1,659 research outputs found
Optimal Decompositions of Barely Separable States
Two families of bipartite mixed quantum states are studied for which it is
proved that the number of members in the optimal-decomposition ensemble --- the
ensemble realizing the entanglement of formation --- is greater than the rank
of the mixed state. We find examples for which the number of states in this
optimal ensemble can be larger than the rank by an arbitrarily large factor. In
one case the proof relies on the fact that the partial transpose of the mixed
state has zero eigenvalues; in the other case the result arises from the
properties of product bases that are completable only by embedding in a larger
Hilbert space.Comment: 14 Pages (RevTeX), 1 figure (eps). Submitted to the special issue of
the J. Mod. Opt. V2: Change in terminology from "ensemble length" to
"ensemble cardinality
Easy implementable algorithm for the geometric measure of entanglement
We present an easy implementable algorithm for approximating the geometric
measure of entanglement from above. The algorithm can be applied to any
multipartite mixed state. It involves only the solution of an eigenproblem and
finding a singular value decomposition, no further numerical techniques are
needed. To provide examples, the algorithm was applied to the isotropic states
of 3 qubits and the 3-qubit XX model with external magnetic field.Comment: 9 pages, 3 figure
Measures of entanglement in multipartite bound entangled states
Bound entangled states are states that are entangled but from which no
entanglement can be distilled if all parties are allowed only local operations
and classical communication. However, in creating these states one needs
nonzero entanglement resources to start with. Here, the entanglement of two
distinct multipartite bound entangled states is determined analytically in
terms of a geometric measure of entanglement and a related quantity. The
results are compared with those for the negativity and the relative entropy of
entanglement.Comment: 5 pages, no figure; title change
Linking a distance measure of entanglement to its convex roof
An important problem in quantum information theory is the quantification of
entanglement in multipartite mixed quantum states. In this work, a connection
between the geometric measure of entanglement and a distance measure of
entanglement is established. We present a new expression for the geometric
measure of entanglement in terms of the maximal fidelity with a separable
state. A direct application of this result provides a closed expression for the
Bures measure of entanglement of two qubits. We also prove that the number of
elements in an optimal decomposition w.r.t. the geometric measure of
entanglement is bounded from above by the Caratheodory bound, and we find
necessary conditions for the structure of an optimal decomposition.Comment: 11 pages, 4 figure
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