# arXiv.org e-Print Archive

### Phase properties of hypergeometric states and negative hypergeometric states

We show that the three quantum states (P$\acute{o}$lya states, the
generalized non-classical states related to Hahn polynomials and negative
hypergeometric states) introduced recently as intermediates states which
interpolate between the binomial states and negative binomial states are
essentially identical. By using the Hermitial-phase-operator formalism, the
phase properties of the hypergeometric states and negative hypergeometric
states are studied in detail. We find that the number of peaks of phase
probability distribution is one for the hypergeometric states and $M$ for the
negative hypergeometric states.Comment: 7 pages, 4 figure

### Calculation of the Deflection of Light Ray near the Sun with Quantum-corrected Newton's Gravitation Law

The deflection of light ray passing near the Sun is calculated with
quantum-corrected Newton's gravitation law. The satisfactory result suggests
that there may exist other theoretical possibilities besides the theory of
relativity.Comment: tciLatex, 5 pages. no figur

### Quantum algorithms which accept hot qubit inputs

Realistic physical implementations of quantum computers can entail tradeoffs
which depart from the ideal model of quantum computation. Although these
tradeoffs have allowed successful demonstration of certain quantum algorithms,
a crucial question is whether they fundamentally limit the computational
capacity of such machines. We study the limitations of a quantum computation
model in which only ensemble averages of measurement observables are
accessible. Furthermore, we stipulate that input qubits may only be prepared in
highly random, ``hot'' mixed states. In general, these limitations are believed
to dramatically detract from the computational power of the system. However, we
construct a class of algorithms for this limited model, which, surprisingly,
are polynomially equivalent to the ideal case. This class includes the well
known Deutsch-Jozsa algorithm.Comment: 4 pages, revtex, submitted June 29, 199

### Discrete Q- and P-symbols for spin s

Non-orthogonal bases of projectors on coherent states are introduced to
expand hermitean operators acting on the Hilbert space of a spin s. It is shown
that the expectation values of a hermitean operator A in a family of
(2s+1)(2s+1) spin-coherent states determine the operator unambiguously. In
other words, knowing the Q-symbol of A at (2s+1)(2s+1) points on the unit
sphere is already sufficient in order to recover the operator. This provides a
straightforward method to reconstruct the mixed state of a spin since its
density matrix is explicitly parametrized in terms of expectation values.
Furthermore, a discrete P-symbol emerges naturally which is related to a basis
dual to the original one.Comment: 6 pages, Latex2

### Single-particle Bell-type Inequality

It is generally believed that Bell's inequality holds for the case of
entangled states, including two correlated particles or special states of a
single particle. Here, we derive a single-particle Bell's inequality for two
correlated spin states at two successive times, appealing to the statistical
independence condition in an ideal experiment, for a locally causal hidden
variables theory. We show that regardless of the locality assumption, the
inequality can be violated by some quantum predictions.Comment: 14 pages, 1 figure, Latex file, To appear in Annales de la Fondation
Louis de Brogli

### Secure Classical Bit Commitment using Fixed Capacity Communication Channels

If mutually mistrustful parties A and B control two or more appropriately
located sites, special relativity can be used to guarantee that a pair of
messages exchanged by A and B are independent. In earlier work, we used this
fact to define a relativistic bit commitment protocol, RBC1, in which security
is maintained by exchanging a sequence of messages whose transmission rate
increases exponentially in time. We define here a new relativistic protocol,
RBC2, which requires only a constant transmission rate and could be practically
implemented. We prove that RBC2 allows a bit commitment to be indefinitely
maintained with unconditional security against all classical attacks. We
examine its security against quantum attacks, and show that it is immune from
the class of attacks shown by Mayers and Lo-Chau to render non-relativistic
quantum bit commitment protocols insecure.Comment: Proofs of classical security simplified and extended. Precise
estimates for practical implementation, showing near perfect security
attainable for separations of 10 km. New definitions of successful unveiling
and of effective commitment in a redundant bit commitment scheme. New
discussion of the deniability of relativistic bit commitments and (a point
due to Mueller-Quade and Unruh) their retractability. 32 pages, revtex
preprint format. Erratum on p329 of published version correcte

### Aharonov-Bohm Effect and Coordinate Transformations

Resorting to a Gedankenexperiment which is very similar to the famous
Aharonov-Bohm proposal it will be shown that, in the case of a Minkowskian
spacetime, we may use a nonrelativistic quantum particle and a noninertial
coordinate system and obtain geometric information of regions that are, to this
particle, forbidden. This shows that the outcome of a nonrelativistic quantum
process is determined not only by the features of geometry at those points at
which the process takes place, but also by geometric parameters of regions in
which the quantum system can not enter. From this fact we could claim that
geometry at the quantum level plays a non-local role. Indeed, the measurement
outputs of some nonrelativistic quantum experiments are determined not only by
the geometry of the region in which the experiment takes place, but also by the
geometric properties of spacetime volumes which are, in some way, forbidden in
the experiment.Comment: 11 pages, 1 figure, accepted in Mod. Phys. Letts.

### Semiclassical interferences and catastrophes in the ionization of Rydberg atoms by half-cycle pulses

A multi-dimensional semiclassical description of excitation of a Rydberg
electron by half-cycle pulses is developed and applied to the study of energy-
and angle-resolved ionization spectra. Characteristic novel phenomena
observable in these spectra such as interference oscillations and semiclassical
glory and rainbow scattering are discussed and related to the underlying
classical dynamics of the Rydberg electron. Modifications to the predictions of
the impulse approximation are examined that arise due to finite pulse
durations

### Probabilistic exact cloning and probabilistic no-signalling

We show that non-local resources cannot be used for probabilistic signalling
even if one can produce exact clones with the help of a probabilistic quantum
cloning machine (PQCM). We show that PQCM cannot help to distinguish two
statistical mixtures at a remote location. Thus quantum theory rules out the
possibility of sending superluminal signals not only deterministically but also
probabilistically. We give a bound on the success probability of producing
multiple clones in an entangled system.Comment: Latex file, 6 pages, minor correction

### A simple proof of the converse of Hardy's theorem

In this paper we provide a simple proof of the fact that for a system of two
spin-1/2 particles, and for a choice of observables, there is a unique state
which shows Hardy-type nonlocality. Moreover, an explicit expression for the
probability that an ensemble of particle pairs prepared in such a state
exhibits a Hardy-type nonlocality contradiction is given in terms of two
independent parameters related to the observables involved. Incidentally, a
wrong statement expressed in Mermin's proof of the converse [N.D. Mermin, Am.
J. Phys. 62, 880 (1994)] is pointed out.Comment: LaTeX, 16 pages + 2 eps figure

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