30,532 research outputs found
On measure expansive diffeomorphisms
Let be a diffeomorphism defined on a compact boundaryless
-dimensional manifold , . C. Morales has proposed the notion of
measure expansiveness. In this note we show that diffeomorphisms in a residual
subset far from homoclinic tangencies are measure expansive.
We also show that surface diffeomorphisms presenting homoclinic tangencies
can be -approximated by non-measure expansive diffeomorphisms
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
Local hidden-variable models and negative-probability measures
Elaborating on a previous work by Han et al., we give a general,
basis-independent proof of the necessity of negative probability measures in
order for a class of local hidden-variable (LHV) models to violate the
Bell-CHSH inequality. Moreover, we obtain general solutions for LHV-induced
probability measures that reproduce any consistent set of probabilities.Comment: LaTeX file, 10 page
Generalization of the Deutsch algorithm using two qudits
Deutsch's algorithm for two qubits (one control qubit plus one auxiliary
qubit) is extended to two -dimensional quantum systems or qudits for the
case in which is equal to , . This allows one to classify
a certain oracle function by just one query, instead of the queries
required by classical means. The given algorithm for two qudits also solves
efficiently the Bernstein-Vazirani problem. Entanglement does not occur at any
step of the computation.Comment: LaTeX file, 7 page
Quantum perfect correlations and Hardy's nonlocality theorem
In this paper the failure of Hardy's nonlocality proof for the class of
maximally entangled states is considered. A detailed analysis shows that the
incompatibility of the Hardy equations for this class of states physically
originates from the fact that the existence of quantum perfect correlations for
the three pairs of two-valued observables (D_11,D_21), (D_11,D_22) and
(D_12,D_21) [in the sense of having with certainty equal (different) readings
for a joint measurement of any one of the pairs (D_11,D_21), (D_11,D_22), and
(D_12,D_21)], necessarily entails perfect correlation for the pair of
observables (D_12,D_22) [in the sense of having with certainty equal
(different) readings for a joint measurement of the pair (D_12,D_22)]. Indeed,
the set of these four perfect correlations is found to satisfy the CHSH
inequality, and then no violations of local realism will arise for the
maximally entangled state as far as the four observables D_ij, i,j = 1,2, are
concerned. The connection between this fact and the impossibility for the
quantum mechanical predictions to give the maximum possible theoretical
violation of the CHSH inequality is pointed out. Moreover, it is generally
proved that the fulfillment of all the Hardy nonlocality conditions necessarily
entails a violation of the resulting CHSH inequality. The largest violation of
this latter inequality is determined.Comment: LaTeX, 24 pages, 1 figur
Primarity of direct sums of Orlicz spaces and Marcinkiewicz spaces
Let be either an Orlicz sequence space or a Marcinkiewicz
sequence space. We take advantage of the recent advances in the theory of
factorization of the identity carried on in [R. Lechner, Subsymmetric weak*
Schauder bases and factorization of the identity, arXiv:1804.01372 [math.FA]]
to provide conditions on that ensure that, for any , the infinite direct sum of in the sense of
is a primary Banach space, enlarging this way the list of Banach spaces that
are known to be primary
Quantum mechanical probabilities and general probabilistic constraints for Einstein-Podolsky-Rosen-Bohm experiments
Relativistic causality, namely, the impossibility of signaling at
superluminal speeds, restricts the kinds of correlations which can occur
between different parts of a composite physical system. Here we establish the
basic restrictions which relativistic causality imposes on the joint
probabilities involved in an experiment of the Einstein-Podolsky-Rosen-Bohm
type. Quantum mechanics, on the other hand, places further restrictions beyond
those required by general considerations like causality and consistency. We
illustrate this fact by considering the sum of correlations involved in the
CHSH inequality. Within the general framework of the CHSH inequality, we also
consider the nonlocality theorem derived by Hardy, and discuss the constraints
that relativistic causality, on the one hand, and quantum mechanics, on the
other hand, impose on it. Finally, we derive a simple inequality which can be
used to test quantum mechanics against general probabilistic theories.Comment: LaTeX, 16 pages, no figures; Final version, to be published in Found.
Phys. Letter
Chaotic Transport and Current Reversal in Deterministic Ratchets
We address the problem of the classical deterministic dynamics of a particle
in a periodic asymmetric potential of the ratchet type. We take into account
the inertial term in order to understand the role of the chaotic dynamics in
the transport properties. By a comparison between the bifurcation diagram and
the current, we identify the origin of the current reversal as a bifurcation
from a chaotic to a periodic regime. Close to this bifurcation, we observed
trajectories revealing intermittent chaos and anomalous deterministic
diffusion.Comment: (7 figures) To appear in Physical Review Letters (in January 2000
Traversal-time distribution for a classical time-modulated barrier
The classical problem of a time-modulated barrier, inspired by the Buttiker
and Landauer model to study the tunneling times, is analyzed. We show that the
traversal-time distribution of an ensemble of non-interacting particles that
arrives at the oscillating barrier, obeys a distribution with a power-law tail.Comment: (10 pages, 8 figures) To appear in Physics Letters A. See also
http://scifunam.ifisicacu.unam.mx/jlm/mateos.htm
Degree of entanglement for two qutrits in a pure state
In this paper, a new measure of entanglement for general pure bipartite
states of two qutrits is formulated.Comment: LaTeX file, 8 pages, 1 figur
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