39,845 research outputs found
Nonviolation of Bell's Inequality in Translation Invariant Systems
The nature of quantum correlations in strongly correlated systems has been a
subject of intense research. In particular, it has been realized that
entanglement and quantum discord are present at quantum phase transitions and
able to characterize it. Surprisingly, it has been shown for a number of
different systems that qubit pairwise states, even when highly entangled, do
not violate Bell's inequalities, being in this sense local. Here we show that
such a local character of quantum correlations is in fact general for
translation invariant systems and has its origins in the monogamy trade-off
obeyed by tripartite Bell correlations. We illustrate this result in a quantum
spin chain with a soft breaking of translation symmetry. In addition, we extend
the monogamy inequality to the -qubit scenario, showing that the bound
increases with and providing examples of its saturation through uniformly
generated random pure states.Comment: Published erratum added at the en
Corrections to Finite Size Scaling in Percolation
A 1/L-expansion for percolation problems is proposed, where L is the lattice
finite length. The square lattice with 27 different sizes L = 18, 22 ... 1594
is considered. Certain spanning probabilities were determined by Monte Carlo
simulations, as continuous functions of the site occupation probability p. We
estimate the critical threshold pc by applying the quoted expansion to these
data. Also, the universal spanning probability at pc for an annulus with aspect
ratio r=1/2 is estimated as C = 0.876657(45)
Overcoming ambiguities in classical and quantum correlation measures
We identify ambiguities in the available frameworks for defining quantum,
classical, and total correlations as measured by discordlike quantifiers. More
specifically, we determine situations for which either classical or quantum
correlations are not uniquely defined due to degeneracies arising from the
optimization procedure over the state space. In order to remove such
degeneracies, we introduce a general approach where correlations are
independently defined, escaping therefore from a degenerate subspace. As an
illustration, we analyze the trace-norm geometric quantum discord for two-qubit
Bell-diagonal states.Comment: 5 pages, 2 figures. v2: Minor corrections. Published versio
Compactly Supported Wavelets Derived From Legendre Polynomials: Spherical Harmonic Wavelets
A new family of wavelets is introduced, which is associated with Legendre
polynomials. These wavelets, termed spherical harmonic or Legendre wavelets,
possess compact support. The method for the wavelet construction is derived
from the association of ordinary second order differential equations with
multiresolution filters. The low-pass filter associated with Legendre
multiresolution analysis is a linear phase finite impulse response filter
(FIR).Comment: 6 pages, 6 figures, 1 table In: Computational Methods in Circuits and
Systems Applications, WSEAS press, pp.211-215, 2003. ISBN: 960-8052-88-
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