6,964 research outputs found
General correlation functions of the Clauser-Horne-Shimony-Holt inequality for arbitrarily high-dimensional systems
We generalize the correlation functions of the Clauser-Horne-Shimony-Holt
(CHSH) inequality to arbitrarily high-dimensional systems. Based on this
generalization, we construct the general CHSH inequality for bipartite quantum
systems of arbitrarily high dimensionality, which takes the same simple form as
CHSH inequality for two-dimension. This inequality is optimal in the same sense
as the CHSH inequality for two dimensional systems, namely, the maximal amount
by which the inequality is violated consists with the maximal resistance to
noise. We also discuss the physical meaning and general definition of the
correlation functions. Furthermore, by giving another specific set of the
correlation functions with the same physical meaning, we realize the inequality
presented in [Phys. Rev. Lett. {\bf 88,}040404 (2002)].Comment: 4 pages, accepted by Phys. Rev. Let
The Complexity of Testing Monomials in Multivariate Polynomials
The work in this paper is to initiate a theory of testing monomials in
multivariate polynomials. The central question is to ask whether a polynomial
represented by certain economically compact structure has a multilinear
monomial in its sum-product expansion. The complexity aspects of this problem
and its variants are investigated with two folds of objectives. One is to
understand how this problem relates to critical problems in complexity, and if
so to what extent. The other is to exploit possibilities of applying algebraic
properties of polynomials to the study of those problems. A series of results
about and polynomials are obtained in this paper,
laying a basis for further study along this line
Dependence of Temporal Properties on Energy in Long-Lag, Wide-Pulse Gamma-Ray Bursts
We employed a sample compiled by Norris et al. (2005, ApJ, 625, 324) to study
the dependence of the pulse temporal properties on energy in long-lag,
wide-pulse gamma-ray bursts. Our analysis shows that the pulse peak time, rise
time scale and decay time scale are power law functions of energy, which is a
preliminary report on the relationships between the three quantities and
energy. The power law indexes associated with the pulse width, rise time scale
and decay time scale are correlated and the correlation between the indexes
associated with the pulse width and the decay time scale is more obvious. In
addition, we have found that the pulse peak lag is strongly correlated with the
CCF lag, but the centroid lag is less correlated with the peak lag and CCF lag.
Based on these results and some previous investigations, we tend to believe
that all energy-dependent pulse temporal properties may come from the joint
contribution of both the hydrodynamic processes of the outflows and the
curvature effect, where the energy-dependent spectral lag may be mainly
dominated by the dynamic process and the energy-dependent pulse width may be
mainly determined by the curvature effect.Comment: 20 pages, 7 figures, added references, matched to published version,
accepted for publication in PAS
Quantum phase transition in a three-level atom-molecule system
We adopt a three-level bosonic model to investigate the quantum phase
transition in an ultracold atom-molecule conversion system which includes one
atomic mode and two molecular modes. Through thoroughly exploring the
properties of energy level structure, fidelity, and adiabatical geometric
phase, we confirm that the system exists a second-order phase transition from
an atommolecule mixture phase to a pure molecule phase. We give the explicit
expression of the critical point and obtain two scaling laws to characterize
this transition. In particular we find that both the critical exponents and the
behaviors of ground-state geometric phase change obviously in contrast to a
similar two-level model. Our analytical calculations show that the ground-state
geometric phase jumps from zero to ?pi/3 at the critical point. This
discontinuous behavior has been checked by numerical simulations and it can be
used to identify the phase transition in the system.Comment: 8 pages,8 figure
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