207 research outputs found
Quantum Entanglement: Separability, Measure, Fidelity of Teleportation and Distillation
Quantum entanglement plays crucial roles in quantum information processing.
Quantum entangled states have become the key ingredient in the rapidly
expanding field of quantum information science. Although the nonclassical
nature of entanglement has been recognized for many years, considerable efforts
have been taken to understand and characterize its properties recently. In this
review, we introduce some recent results in the theory of quantum entanglement.
In particular separability criteria based on the Bloch representation,
covariance matrix, normal form and entanglement witness; lower bounds,
subadditivity property of concurrence and tangle; fully entangled fraction
related to the optimal fidelity of quantum teleportation and entanglement
distillation will be discussed in detail.Comment: 63 pages, 4 figure
Measure of multipartite entanglement with computable lower bounds
In this paper, we present a measure of multipartite entanglement
(-nonseparable), -ME concurrence that
unambiguously detects all -nonseparable states in arbitrary dimensions,
where the special case, 2-ME concurrence , is a
measure of genuine multipartite entanglement. The new measure -ME
concurrence satisfies important characteristics of an entanglement measure
including entanglement monotone, vanishing on -separable states, convexity,
subadditivity and strictly greater than zero for all -nonseparable states.
Two powerful lower bounds on this measure are given. These lower bounds are
experimentally implementable without quantum state tomography and are easily
computable as no optimization or eigenvalue evaluation is needed. We illustrate
detailed examples in which the given bounds perform better than other known
detection criteria.Comment: 12 pages, 3 figure
Entanglement and magnetic order
In recent years quantum statistical mechanics have benefited of cultural
interchanges with quantum information science. There is a bulk of evidence that
quantifying the entanglement allows a fine analysis of many relevant properties
of many-body quantum systems. Here we review the relation between entanglement
and the various type of magnetic order occurring in interacting spin systems.Comment: 29 pages, 10 eps figures. Review article for the special issue
"Entanglement entropy in extended systems" in J. Phys. A, edited by P.
Calabrese, J. Cardy and B. Doyo
Multi-partite analysis of average-subsystem entropies
So-called average subsystem entropies are defined by first taking partial
traces over some pure state to define density matrices, then calculating the
subsystem entropies, and finally averaging over the pure states to define the
average subsystem entropies. These quantities are standard tools in quantum
information theory, most typically applied in bipartite systems. We shall first
present some extensions to the usual bipartite analysis, (including a
calculation of the average tangle, and a bound on the average concurrence),
follow this with some useful results for tripartite systems, and finally extend
the discussion to arbitrary multi-partite systems. A particularly nice feature
of tri-partite and multi-partite analyses is that this framework allows one to
introduce an "environment" for small subsystems to couple to.Comment: Minor changes. 1 reference added. Published versio
General Monogamy Inequality for Bipartite Qubit Entanglement
We consider multipartite states of qubits and prove that their bipartite
quantum entanglement, as quantified by the concurrence, satisfies a monogamy
inequality conjectured by Coffman, Kundu, and Wootters. We relate this monogamy
inequality to the concept of frustration of correlations in quantum spin
systems.Comment: Fixed spelling mistake. Added references. Fixed error in
transformation law. Shorter and more explicit proof of capacity formula.
Reference added. Rewritten introduction and conclusion
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