532 research outputs found
Quantum discord and information deficit in spin chains
We examine the behavior of quantum correlations of spin pairs in a finite
anisotropic spin chain immersed in a transverse magnetic field, through
the analysis of the quantum discord and the conventional and quadratic one
way-information deficits. We first provide a brief review of these measures,
showing that the last ones can be obtained as particular cases of a generalized
information deficit based on general entropic forms. All these measures
coincide with an entanglement entropy in the case of pure states, but can be
non-zero in separable mixed states, vanishing just for classically correlated
states. It is then shown that their behavior in the exact ground state of the
chain exhibits similar features, deviating significantly from that of the pair
entanglement below the critical field. In contrast with entanglement, they
reach full range in this region, becoming independent of the pair separation
and coupling range in the immediate vicinity of the factorizing field. It is
also shown, however, that significant differences between the quantum discord
and the information deficits arise in the local minimizing measurement that
defines them. Both analytical and numerical results are provided.Comment: 14 pages, 5 figure
Local Rigidity in Sandpile Models
We address the problem of the role of the concept of local rigidity in the
family of sandpile systems. We define rigidity as the ratio between the
critical energy and the amplitude of the external perturbation and we show, in
the framework of the Dynamically Driven Renormalization Group (DDRG), that any
finite value of the rigidity in a generalized sandpile model renormalizes to an
infinite value at the fixed point, i.e. on a large scale. The fixed point value
of the rigidity allows then for a non ambiguous distinction between
sandpile-like systems and diffusive systems. Numerical simulations support our
analytical results.Comment: to be published in Phys. Rev.
Quantum discord in finite XY chains
We examine the quantum discord between two spins in the exact ground state of
finite spin 1/2 arrays with anisotropic XY couplings in a transverse field B.
It is shown that in the vicinity of the factorizing field B_s, the discord
approaches a common finite non-negligible limit which is independent of the
pair separation and the coupling range. An analytic expression of this limit is
provided. The discord of a mixture of aligned pairs in two different
directions, crucial for the previous results, is analyzed in detail, including
the evaluation of coherence effects, relevant in small samples and responsible
for a parity splitting at B_s. Exact results for finite chains with first
neighbor and full range couplings and their interpretation in terms of such
mixtures are provided.Comment: 9 pages, 6 figure
Quantum correlations and least disturbing local measurements
We examine the evaluation of the minimum information loss due to an unread
local measurement in mixed states of bipartite systems, for a general entropic
form. Such quantity provides a measure of quantum correlations, reducing for
pure states to the generalized entanglement entropy, while in the case of mixed
states it vanishes just for classically correlated states with respect to the
measured system, as the quantum discord. General stationary conditions are
provided, together with their explicit form for general two-qubit states.
Closed expressions for the minimum information loss as measured by quadratic
and cubic entropies are also derived for general states of two-qubit systems.
As application, we analyze the case of states with maximally mixed marginals,
where a general evaluation is provided, as well as X states and the mixture of
two aligned states.Comment: 10 pages, 3 figure
Discord and information deficit in the XX chain
We examine the quantum correlations of spin pairs in the cyclic spin 1/2
chain in a transverse field, through the analysis of the quantum discord, the
geometric discord and the information deficit. It is shown that while these
quantities provide the same qualitative information, being non-zero for all
temperatures and separations and exhibiting the same type of asymptotic
behavior for large temperatures or separations, important differences arise in
the minimizing local measurement that defines them. Whereas the quantum discord
prefers a spin measurement perpendicular to the transverse field, the geometric
discord and information deficit exhibit a perpendicular to parallel transition
as the field increases, which subsists at all temperatures and for all
separations. Moreover, it is shown that such transition signals the change from
a Bell state to an aligned separable state of the dominant eigenstate of the
reduced density matrix of the pair. Full exact results for both the
thermodynamic limit and the finite chain are provided, through the
Jordan-Wigner fermionization.Comment: 23 pages, 6 figures. References adde
Generalized entropic measures of quantum correlations
We propose a general measure of non-classical correlations for bipartite
systems based on generalized entropic functions and majorization properties.
Defined as the minimum information loss due to a local measurement, in the case
of pure states it reduces to the generalized entanglement entropy, i.e., the
generalized entropy of the reduced state. However, in the case of mixed states
it can be non-zero in separable states, vanishing just for states diagonal in a
general product basis, like the Quantum Discord. Simple quadratic measures of
quantum correlations arise as a particular case of the present formalism. The
minimum information loss due to a joint local measurement is also discussed.
The evaluation of these measures in a few simple relevant cases is as well
provided, together with comparison with the corresponding entanglement
monotones.Comment: 9 pages, 2 figure
Toward Defining Literacy
Literacy is a topic much on the public\u27s mind these days. It is one of those subjects on which all laypersons think they are experts. When it comes time, however, to establish measures of illiteracy rates or to set policies, it becomes apparent that we know less than we thought we did. It is small comfort to know that specialists also have their differences
Anderson Localization in Euclidean Random Matrices
We study spectra and localization properties of Euclidean random matrices.
The problem is approximately mapped onto that of a matrix defined on a random
graph. We introduce a powerful method to find the density of states and the
localization threshold. We solve numerically an exact equation for the
probability distribution function of the diagonal element of the the resolvent
matrix, with a population dynamics algorithm, and we show how this can be used
to find the localization threshold. An application of the method in the context
of the Instantaneous Normal Modes of a liquid system is given.Comment: 4 page
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