575 research outputs found
Probability density function characterization of multipartite entanglement
We propose a method to characterize and quantify multipartite entanglement
for pure states. The method hinges upon the study of the probability density
function of bipartite entanglement and is tested on an ensemble of qubits in a
variety of situations. This characterization is also compared to several
measures of multipartite entanglement.Comment: 7 pages, 2 figures; published version; title changed; further
explanations and comparison with several measures of multipartite
entanglement adde
Statistical mechanics of multipartite entanglement
We characterize the multipartite entanglement of a system of n qubits in
terms of the distribution function of the bipartite purity over all balanced
bipartitions. We search for those (maximally multipartite entangled) states
whose purity is minimum for all bipartitions and recast this optimization
problem into a problem of statistical mechanics.Comment: final versio
Multipartite Entanglement and Frustration
Some features of the global entanglement of a composed quantum system can be
quantified in terms of the purity of a balanced bipartition, made up of half of
its subsystems. For the given bipartition, purity can always be minimized by
taking a suitable (pure) state. When many bipartitions are considered, the
requirement that purity be minimal for all bipartitions can engender conflicts
and frustration arises. This unearths an interesting link between frustration
and multipartite entanglement, defined as the average purity over all
(balanced) bipartitions.Comment: 15 pages, 7 figure
Characterizing and measuring multipartite Entanglement
A method is proposed to characterize and quantify multipartite entanglement
in terms of the probability density function of bipartite entanglement over all
possible balanced bipartitions of an ensemble of qubits. The method is tested
on a class of random pure states.Comment: 7 pages, 5 figures. Submitted to "International Journal of Quantum
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Classical Statistical Mechanics Approach to Multipartite Entanglement
We characterize the multipartite entanglement of a system of n qubits in
terms of the distribution function of the bipartite purity over balanced
bipartitions. We search for maximally multipartite entangled states, whose
average purity is minimal, and recast this optimization problem into a problem
of statistical mechanics, by introducing a cost function, a fictitious
temperature and a partition function. By investigating the high-temperature
expansion, we obtain the first three moments of the distribution. We find that
the problem exhibits frustration.Comment: 38 pages, 10 figures, published versio
Multipartite entanglement in qubit systems
We introduce a potential of multipartite entanglement for a system of n
qubits, as the average over all balanced bipartitions of a bipartite
entanglement measure, the purity. We study in detail its expression and look
for its minimizers, the maximally multipartite entangled states. They have a
bipartite entanglement that does not depend on the bipartition and is maximal
for all possible bipartitions. We investigate their structure and consider
several examples for small n.Comment: 42 page
Gaussian maximally multipartite entangled states
We study maximally multipartite entangled states in the context of Gaussian
continuous variable quantum systems. By considering multimode Gaussian states
with constrained energy, we show that perfect maximally multipartite entangled
states, which exhibit the maximum amount of bipartite entanglement for all
bipartitions, only exist for systems containing n=2 or 3 modes. We further
numerically investigate the structure of these states and their frustration for
n<=7.Comment: 6 pages, 2 figures, comments are welcom
Robust and efficient generator of almost maximal multipartite entanglement
Quantum chaotic maps can efficiently generate pseudo-random states carrying
almost maximal multipartite entanglement, as characterized by the probability
distribution of bipartite entanglement between all possible bipartitions of the
system. We show that such multipartite entanglement is robust, in the sense
that, when realistic noise is considered, distillable entanglement of
bipartitions remains almost maximal up to a noise strength that drops only
polynomially with the number of qubits.Comment: 4 pages, 4 figures. Published versio
Multipartite entanglement characterization of a quantum phase transition
A probability density characterization of multipartite entanglement is tested
on the one-dimensional quantum Ising model in a transverse field. The average
and second moment of the probability distribution are numerically shown to be
good indicators of the quantum phase transition. We comment on multipartite
entanglement generation at a quantum phase transition.Comment: 10 pages, 6 figures, final versio
Maximally multipartite entangled states
We introduce the notion of maximally multipartite entangled states of n
qubits as a generalization of the bipartite case. These pure states have a
bipartite entanglement that does not depend on the bipartition and is maximal
for all possible bipartitions. They are solutions of a minimization problem.
Examples for small n are investigated, both analytically and numerically.Comment: 5 pages, 1 figure, final verso
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