurement device. In such a framework, quantum
measurement is not accompanied by a wave-function collapse, or a quantum jump.
The theory is applied to the measurement of incompatible variables, giving rise
to a stronger entropic uncertainty relation than heretofore known. It is also
applied to standard quantum measurement situations such as the Stern-Gerlach
and double-slit experiments to illustrate how randomness, inherent in the
conventional quantum probabilities, arises in a unitary framework. Finally, the
present view clarifies the relationship between classical and quantum concepts.


title:
A note on the supplementary variables in spin-measuring equipments in
  the EPR-Bell experiment

abstract:
  We discuss supplementary (or hidden) variables in spin-measuring equipments
in EPR-Bell experiment. This theme was considered in a Bell's later work. We
generalize it. First, we show why the original supplementary variable $\lambda$
is not to be regarded to include supplementary variables in spin-measuring
equipments (why supplementary variables should be introduced additionally in
spin-measuring equipments) Next, we show the followings. When the supplementary
variables introduced in spin-measuring equipments have local correlations, the
Bell inequality is recovered. On the other hand, when they have nonlocal
correlations, the Bell inequality is not recovered. This fact is in accord with
the fact that the Bell inequality is derived for local realistic models.


title:
Action and Passion at a Distance: An Essay in Honor of Professor Abner
  Shimony

abstract:
  Quantum mechanics permits nonlocality---both nonlocal correlations and
nonlocal equations of motion---while respecting relativistic causality. Is
quantum mechanics the unique theory that reconciles nonlocality and causality?
We consider two models, going beyond quantum mechanics, of
nonlocality---``superquantum" correlations, and nonlocal ``jamming" of
correlations---and derive new results for the jamming model. In one space
dimension, jamming allows reversal of the sequence of cause and effect; in
higher dimensions, however, effect never precedes cause.


title: Quantum Error Correction and Orthogonal Geometry

abstract:
  A group theoretic framework is introduced that simplifies the description of
known quantum error-correcting codes and greatly facilitates the construction
of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1
error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors,
and 1 to 29 qubits correcting 5 errors.


title: Two-Photon Algebra Eigenstates: A Unified Approach to Squeezing

abstract:
  We use the concept of the algebra eigenstates that provides a unified
description of the generalized coherent states (belonging to different sets)
and of the intelligent states associated with a dynamical symmetry group. The
formalism is applied to the two-photon algebra and the corresponding algebra
eigenstates are studied by using the Fock-Bargmann analytic representation.
This formalism yields a unified analytic approach to various types of
single-mode photon states generated by squeezing and displacing
transformations.


title: On the Security of Quantum Cryptography Against Collective Attacks

abstract:
  We present strong attacks against quantum key distribution schemes which use
quantum memories and quantum gates to attack directly the final key. We analyze
a specific attack of this type, for which we find the density matrices
available to the eavesdropper and the optimal information which can be
extracted from them. We prove security against this attack and discuss security
against any attack allowed by the rules of quantum mechanics.


title: Understanding the quantum Zeno effect

abstract:
  The quantum Zeno effect consists in the hindrance of the evolution of a
quantum system that is very frequently monitored and found to be in its initial
state at every single measurement. On the basis of the correct formula for the
survival probability, i.e. the probability of finding the system in its initial
state at every single measurement, we critically analyze a recent proposal and
experimental test, that make use of an oscillating system.


title: Error symmetrization in quantum computers

abstract:
  It is possible to reduce some types of quantum computation errors by
symmetrizing the quantum state of a redundant array. Various models are
discussed.


title: Bounds on Information and the Security of Quantum Cryptography

abstract:
  Strong attacks against quantum key distribution use quantum memories and
quantum gates to attack directly the final key. In this paper we extend a novel
security result recently obtained, to demonstrate proofs of security against a
wide class of such attacks. To reach this goal we calculate
information-dependent reduced density matrices, we study the geometry of
quantum mixed states, and we find bounds on the information leaked to an
eavesdropper. Our result suggests that quantum cryptography is ultimately
secure.


title: Fault-tolerant quantum computation

abstract:
  Recently, it was realized that use of the properties of quantum mechanics
might speed up certain computations dramatically. Interest in quantum
computation has since been growing. One of the main difficulties of realizing
quantum computation is that decoherence tends to destroy the information in a
superposition of states in a quantum computer, thus making long computations
impossible. A futher difficulty is that inaccuracies in quantum state
transformations throughout the computation accumulate, rendering the output of
long computations unreliable. It was previously known that a quantum circuit
with t gates could tolerate O(1/t) amounts of inaccuracy and decoherence per
gate. We show, for any quantum computation with t gates, how to build a
polynomial size quantum circuit that can tolerate O(1/(log t)^c) amounts of
inaccuracy and decoherence per gate, for some constant c. We do this by showing
how to compute using quantum error correcting codes. These codes were
previously known to provide resistance to errors while storing and transmitting
quantum data.


title: Quantum dephasing by chaos

abstract:
  We examine whether the chaotic behavior of classical systems with a limited
number of degrees of freedom can produce quantum dephasing, against the
conventional idea that dephasing takes place only in large systems with a huge
number of constituents and complicated internal interactions. On the basis of
this analysis, we briefly discuss the possibility of defining quantum chaos and
of inventing a ``chaos detector".


title: Quantum Logical Operations on Encoded Qubits

abstract:
  We show how to carry out quantum logical operations (controlled-not and
Toffoli gates) on encoded qubits for several encodings which protect against
various 1-bit errors. This improves the reliability of these operations by
allowing one to correct for one bit errors which either preexisted or occurred
in course of operation. The logical operations we consider allow one to cary
out the vast majority of the steps in the quantum factoring algorithm. Thus,
our results help bring quantum factoring and other quantum computations closer
to reality


title: Information Gain vs. State Disturbance in Quantum Theory

abstract:
  The engine that powers quantum cryptography is the principle that there are
no physical means for gathering information about the identity of a quantum
system's state (when it is known to be prepared in one of a set of
nonorthogonal states) without disturbing the system in a statistically
detectable way. This situation is often mistakenly described as a consequence
of the ``Heisenberg uncertainty principle.'' A more accurate account is that it
is a unique feature of quantum phenomena that rests ultimately on the Hilbert
space structure of the theory along with the fact that time evolutions for
isolated systems are unitary. In this paper I explore several aspects of the
``information / disturbance principle'' in an attempt to make it firmly
quantitative for both pure and mixed states. The final section briefly explores
the extent to which such a principle can be taken as a foundation for unitary
dynamics rather than as a consequence.


title:
Generalized Moyal structures in phase space, kinetic equations and their
  classical limit: I. General Formalism

abstract:
  Generalised Wigner and Weyl transformations of quantum operators are defined
and their properties, as well as those of the algebraic structure induced on
the phase-space are studied. Using such transformations, quantum linear
evolution equations are given a phase-space representation. In particular this
is done for the general kinetic equation of the Lindblad type. The resulting
expressions are better suited for the passage to the classical limit and for a
general comparison of classical and quantum systems. In this context a
preliminary discussion of a number of problems of kinetic theory of open
systems is given, whereas explicit applications are made in the next paper of
the series.


title:
Generalized Moyal structures in phase space, kinetic equations and their
  classical limit: II. Applications to harmonic oscillator models

abstract:
  The formalism of generalized Wigner transformations developped in a previous
paper, is applied to kinetic equations of the Lindblad type for quantum
harmonic oscillator models. It is first applied to an oscillator coupled to an
equilibrium chain of other oscillators having nearest-neighbour interactions.
The kinetic equation is derived without using the so called rotating-wave
approximation. Then it is shown that the classical limit of the corresponding
phase-space equation is independent of the ordering of operators corresponding
to the inverse of the generalized Wigner transformation, provided the latter is
involutive. Moreover, this limit equation, which conserves the probabilistic
nature of the distribution function and obeys an H-theorem, coincides with the
kinetic equation for the corresponding classical system, which is derived
independently and is distinct from that usually obtained in the litterature and
not sharing the above properties. Finally the same formalism is applied to more
general model equations used in quantum optics and it is shown that the above
results remain unaltered.


title: System and Its Uncertainty Quanta: Theory of General System (I)

abstract:
  The concept of uncertainty quanta for a general system is introduced and
applied to some important problems in physics and mathematics. EPR paradox
gives new clue to the further understanding of particle correlation which turns
out to be the nature of this world. Randomness in quantum mechanics,
statistical physics and chaos is integrated. A picture for a new kind of
mathematics is put forward.


title: Where Has Entropy Gone: Theory of General System (II)

abstract:
  A pair of symmetric expressions for the second law of thermodynamics is put
forward. The conservation and transfer of entropy is discussed and applied to
problems like biology, culture and life itself. A new explanation is given to
the cosmic expansion with the concept of diversity in this theory. The problem
of contingency and necessity is also discussed.


title: Quantum Cosmology: Theory of General System (III)

abstract:
  The concepts of the perfect system and degeneracy are introduced. A special
symmetry is found which is related to the entropy invariant. The inversion
relation of system is obtained which is used to give the oppsite direction of
time to classical sencond law of thermodanymics. The nature of time is
discussed together with causality relation. A new understanding of quantum
mechanics is put forward which describes a new picture of the world.


title: Calculation of Electric Unit charge

abstract:
  Considering the stresses due to the vacuum fluctuation and the electric
charge loaded over the surface of a spherical cavity, we estimate the maximum
value of the charge. Since this value is independent of the cavity size and
parameter free, it is regarded as the electric unit charge. Our result is $Q=
1.55\times 10^{-19}$ Coulomb which implies the relevant fine structure constant
$\alpha=1/145.90$.


title: Simple Quantum Error Correcting Codes

abstract:
  Methods of finding good quantum error correcting codes are discussed, and
many example codes are presented. The recipe C_2^{\perp} \subseteq C_1, where
C_1 and C_2 are classical codes, is used to obtain codes for up to 16
information qubits with correction of small numbers of errors. The results are
tabulated. More efficient codes are obtained by allowing C_1 to have reduced
distance, and introducing sign changes among the code words in a systematic
manner. This systematic approach leads to single-error correcting codes for 3,
4 and 5 information qubits with block lengths of 8, 10 and 11 qubits
respectively.


title:
Quantum Ballistic Evolution in Quantum Mechanics: Application to Quantum
  Computers

abstract:
  Quantum computers are important examples of processes whose evolution can be
described in terms of iterations of single step operators or their adjoints.
Based on this, Hamiltonian evolution of processes with associated step
operators $T$ is investigated here. The main limitation of this paper is to
processes which evolve quantum ballistically, i.e. motion restricted to a
collection of nonintersecting or distinct paths on an arbitrary basis. The main
goal of this paper is proof of a theorem which gives necessary and sufficient
conditions that T must satisfy so that there exists a Hamiltonian description
of quantum ballistic evolution for the process, namely, that T is a partial
isometry and is orthogonality preserving and stable on some basis. Simple
examples of quantum ballistic evolution for quantum Turing machines with one
and with more than one type of elementary step are discussed. It is seen that
for nondeterministic machines the basis set can be quite complex with much
entanglement present. It is also proved that, given a step operator T for an
arbitrary deterministic quantum Turing machine, it is decidable if T is stable
and orthogonality preserving, and if quantum ballistic evolution is possible.
The proof fails if T is a step operator for a nondeterministic machine. It is
an open question if such a decision procedure exists for nondeterministic
machines. This problem does not occur in classical mechanics.


title: Unitarity in one dimensional nonlinear quantum cellular automata

abstract:
  Unitarity of the global evolution is an extremely stringent condition on
finite state models in discrete spacetime. Quantum cellular automata, in
particular, are tightly constrained. In previous work we proved a simple No-go
Theorem which precludes nontrivial homogeneous evolution for linear quantum
cellular automata. Here we carefully define general quantum cellular automata
in order to investigate the possibility that there be nontrivial homogeneous
unitary evolution when the local rule is nonlinear. Since the unitary global
transition amplitudes are constructed from the product of local transition
amplitudes, infinite lattices require different treatment than periodic ones.
We prove Unitarity Theorems for both cases, expressing the equivalence in $1+1$
dimensions of global unitarity and certain sets of constraints on the local
rule, and then show that these constraints can be solved to give a variety of
multiparameter families of nonlinear quantum cellular automata. The Unitarity
Theorems, together with a Surjectivity Theorem for the infinite case, also
imply that unitarity is decidable for one dimensional cellular automata.


title: Quaternionic quantum interferometry

abstract:
  If scattering amplitudes are ordinary complex numbers (not quaternions) there
is a universal algebraic relationship between the six coherent cross sections
of any three scatterers (taken singly and pairwise). A violation of this
relationship would indicate either that scattering amplitudes are quaternions,
or that the superposition principle fails. Some possible experimental tests
involve neutron interferometry, K_S-meson regeneration, and low energy
proton-proton scattering.


title: How much does it cost to teleport?

abstract:
  We show that the entropy of entanglement of a state characterizes its ability
to teleport. In particular, in order to teleport faithfully an unknown quantum
$N$-state, the two users must share an entangled state with at least $\log_2 N$
bits entropy of entanglement. We also note that the maximum capacity for a
mixed state ${\cal M}$ to teleport equals the maximum amount of entanglement
entropy that can be distilled out from ${\cal M}$. Our result, therefore,
provides an alternative interpretation for entanglement purification.


title: Why quantum bit commitment and ideal quantum coin tossing are impossible

abstract:
  There had been well known claims of ``provably unbreakable'' quantum
protocols for bit commitment and coin tossing. However, we, and independently
Mayers, showed that all proposed quantum bit commitment (and therefore coin
tossing) schemes are, in principle, insecure because the sender, Alice, can
always cheat successfully by using an EPR-type of attack and delaying her
measurements. One might wonder if secure quantum bit commitment and coin
tossing protocols exist at all. Here we prove that an EPR-type of attack by
Alice will, in principle, break {\em any} realistic quantum bit commitment and
{\em ideal} coin tossing scheme. Therefore, provided that Alice has a quantum
computer and is capable of storing quantum signals for an arbitrary length of
time, all those schemes are insecure. Since bit commitment and coin tossing are
useful primitives for building up more sophisticated protocols such as
zero-knowledge proofs, our results cast very serious doubt on the security of
quantum cryptography in the so-called ``post-cold-war'' applications.


title: Applications of the Complex Geometric "Phase" for Meta-stable Systems

abstract:
  Garrison and Wright showed that upon undergoing cyclic quantum evolution a
meta-stable state acquires both a geometric phase and a geometric decay
probability. This is described by a complex geometric ``phase'' associated with
the cyclic evolution of two states and is closely related to the two state
formalism developed by Aharonov et al.. Applications of the complex geometric
phase to the Born--Oppenheimer approximation and the Aharonov--Bohm effect are
considered. A simple experiment based on the optical properties of absorbing
birefringent crystals is proposed.


title:
Perturbative Scattering Phase Shifts in One-Dimension: Closed-form
  Results

abstract:
  A simple closed form expression is obtained for the scattering phase shift
perturbatively to any given order in effective one-dimensional problems. The
result is a hierarchical scheme, expressible in quadratures, requiring only
knowledge of the zeroth order solution and the perturbation potential.


title: Exponential Decay of Wavelength in a Dissipative System

abstract:
  Applying a technique developed in a recent work[1] to calculate wavefunction
evolution in a dissipative system with Ohmic friction, we show that the
wavelength of the wavefunction decays exponentially, while the Brownian motion
width gradually increases. In an interference experiment, when these two
parameters become equal, the Brownian motion erases the fringes, the system
thus approaches classical limit. We show that the wavelength decay is an
observable phenomenon.


title: Proposing Quantum Relativity and Finite Program

abstract:
  We show monistic realism consistent with quantum theory may be restored by
extending the essential idea of relativity in such a way that every physical
system is eligible, in principle, for an observing system. As a result, a
common logical basis of quantum theory and relativity, and hence that of modern
quantum gauge theories emerges. Supported by this logic, we propose to
reconstruct physics solely from finite EPR complexes. Along the discussion an
interpretation of String theory is provided. Aside from conceptual appeal and a
priori mathematical finiteness, our point of view drastically explains in a
rather trivial fashion some basic problems which are otherwise unlikely to be
resolved: Namely, the increase of entropy in macro scales, and the issue of the
cosmic coincidence. In fact, the expansion of the universe may be given a
tautological reasoning in our context.


title: Fault-Tolerant Error Correction with Efficient Quantum Codes

abstract:
  We exhibit a simple, systematic procedure for detecting and correcting errors
using any of the recently reported quantum error-correcting codes. The
procedure is shown explicitly for a code in which one qubit is mapped into
five. The quantum networks obtained are fault tolerant, that is, they can
function successfully even if errors occur during the error correction. Our
construction is derived using a recently introduced group-theoretic framework
for unifying all known quantum codes.


title: Functional Forms for the Squeeze and the Time-Displacement Operators

abstract:
  Using Baker-Campbell-Hausdorff relations, the squeeze and harmonic-oscillator
time-displacement operators are given in the form $\exp[\delta I] \exp[\alpha
(x^2)]\exp[\beta(x\partial)] \exp[\gamma (\partial)^2]$, where $\alpha$,
$\beta$, $\gamma$, and $\delta$ are explicitly determined. Applications are
discussed.


title:
Resummation of anisotropic quartic oscillator. Crossover from
  anisotropic to isotropic large-order behavior

abstract:
  We present an approximative calculation of the ground-state energy for the
anisotropic anharmonic oscillator Using an instanton solution of the isotropic
action $\delta = 0$, we obtain the imaginary part of the ground-state energy
for small negative $g$ as a series expansion in the anisotropy parameter
$\delta$. From this, the large-order behavior of the $g$-expansions
accompanying each power of $\delta$ are obtained by means of a dispersion
relation in $g$. These $g$-expansions are summed by a Borel transformation,
yielding an approximation to the ground-state energy for the region near the
isotropic limit. This approximation is found to be excellent in a rather wide
region of $\delta$ around $\delta = 0$. Special attention is devoted to the
immediate vicinity of the isotropic point. Using a simple model integral we
show that the large-order behavior of an $\delta$-dependent series expansion in
$g$ undergoes a crossover from an isotropic to an anisotropic regime as the
order $k$ of the expansion coefficients passes the value $k_{{\rm cross} \sim
1/ |{\delta}|$.


title: Tight bounds on quantum searching

abstract:
  We provide a tight analysis of Grover's recent algorithm for quantum database
searching. We give a simple closed-form formula for the probability of success
after any given number of iterations of the algorithm. This allows us to
determine the number of iterations necessary to achieve almost certainty of
finding the answer. Furthermore, we analyse the behaviour of the algorithm when
the element to be found appears more than once in the table and we provide a
new algorithm to find such an element even when the number of solutions is not
known ahead of time. Using techniques from Shor's quantum factoring algorithm
in addition to Grover's approach, we introduce a new technique for approximate
quantum counting, which allows to estimate the number of solutions. Finally we
provide a lower bound on the efficiency of any possible quantum database
searching algorithm and we show that Grover's algorithm nearly comes within a
factor 2 of being optimal in terms of the number of probes required in the
table.


title: Teleportation as a quantum computation

abstract:
  An explicit quantum circuit is given to implement quantum teleportation. This
circuit makes teleportation straightforward to anyone who believes that quantum
computation is a reasonable proposition. It could also be genuinely used inside
a quantum computer if teleportation is needed to move quantum information
around. An unusual feature of this circuit is that there are points in the
computation at which the quantum information can be completely disrupted by a
measurement (or some types of interaction with the environment) without ill
effects: the same final result is obtained whether or not these measurements
takes place.


title: Bose-Einstein Correlations and Sonoluminescence

abstract:
  Sonoluminescence may be studied in detail by intensity correlations among the
emitted photons. As an example, we discuss an experiment to measure the size of
the light-emitting region by the Hanbury Brown-Twiss effect. We show that
single bubble sonoluminescence is almost ideally suited for study by this
method and that plausible values for the physical parameters are within easy
experimental reach. A sequence of two and higher order photon correlation
experiments is outlined.


title: On the Consistent Effect Histories Approach to Quantum Mechanics

abstract:
  A formulation of the consistent histories approach to quantum mechanics in
terms of generalized observables (POV measures) and effect operators is
provided. The usual notion of `history' is generalized to the notion of `effect
history'. The space of effect histories carries the structure of a D-poset.
Recent results of J.D. Maitland Wright imply that every decoherence functional
defined for ordinary histories can be uniquely extended to a bi-additive
decoherence functional on the space of effect histories. Omnes' logical
interpretation is generalized to the present context. The result of this work
considerably generalizes and simplifies the earlier formulation of the
consistent effect histories approach to quantum mechanics communicated in a
previous work of this author.


title: Separability of Mixed States: Necessary and Sufficient Conditions

abstract:
  We provide necessary and sufficient conditions for separability of mixed
states. As a result we obtain a simple criterion of separability for $2\times2$
and $2\times3$ systems. Here, the positivity of the partial transposition of a
state is necessary and sufficient for its separability. However, it is not the
case in general. Some examples of mixtures which demonstrate the utility of the
criterion are considered.


title: Quantum Information Theory of Entanglement and Measurement

abstract:
  We present a quantum information theory that allows for a consistent
description of entanglement. It parallels classical (Shannon) information
theory but is based entirely on density matrices (rather than probability
distributions) for the description of quantum ensembles. We find that quantum
conditional entropies can be negative for entangled systems, which leads to a
violation of well-known bounds in Shannon information theory. Such a unified
information-theoretic description of classical correlation and quantum
entanglement clarifies the link between them: the latter can be viewed as
``super-correlation'' which can induce classical correlation when considering a
tripartite or larger system. Furthermore, negative entropy and the associated
clarification of entanglement paves the way to a natural information-theoretic
description of the measurement process. This model, while unitary and causal,
implies the well-known probabilistic results of conventional quantum mechanics.
It also results in a simple interpretation of the Kholevo theorem limiting the
accessible information in a quantum measurement.


title:
Berry Phases with Real Hamiltonians With and Without a Many-body System
  as a Background

abstract:
  We present both the gauge theoretic description and the numerical
calculations of the Berry phases with the real eigenstates, involving one with
a many-body system as a background and the other with no such background. We
demonstrate that for the former the sign of the Berry phase factor for a spin
$\f{1}{2}$ particle (hole) coupled to a slow subsystem (phonon) depends on both
the strength of electron correlations and the characteristics of the closed
paths, unlike the cases for the latter.


title:
Phase Space Representation for Open Quantum Systems within the Lindblad
  Theory

abstract:
  The Lindblad master equation for an open quantum system with a Hamiltonian
containing an arbitrary potential is written as an equation for the Wigner
distribution function in the phase space representation. The time derivative of
this function is given by a sum of three parts: the classical one, the quantum
corrections and the contribution due to the opening of the system. In the
particular case of a harmonic oscillator, quantum corrections do not exist.


title:
A generalized Pancharatnam geometric phase formula for three level
  systems

abstract:
  We describe a generalisation of the well known Pancharatnam geometric phase
formula for two level systems, to evolution of a three-level system along a
geodesic triangle in state space. This is achieved by using a recently
developed generalisation of the Poincare sphere method, to represent pure
states of a three-level quantum system in a convenient geometrical manner. The
construction depends on the properties of the group $SU(3)\/$ and its
generators in the defining representation, and uses geometrical objects and
operations in an eight dimensional real Euclidean space. Implications for an
n-level system are also discussed.


title: A fast quantum mechanical algorithm for database search

abstract:
  Imagine a phone directory containing N names arranged in completely random
order. In order to find someone's phone number with a 50% probability, any
classical algorithm (whether deterministic or probabilistic) will need to look
at a minimum of N/2 names. Quantum mechanical systems can be in a superposition
of states and simultaneously examine multiple names. By properly adjusting the
phases of various operations, successful computations reinforce each other
while others interfere randomly. As a result, the desired phone number can be
obtained in only O(sqrt(N)) steps. The algorithm is within a small constant
factor of the fastest possible quantum mechanical algorithm.


title: Unconditionally secure quantum bit commitment is impossible

abstract:
  The claim of quantum cryptography has always been that it can provide
protocols that are unconditionally secure, that is, for which the security does
not depend on any restriction on the time, space or technology available to the
cheaters. We show that this claim does not hold for any quantum bit commitment
protocol. Since many cryptographic tasks use bit commitment as a basic
primitive, this result implies a severe setback for quantum cryptography. The
model used encompasses all reasonable implementations of quantum bit commitment
protocols in which the participants have not met before, including those that
make use of the theory of special relativity.


title: The tunneling time for a wave packet as measured with a physical clock

abstract:
  We study the time required for a wave packet to tunnel beyond a square
barrier, or to be reflected, by envisaging a physical clock which ticks only
when the particle is within the barrier region. The clock consists in a
magnetic moment initially aligned with the $x$ axis which in the barrier region
precesses around a constant magnetic field aligned with the $z$ axis, the
motion being in the $y$ direction. The values of the $x$ and $y$ components of
the magnetic moment beyond or in front of the barrier allow to assign a
tunneling or reflection time to every fraction of the packet which emerges from
the barrier and to calculate tunneling times $\tau_{\rm T,x}$ and $\tau_{\rm
T,y}$ and reflection times $\tau_{\rm R,x}$ and $\tau_{\rm R,y}$. The times
$\tau_{\rm T,x}$ and $\tau_{\rm T,y}$ ($\tau_{\rm R,x}$ and $\tau_{\rm R,y}$)
are remarkably equal, and independent of the initial position (in front of the
barrier) of the packet.


title:
Heisenberg-picture approach to the exact quantum motion of a
  time-dependent forced harmonic oscillator

abstract:
  In the Heisenberg picture, the generalized invariant and exact quantum
motions are found for a time-dependent forced harmonic oscillator. We find the
eigenstate and the coherent state of the invariant and show that the
dispersions of these quantum states do not depend on the external force. Our
formalism is applied to several interesting cases.


title: A Local Model of Explicit Wavefunction Collapse

abstract:
  A model of spontaneous wavefunction collapse, which is explicitly local and
Lorentz-invariant, is defined. Some of the predictions of the model for
specific experimental situations are derived. It is shown that, although
incompatible collapses, e.g. on opposite sides of an EPR-type of experiment,
can occur, they will not persist in time and that eventually only compatible
results will be obtained. The probabilities of particular results, however,
will in general not agree with the predictions of quantum theory. We argue that
it is unlikely that the deviations would have been seen in any experiment yet
performed.


title: Classical and Fluctuating Paths in Spaces with Curvature and Torsion

abstract:
  This conference talk elaborates on a recently discovered mapping procedure by
which classical orbits and path integrals for the motion of a point particle in
flat space can be transformed correctly into those in curved space. This
procedure evolved from well established methods in the theory of plastic
deformations where crystals with defects are described mathematically by
applying nonholonomic coordinate transformations to ideal crystals. In the
context of time-sliced path integrals, there seems to exists a quantum
equivalence principle which determines the measures of fluctating orbits in
spaces with curvature and torsion. The nonholonomic transformations produce a
nontrivial Jacobian in the path measure which in a curved space produces
  an additional term proportional to the curvature scalar canceling a similar
term found earlier by DeWitt from a naive formulation of Feynman's time-sliced
path integral. This cancelation is important in correctly describing
semiclassically and quantum mechanically various systems such as the hydrogen
atom, a particle on the surface of a sphere, and a spinning top. It is also
indispensible for the process of bosonization, by which Fermi particles are
redescribed in terms of Bose fields.


title: Bell's inequality for the Mach-Zehnder interferometer

abstract:
  We show that no local, hidden variable model can be given for two-channel
states exhibiting both a sufficiently high interference visibility and a
sufficient degree of anticorrelation in a Mach-Zehnder interferometer.


title: Quantum Key Distribution and String Oblivious Transfer in Noisy Channels

abstract:
  We prove the unconditional security of a quantum key distribution (QKD)
protocol on a noisy channel against the most general attack allowed by quantum
physics. We use the fact that in a previous paper we have reduced the proof of
the unconditionally security of this QKD protocol to a proof that a
corresponding Quantum String Oblivious Transfer (String-QOT) protocol would be
unconditionally secure against Bob if implemented on top of an unconditionally
secure bit commitment scheme. We prove a lemma that extends a security proof
given by Yao for a (one bit) QOT protocol to this String-QOT protocol. This
result and the reduction mentioned above implies the unconditional security of
our QKD protocol despite our previous proof that unconditionally secure bit
commitment schemes are impossible.


title: Consistent Histories and Quantum Reasoning

abstract:
  A system of quantum reasoning for a closed system is developed by treating
non-relativistic quantum mechanics as a stochastic theory. The sample space
corresponds to a decomposition, as a sum of orthogonal projectors, of the
identity operator on a Hilbert space of histories. Provided a consistency
condition is satisfied, the corresponding Boolean algebra of histories, called
a {\it framework}, can be assigned probabilities in the usual way, and within a
single framework quantum reasoning is identical to ordinary probabilistic
reasoning. A refinement rule, which allows a probability distribution to be
extended from one framework to a larger (refined) framework, incorporates the
dynamical laws of quantum theory. Two or more frameworks which are incompatible
because they possess no common refinement cannot be simultaneously employed to
describe a single physical system.


title:
Mean Field and Collisional Dynamics of Interacting Fermion-Boson systems
  in a Soluble Model

abstract:
  A general time-dependent projection technique is applied to the study of the
dynamics of quantum correlations in a system consisting of interacting
fermionic and bosonic subsystems, described by the Jaynes-Cummings Hamiltonian.
The amplitude modulation of the Rabi oscillations which occur for a strong,
coherent initial bosonic field is obtained from the spin intrinsic
depolarization resulting from collisional corrections to the mean-field
approximation.

categories: quant-ph atom-ph math-ph math.MP nlin.SI nucl-th solv-int


title: Is there anything non-classical?

abstract:
  It is argued that quantum logic and quantum probability theory are
fascinating mathematical theories but without any relevance to our real world.


title:
Wigner Distributions and the Joint Measurement of Incompatible
  Observables

abstract:
  A theory of joint nonideal measurement of incompatible observables is used in
order to assess the relative merits of quantum tomography and certain
measurements of generalized observables, with respect to completeness of the
obtained information. A method is studied for calculating a Wigner distribution
from the joint probability distribution obtained in a joint measurement.


title: Photon tunneling through absorbing dielectric barriers

abstract:
  Using a recently developed formalism of quantization of radiation in the
presence of absorbing dielectric bodies, the problem of photon tunneling
through absorbing barriers is studied. The multilayer barriers are described in
terms of multistep complex permittivities in the frequency domain which satisfy
the Kramers--Kronig relations. From the resulting input--output relations it is
shown that losses in the layers may considerably change the photon tunneling
times observed in two-photon interference experiments. It is further shown that
for sufficiently large numbers of layers interference fringes are observed that
cannot be related to a single traversal time.


title: Condensate fluctuations of a trapped, ideal Bose gas

abstract:
  For a non-self-interacting Bose gas with a fixed, large number of particles
confined to a trap, as the ground state occupation becomes macroscopic, the
condensate number fluctuations remain micrscopic. However, this is the only
significant aspect in which the grand canonical description differs from
canonical or microcanonical in the thermodynamic limit. General arguments and
estimates including some vanishingly small quantities are compared to explicit,
fixed-number calculations for 10^2 to 10^6 particles.


title: Quantum teleportation circuitry

abstract:
  This paper is withdrawn as it is equivalent to the paper quant-ph/9605035 by
Gilles Brassard.


title: Algebraic Formulation of the Operatorial Perturbation Theory. Part I

abstract:
  A new totally algebraic formalism based on general, abstract ladder operators
has been proposed. This approach heavily grounds in the superoperator formalism
of Primas. However it is necessary to introduce many improvements in his
formalism. In this regard, it has been introduced a new set of superoperators
featured by their algebraic structure. Also, two lemmas and one theorem have
been developed in order to algebraically reformulate the theory on more
rigorous grounds. Finally, we have been able to build a coherent and
self-contained formalism independent on any matricial representation , removing
in this way the degeneracy problem .


title: The entanglement fidelity and quantum error correction

abstract:
  Two new expressions for the entanglement fidelity recently introduced by
Schumacher (LANL e-print quant-ph/9604023, to appear in Phys. Rev. A) are
derived. These expressions show that it is the entanglement fidelity which must
be maximized when performing error correction on qubits for quantum computers,
not the fidelity, which is the most-often used generalization of the
probability for storing a qubit correctly.


title:
Algebraic Formulation of the Operatorial Perturbation Theory. Part 2.
  Aplications

abstract:
  The algebraic approach to operator perturbation method has been applied to
two quantum--mechanical systems ``The Stark Effect in the Harmonic Oscillator''
and ``The Generalized Zeeman Effect''. To that end, two realizations of the
superoperators involved in the formalism have been carried out. The first of
them has been based on the Heisenberg--Dirac algebra of $\hat{a}^\dagger$,
$\hat{a}$, $\hat{1}$ operators, the second one has been based in the angular
momemtum algebra of $\hat{L}_+$, $\hat{L}_-$ and $\hat{L}_0$ operators. The
successful results achieved in predicting the discrete spectra of both systems
have put in evidence the reliability and accuracy of the theory.


title: Direct sampling of the Susskind-Glogower phase distributions

abstract:
  Coarse-grained phase distributions are introduced that approximate to the
Susskind--Glogower cosine and sine phase distributions. The integral relations
between the phase distributions and the phase-parametrized field-strength
distributions observable in balanced homodyning are derived and the integral
kernels are analyzed. It is shown that the phase distributions can be directly
sampled from the field-strength distributions which offers the possibility of
measuring the Susskind--Glogower cosine and sine phase distributions with
sufficiently well accuracy. Numerical simulations are performed to demonstrate
the applicability of the method.


title: Complementarity and Phase Distributions for Angular Momentum Systems

abstract:
  Interferences in the distributions of complementary variables for angular
momentum - two level systems are discussed. A quantum phase distribution is
introduced for angular momentum. Explicit results for the phase distributions
and the number distributions for atomic coherent states, squeezed states and
superpositions of coherent states are given. These results clearly demonstrate
the issue of complementarity and provide us with results analogous to those for
the radiation field.


title: Sonoluminescence as Quantum Vaccum Radiation

abstract:
  We argue that the available experimental data is not compatible with models
of sonoluminescence which invoke dynamical properties of the interface without
regard to the compositional properties of the trapped gas inside the bubble.


title: Quantum Mechanics in Terms of Realism

abstract:
  .We expound an alternative to the Copenhagen interpretation of the formalism
of nonrelativistic quantum mechanics. The basic difference is that the new
interpretation is formulated in the language of epistemological realism. The
{\psi} function is no longer interpreted as a probability amplitude of the
observed behaviour of elementary particles but as an objective physical field
representing the particles themselves. The particles are thus extended objects
whose extension varies in time according to the variation of {\psi}. They are
considered as fundamental regions of space with some kind of nonlocality. There
is no wave-particle duality. The point-particle-like behaviour is explained by
spatial contraction in a deterministic reduction process.


title: Quantum logic as a sum over classical logic gates

abstract:
  It is shown that certain natural quantum logic gates, {\it i.e.} unitary time
evolution matrices for spin-\frac{1}{2} quantum spins, can be represented as
sums, with appropriate phases, over classical logic gates, in a direct analogy
with the Feynman path integral representation of quantum mechanics. On the
other hand, it is shown that a natural quantum gate obtained by analytically
continuing the transfer matrix of the anisotropic nearest-neighbour Ising model
to imaginary time, does not admit such a representation.


title:
A Proposed Experiment Showing that Classical Fields Can Violate Bell's
  Inequalities

abstract:
  We show one can use classical fields to modify a quantum optics experiment so
that Bell's inequalities will be violated. This happens with continuous random
variables that are local, but we need to use the correlation matrix to prove
there can be no joint probability distribution of the observables.


title: Violation of Bell's Inequalities with a Local Theory of Photons

abstract:
  We use a local theory of photons purely as particles to model the
single-photon experiment proposed by Tan, Walls, and Collett. Like Tan et al.
we are able to derive a violation of Bell's inequalities for photon counts
coincidence measurements. Our local probabilistic theory does not use any
specific quantum mechanical calculations.


title: Quantum Adiabatic Approximation, Quantum Action, and Berry's Phase

abstract:
  An alternative interpretation of the quantum adiabatic approximation is
presented. This interpretation is based on the ideas originally advocated by
David Bohm in his quest for establishing a hidden variable alternative to
quantum mechanics. It indicates that the validity of the quantum adiabatic
approximation is a sufficient condition for the separability of the quantum
action function in the time variable. The implications of this interpretation
for Berry's adiabatic phase and its semi-classical limit are also discussed.


title:
Comment on Cyclic quantum-evolution dependence on the Hamiltonian and
  geometric phase

abstract:
  It is shown that the analysis and the main result of the article by L-A. Wu
[Phys. Rev. A 53, 2053 (1996)] are completely erroneous.


title:
Factorisation of analytic representations in the unit disk and
  number-phase statistics of a quantum harmonic oscillator

abstract:
  The inner-outer part factorisation of analytic representations in the unit
disk is used for an effective characterisation of the number-phase statistical
properties of a quantum harmonic oscillator. It is shown that the factorisation
is intimately connected to the number-phase Weyl semigroup and its properties.
In the Barut-Girardello analytic representation the factorisation is
implemented as a convolution. Several examples are given which demonstrate the
physical significance of the factorisation and its role for quantum statistics.
In particular, we study the effect of phase-space interference on the
factorisation properties of a superposition state.


title: Quantum damping of position due to energy measurements

abstract:
  Quantum theory for measurements of energy is introduced and its consequences
for the average position of monitored dynamical systems are analyzed. It turns
out that energy measurements lead to a localization of the expectation values
of other observables. This is manifested, in the case of position, as a damping
of the motion without classical analogue. Quantum damping of position for an
atom bouncing on a reflecting surface in presence of a homogeneous
gravitational field is dealt in detail and the connection with an experiment
already performed in the classical regime is studied. We show that quantum
damping is testable provided that the same measurement strength obtained in the
experimental verification of the quantum Zeno effect in atomic spectroscopy [W.
M. Itano et al., Phys. Rev. A {\bf 41}, 2295 (1990)] is made available.


title: Quantum jumps as decoherent histories

abstract:
  Quantum open systems are described in the Markovian limit by master equations
in Lindblad form. I argue that common ``quantum jumps'' techniques, which solve
the master equation by unraveling its evolution into stochastic trajectories in
Hilbert space, correspond closely to a particular set of decoherent histories.
This is illustrated by a simple model of a photon counting experiment.


title: Measurement of Arbitrary Observables of a Trapped Ion

abstract:
  We describe a method to perform a single quantum measurement of an arbitrary
observable of a single ion moving in a harmonic potential. We illustrate the
measurement procedure with explicit examples, namely the position and phase
observables.


title: Teleportation, Bell's Inequalities and Inseparability

abstract:
  Relations between teleportation, Bell's inequalities and inseparability are
investigated. It is shown that any mixed two spin-$1\over2$ state which
violates the Bell-CHSH inequality is useful for teleportation. The result is
extended to any Bell's inequalities constructed of the expectation values of
products of spin operators. It is also shown that there exist inseparable
states which are not useful for teleportation within the standard scheme.


title: Correct interpretation of trace normalized density matrices as ensembles

abstract:
  A density operator, $\rho = {P}_{\alpha } |\alpha > <\alpha | + {P}_{\beta }
|\beta > <\beta |$, with ${P}_{\alpha }$ and ${P}_{\beta }$ linearly
independent normalized wave functions, must be traced normalized, so
${P}_{\beta } = 1 - {P}_{\alpha }$. However, unless $<\alpha |\beta > = 0$,
${P}_{\alpha }$ and ${P}_{\beta }$ cannot be interpreted as probabilities of
finding $|\alpha >$ and $|\beta >$ respectively.
  We show that a density matrix comprised of two (${P}_{\alpha }$ and
${P}_{\beta }$ nonzero) non-orthogonal projectors have unique spectral
decomposition into diagonal form with orthogonal projectors. Only then,
according to axioms of Von Neumann and Fock, can we have probability
interpretation of that density matrix, only then can the diagonal elements be
interpreted as probabilities of an ensemble.
  Those probabilities on the diagonal are not ${P}_{\alpha }$ and
${P}_{\beta}$. Further, only in the case of orthogonal projectors can we have
the degenerate situation in which multiple ensembles are permitted.


title: Motion Induced Radiation from a Vibrating Cavity

abstract:
  We study the radiation emitted by a cavity moving in vacuum. We give a
quantitative estimate of the photon production inside the cavity as well as of
the photon flux radiated from the cavity. A resonance enhancement occurs not
only when the cavity length is modulated but also for a global oscillation of
the cavity. For a high finesse cavity the emitted radiation surpasses radiation
from a single mirror by orders of magnitude.


title: Space-Time Localisation with Quantum Fields

abstract:
  We introduce observables associated with the space-time position of a quantum
point defined by the intersection of two light pulses. The time observable is
canonically conjugated to the energy. Conformal symmetry of massless quantum
fields is used first to build the definition of these observables and then to
describe their relativistic properties under frame transformations. The
transformations to accelerated frames of the space-time observables depart from
the laws of classical relativity. The Einstein laws for the shifts of clock
rates and frequencies are recovered in the quantum description, and their
formulation provides a conformal metric factor behaving as a quantum
observable.


title: Dirac's Canonical Quantization Programme

abstract:
  This is a collection of lectures given at the University of Heidelberg,
especially but not exclusively for people who want to learn something about the
canonical approach to quantum gravity, which is however not included in these
lectures. They are about Dirac's general method to construct a quantum theory
out of a classical theory, which has to be defined in terms of a Lagrangian.
The classical Hamiltonian formalism is reviewed, with emphasis on the relation
between constraints and gauge symmetries, and quantization is carried out
without any kind of gauge fixing. The method is applied to three examples: the
free electro-magnetic field, the relativistic point particle, and the very
first steps of string theory are carried out.


title: Adiabatic Product Expansion

abstract:
  The time-evolution operator for an explicitly time-dependent Hamiltonian is
expressed as the product of a sequence of unitary operators. These are obtained
by successive time-dependent unitary transformations of the Hilbert space
followed by the adiabatic approximation at each step. The resulting adiabatic
product expansion yields a generalization of the quantum adiabatic
approximation. Furthermore, it leads to an infinite class of exactly solvable
models.


title:
The metron model: Elements of a unified deterministic theory of fields
  and particles

abstract:
  Keywords (parts 1-4): metron / unified theory / wave particle duality /
higher-dimensional gravity / solitons / Maxwell-Dirac-Einstein system /
Standard Model / EPR paradox / Bell's theorem / arrow of time


title:
Reconstructing the density operator by using generalized field
  quadratures

abstract:
  The Wigner function for one and two-mode quantum systems is explicitely
expressed in terms of the marginal distribution for the generic linearly
transformed quadratures. Then, also the density operator of those systems is
written in terms of the marginal distribution of these quadratures. Some
examples to apply this formalism, and a reduction to the usual optical homodyne
tomography are considered.


title: The Canonical Form of the Rabi Hamiltonian

abstract:
  The Rabi Hamiltonian, describing the coupling of a two-level system to a
single quantized boson mode, is studied in the Bargmann-Fock representation.
The corresponding system of differential equations is transformed into a
canonical form in which all regular singularities between zero and infinity
have been removed. The canonical or Birkhoff-transformed equations give rise to
a two-dimensional eigenvalue problem, involving the energy and a
transformational parameter which affects the coupling strength. The known
isolated exact solutions of the Rabi Hamiltonian are found to correspond to the
uncoupled form of the canonical system.


title: Geometric Foundation of Spin and Isospin

abstract:
  Various theories of spinning particles are interpreted as realizing elements
of an underlying geometric theory. Classical particles are described by
trajectories on the Poincare group. Upon quantization an eleven-dimensional
Kaluza-Klein type theory is obtained which incorporates spin and isospin in a
local SL(2,C) x U(1) x SU(2) theory with broken U(1)x SU(2) part.


title:
Quantum Mechanics as a Classical Theory XI: Thermodynamics and
  Equilibrium

abstract:
  In this continuation paper the theory is further extended to reveal the
connection between its formal aparatus, dealing with microscopic quantities,
and the formal aparatus of thermodynamics, related to macroscopic properties of
large systems. We will also derive the Born-Sommerfeld quantization rules from
the formalism of the infinitesimal Wigner-Moyal transformations and, as a
consequence of this result, we will also make a connection between the later
and the path integral approach of Feynman. Some insights of the relation
between quantum mechanics and equilibrium states will be given as a natural
development of the interpretation of the above results.


title:
Quantum Mechanics as a Classical Theory XII: Diffraction and
  Interference

abstract:
  In this paper we will be concerned with the explanation of the interference
and diffraction patterns observed as an outcome of the Young double slit
experiment. We will show that such explanation may be given {\it only} in terms
of a corpuscular theory, which has been our approach since the first paper of
this series. This explanation will be accomplished with an extension we make
here of the domain of applicability of the Born-Sommerfeld rules that we
derived in paper XI of this series.


title: Quantum measurement in a family of hidden-variable theories

abstract:
  The measurement process for hidden-configuration formulations of quantum
mechanics is analysed. It is shown how a satisfactory description of quantum
measurement can be given in this framework. The unified treatment of
hidden-configuration theories, including Bohmian mechanics and Nelson's
stochastic mechanics, helps in understanding the true reasons why the problem
of quantum measurement can succesfully be solved within such theories.


title:
Low Energy Wave Packet Tunneling from a Parabolic Potential Well through
  a High Potential Barrier

abstract:
  The problem of wave packet tunneling from a parabolic potential well through
a barrier represented by a power potential is considered in the case when the
barrier height is much greater than the oscillator ground state energy, and the
difference between the average energy of the packet and the nearest oscillator
eigenvalue is sufficiently small. The universal Poisson distribution of the
partial tunneling rates from the oscillator energy levels is discovered. The
explicit expressions for the tunneling rates of different types of packets
(coherent, squeezed, even/odd, thermal, etc.) are given in terms of the
exponential and modified Bessel functions. The tunneling rates turn out very
sensitive to the energy distributions in the packets, and they may exceed
significantly the tunneling rate from the energy state with the same average
number of quanta.


title: Laser Pulses as Measurements. Application to the Quantum Zeno Effect

abstract:
  Short pulses of a probe laser have been used in the past to measure whether a
two-level atom is in its ground or excited state. The probe pulse couples the
ground state to a third, auxiliary, level of the atom. Occurrence or absence of
resonance fluorescence were taken to mean that the atom was found in its ground
or excited state, respectively. In this paper we investigate to what extent
this procedure results in an effective measurement to which the projection
postulate can be applied, at least approximately. We discuss in detail the
complications arising from an additional time development of the two-level
system proper during a probe pulse. We extend our previous results for weak
probe pulses to the general case and show that one can model an ideal
(projection-postulate) measurement much better with a strong than a weak probe
pulse. In an application to the quantum Zeno effect we calculate the slow-down
of the atomic time development under n repeated probe pulse measurements and
determine the corrections compared to the case of n ideal measurements.


abstract:
  Information-theoretic aspects of quantum inseparability of mixed states are
investigated in terms of the $\alpha$-entropy inequalities and teleportation
fidelity. Inseparability of mixed states is defined and a complete
characterization of the inseparable $2\times2$ systems with maximally
disordered subsystems is presented within the Hilbert-Schmidt space formalism.
A connection between teleportation and negative conditional $\alpha$-entropy is
also emphasized.


title: Intrinsic and Operational Observables in Quantum Mechanics

abstract:
  The concept of intrinsic and operational observables in quantum mechanics is
introduced. It is argued that, in any realistic description of a quantum
measurement that includes a detecting device, it is possible to construct from
the statistics of the recorded raw data a set of operational quantities that
correspond to the intrinsic quantum mechanical observable. Using the concept of
the propensity and the associated operational positive operator valued measure
(POVM) a general description of the operational algebra of quantum mechanical
observables is derived for a wide class of realistic detection schemes. This
general approach is illustrated by the example of an operational Malus
measurement of the spin phases and by an analysis of the operational homodyne
detection of the phase of an optical field with a squeezed vacuum in the unused
ports.


title: Distillability of Inseparable Quantum Systems

abstract:
  We apply the inseparability criterion for $2 \times 2$ systems, local
filtering and Bennett et al. purification protocol [Phys. Rev. Lett. {\bf 76},
722 (1996)] to show how to distill {\it any} inseparable $2\times 2$ system.
The extended protocol is illustrated geometrically by means of the state
parameters in the Hilbert-Schmidt space.


title: Data Compression for Quantum Code

abstract:
  The general scheme of data compression using the quantum noiseless coding
theorem of Schumacher is dicussed for general quantum sources. When the Hilbert
space of the quantum source is decomposable into orthogonal subspaces, one can
first perform classical data compression before performing the quantum data
compression for individual subspaces. For minimizing the resource in quantum
coding, a general parameterization of the dimensions in the Jozsa-Schumacher
quantum data compression scheme is presented.


title: Detection of space-time fluctuations by a model matter interferometer

abstract:
  In papers on primary state diffusion (Percival 1994, 1995), numerical
estimates suggested that fluctuations in the space-time metric on the scale of
the Planck time (10^-44s) could be detected using atom interferometers. In this
paper we first specify a stochastic metric obtained from fluctuations that
propagate with the velocity of light, and then develop the non-Markovian
quantum state diffusion theory required to estimate the resulting decoherence
effects on a model matter interferometer. Both commuting and non-commuting
fluctuations are considered. The effects of the latter are so large that if
they applied to some real atom interferometry experiments they would have
suppressed the observed interference. The model is too crude to conclude that
such fluctuations do not exist, but it does demonstrate that the small
numerical value of the Planck time does not alone prevent experimental access
to Planck-scale phenomena in the laboratory.


title: Generalized Binomial States: Ladder Operator Approach

abstract:
  We show that the binomial states (BS) of Stoler {\it et al.} admit the ladder
and displacement operator formalism. By generalizing the ladder operator
formalism we propose an eigenvalue equation which possesses the number and the
squeezed states as its limiting solutions. The explicit forms of the solutions,
to be referred to as the {\it generalized binomial states} (GBS), are given.
Corresponding to the wide range of the eigenvalue spectrum these GBS have as
widely different properties. Their limits to number and {\it squeezed} states
are investigated in detail. The time evolution of BS is obtained as a special
case of the approach.


title:
The complete solution of the Hamilton-Jacobi equation in Quantum
  Mechanics

abstract:
  An ordinary unambiguous integral representation for the finite propagator of
a quantum system is found by starting of a privileged skeletonization of the
functional action in phase space, provided by the complete solution of the
Hamilton-Jacobi equation. This representation allows to regard the propagator
as the sum of the contributions coming from paths where the momenta generated
by the complete solution of the Hamilton-Jacobi equation are conserved -as it
does happen on the classical trajectory-, but are not restricted to having the
classical values associated with the boundary conditions for the original
coordinates.


title: A Quantum Algorithm for Finding the Minimum

abstract:
  We give a quantum algorithm to find the index y in a table T of size N such
that in time O(c sqrt N), T[y] is minimum with probability at least 1-1/2^c.


title: Indistinguishable particles and hidden variables

abstract:
  An axiomatics for indistinguishability of elementary particles in terms of
hidden variables is presented in a manner which depart from the standard
approaches usually given to hidden variables. Quantum distribution functions
are also discussed and some related lines of work are suggested.


title: Comment on ``Sonoluminescence as Quantum Vacuum Radiation''

abstract:
  We contest the recent claim by C. Eberlein (Physical Review Letters 76 (1996)
3842) that sonoluminescence may be explained in terms of quantum vacuum
radiation. Due to fundamental physical limitations on bubble surface velocity,
the predicted number of photons per flash is indeed much smaller than unity.
Therefore, quantum vacuum radiation cannot be considered as an explanation of
the observed sonoluminescence phenomenon.


title: Peculiarities of Quantum Mechanics: Origins and Meaning

abstract:
  The most peculiar, specifically quantum, features of quantum mechanics ---
quantum nonlocality, indeterminism, interference of probabilities,
quantization, wave function collapse during measurement --- are explained on a
logical-geometrical basis. It is shown that truths of logical statements about
numerical values of quantum observables are quantum observables themselves and
are represented in quantum mechanics by density matrices of pure states.
Structurally, quantum mechanics is a result of applying non-Abelian symmetries
to truth operators and their eigenvectors --- wave functions. Wave functions
contain information about conditional truths of all possible logical statements
about physical observables and their correlations in a given physical system.
These correlations are logical, hence nonlocal, and exist when the system is
not observed. We analyze the physical conditions and logical and
decision-making operations involved in the phenomena of wave function collapse
and unpredictability of the results of measurements. Consistent explanations of
the Stern-Gerlach and EPR-Bohm experiments are presented."


title: Quantum Copying: Beyond the No-Cloning Theorem

abstract:
  We analyze to what extent it is possible to copy arbitrary states of a
two-level quantum system. We show that there exists a "universal quantum
copying machine", which approximately copies quantum mechanical states in such
a way that the quality of its output does not depend on the input. We also
examine a machine which combines a unitary transformation with a selective
measurement to produce good copies of states in a neighborhood of a particular
state. We discuss the problem of measurement of the output states.


title: Coherent State Path Integrals for Systems with Constraints

abstract:
  We outline the principal results of a recent examination of the quantization
of systems with first- and second-class constraints from the point of view of
coherent-state phase-space path integration. Two examples serve to illustrate
the procedures.


title: New Measures for the Quantization of Systems with Constraints

abstract:
  Based on the results of a recent reexamination of the quantization of systems
with first-class and second-class constraints from the point of view of
coherent-state phase-space path integration, we give additional examples of the
quantization procedure for reparameterization invariant Hamiltonians, for
systems for which the original set of Lagrange multipliers are elevated to
dynamical variables, as well as extend the formalism to include cases of
first-class constraints the operator form of which have a spectral gap about
the value zero that characterizes the quantum constraint subspace.


title:
Measuring quantum states: an experimental setup for measuring the
  spatial density matrix

abstract:
  To quantify the effect of decoherence in quantum measurements, it is
desirable to measure not merely the square modulus of the spatial wavefunction,
but the entire density matrix, whose phases carry information about momentum
and how pure the state is. An experimental setup is presented which can measure
the density matrix (or equivalently, the Wigner function) of a beam of
identically prepared charged particles to an arbitrary accuracy, limited only
by count statistics and detector resolution. The particles enter into an
electric field causing simple harmonic oscillation in the transverse direction.
This corresponds to rotating the Wigner function in phase space. With a
slidable detector, the marginal distribution of the Wigner function can be
measured from all angles. Thus the phase-space tomography formalism can be used
to recover the Wigner function by the standard inversion of the Radon
transform. By applying this technique to for instance double-slit experiments
with various degrees of environment-induced decoherence, it should be possible
to make our understanding of decoherence and apparent wave-function collapse
less qualitative and more quantitative.


title:
Analytic representations based on SU(1,1) coherent states and their
  applications

abstract:
  We consider two analytic representations of the SU(1,1) Lie group: the
representation in the unit disk based on the SU(1,1) Perelomov coherent states
and the Barut-Girardello representation based on the eigenstates of the SU(1,1)
lowering generator. We show that these representations are related through a
Laplace transform. A ``weak'' resolution of the identity in terms of the
Perelomov SU(1,1) coherent states is presented which is valid even when the
Bargmann index $k$ is smaller than one half. Various applications of these
results in the context of the two-photon realization of SU(1,1) in quantum
optics are also discussed.


title: Emergence of Weak Values

abstract:
  Various quantum measurement procedures are analyzed and it is shown that
under certain conditions they yield consistently {\em weak values} which might
be very different from the eigenvalues, the allowed outcomes according to the
standard quantum formalism. The weak value outcomes result from peculiar
quantum interference of the pointer variable of the measuring device.


title: A fast quantum mechanical algorithm for estimating the median

abstract:
  Consider the problem of estimating the median of N items to a precision
epsilon, i.e., the estimate should be such that, with a high probability, the
number of items, with values both smaller than and larger than this estimate,
is less than N*(1+epsilon)/2. Any classical algorithm to do this will need at
least O(1/epsilon^2) samples. Quantum mechanical systems can simultaneously
carry out multiple computations due to their wave like properties. This paper
describes an O(1/epsilon) step algorithm for the above estimation.


title: Kinematics and hydrodynamics of spinning particles

abstract:
  In the first part (Sections 1 and 2) of this paper --starting from the Pauli
current, in the ordinary tensorial language-- we obtain the decomposition of
the non-relativistic field velocity into two orthogonal parts: (i) the
"classical part, that is, the 3-velocity w = p/m OF the center-of-mass (CM),
and (ii) the so-called "quantum" part, that is, the 3-velocity V of the motion
IN the CM frame (namely, the internal "spin motion" or zitterbewegung). By
inserting such a complete, composite expression of the velocity into the
kinetic energy term of the non-relativistic classical (i.e., newtonian)
lagrangian, we straightforwardly get the appearance of the so-called "quantum
potential" associated, as it is known, with the Madelung fluid. This result
carries further evidence that the quantum behaviour of micro-systems can be
adirect consequence of the fundamental existence of spin. In the second part
(Sections 3 and 4), we fix our attention on the total 3-velocity v = w + V, it
being now necessary to pass to relativistic (classical) physics; and we show
that the proper time entering the definition of the four-velocity v^mu for
spinning particles has to be the proper time tau of the CM frame. Inserting the
correct Lorentz factor into the definition of v^mu leads to completely new
kinematical properties for v_mu v^mu. The important constraint p_mu v^mu = m,
identically true for scalar particles, but just assumed a priori in all
previous spinning particle theories, is herein derived in a self-consistent
way.


title:
Radiation field quantization in a nonlinear dielectric with dispersion
  and absorption

abstract:
  The problem of quantizing the radiation field inside a nonlinear dielectric
is studied. Based on the quantization of radiation in a linear dielectric which
includes absorption and dispersion, we extend the theory in order to treat also
nonlinear optical processes. We derive propagation equations in space and time
for the quantized radiation field including the effects of linear absorption
and dispersion as well as nonlinear optical effects. As a special case we
derive the propagation equation of a narrow-frequency band light pulse in a
Kerr medium.


title: Pasting Quantum Codes

abstract:
  I describe a method for pasting together certain quantum error-correcting
codes that correct one error to make a single larger one-error quantum code. I
show how to construct codes encoding 7 qubits in 13 qubits using the method, as
well as 15 qubits in 21 qubits and all the other "perfect" codes.


title: Comment on ``Creating Metastable Schroedinger Cat States''

abstract:
  After a careful analysis of the feedback model recently proposed by Slosser
and Milburn [Phys. Rev. Lett. 75, 418 (1995)], we are led to the conclusion
that---under realistic conditions---their scheme is not significantly more
effective in the production of linear superpositions of macroscopically
distinguishable quantum states than the usual quantum-optical Kerr effect.


title:
Interaction-Free Measurement in mesoscopic systems and the reduction
  postulate

abstract:
  We show that a noninvasive,``negative-result measurement'' can be realized in
quantum dot systems. The measurement process is studied by applying the
Schr\"odinger equation to the whole system (including the detector). We
demonstrate that the possibility of observing a particular state out of
coherent superposition leads to collapse of the corresponding nondiagonal
density-matrix elements of the measured system. No additional reduction
postulate is needed. Experimental consequences of the collapse time and the
relativistic requirement are discussed for mesoscopic and optical systems.


title: Efficient Computations of Encodings for Quantum Error Correction

abstract:
  We show how, given any set of generators of the stabilizer of a quantum code,
an efficient gate array that computes the codewords can be constructed. For an
n-qubit code whose stabilizer has d generators, the resulting gate array
consists of O(n d) operations, and converts k-qubit data (where k = n - d) into
n-qubit codewords.


title: Reversible quantum operations and their application to teleportation

abstract:
  Quantum operations provide a general description of the state changes allowed
by quantum mechanics. Simple necessary and sufficient conditions for an ideal
quantum operation to be reversible by a unitary operation are derived in this
paper. These results generalize recent work on reversible measurements by
Mabuchi and Zoller [Phys. Rev. Lett. {\bf 76}, 3108 (1996)]. Quantum
teleportation can be understood as a special case of the problem of reversing
quantum operations. We characterize completely teleportation schemes of the
type proposed by Bennett {\it et al.} [Phys. Rev. Lett. {\bf 70}, 1895 (1993)].


title: Polarization coherent states and geometric phases in quantum optics

abstract:
  Polarization coherent states (PCS) are considered as generalized coherent
states of $SU(2)_p$ group of the polarization invariance of the light fields.
The geometric phases of PCS are introduced in a way, analogous to that used in
the classical polarization optics.


title: Comment on "Sonoluminescence as Quantum Vacuum Radiation"

abstract:
  The insufficiency of the energy radiated in the model of Eberlein is
discussed.


title:
A C++ library using quantum trajectories to solve quantum master
  equations

abstract:
  Quantum trajectory methods can be used for a wide range of open quantum
systems to solve the master equation by unraveling the density operator
evolution into individual stochastic trajectories in Hilbert space. This C++
class library offers a choice of integration algorithms for three important
unravelings of the master equation. Different physical systems are modeled by
different Hamiltonians and environment operators. The program achieves
flexibility and user friendliness, without sacrificing execution speed, through
the way it represents operators and states in Hilbert space. Primary operators,
implemented in the form of simple routines acting on single degrees of freedom,
can be used to build up arbitrarily complex operators in product Hilbert spaces
with arbitrary numbers of components. Standard algebraic notation is used to
build operators and to perform arithmetic operations on operators and states.
States can be represented in a local moving basis, often leading to dramatic
savings of computing resources. The state and operator classes are very general
and can be used independently of the quantum trajectory algorithms. Only a
rudimentary knowledge of C++ is required to use this package.


title: TelePOVM -- New Faces of Teleportation

abstract:
  We show two new aspects of teleportation based on generalized measurements:
I. We present an alternative approach to teleportation based on ``generating
$\rho$-ensembles at spacetime separation''; This approach provides a better
understanding of teleportation. II. We define the concept of {\em conclusive
teleportation} and we show how to teleport a quantum state using any pure
entangled state; we show how to use the conclusive teleportation as a criterion
for non-locality.


title: Quantum Error Correction via Codes over GF(4)

abstract:
  The problem of finding quantum error-correcting codes is transformed into the
problem of finding additive codes over the field GF(4) which are
self-orthogonal with respect to a certain trace inner product. Many new codes
and new bounds are presented, as well as a table of upper and lower bounds on
such codes of length up to 30 qubits.


title: Consistent Histories may be strange, but so is standard Quantum Theory

abstract:
  Interpretational questions that arise in the Consistent Histories formulation
of quantum mechanics are illustrated by the familiar example of a beam passing
through multiple slits.


title:
Displacement-Operator Squeezed States. I. Time-Dependent Systems Having
  Isomorphic Symmetry Algebras

abstract:
  In this paper we use the Lie algebra of space-time symmetries to construct
states which are solutions to the time-dependent Schr\"odinger equation for
systems with potentials $V(x,\tau)=g^{(2)}(\tau)x^2+g^{(1)}(\tau)x
+g^{(0)}(\tau)$. We describe a set of number-operator eigenstates states,
$\{\Psi_n(x,\tau)\}$, that form a complete set of states but which, however,
are usually not energy eigenstates. From the extremal state,
  $\Psi_0$, and a displacement squeeze operator derived using the Lie
symmetries, we construct squeezed states and compute expectation values for
position and momentum as a function of time, $\tau$. We prove a general
expression for the uncertainty relation for position and momentum in terms of
the squeezing parameters. Specific examples, all corresponding to choices of
$V(x,\tau)$ and having isomorphic Lie algebras, will be dealt with in the
following paper (II).