Linking a distance measure of entanglement to its convex roof

Details Linking a distance measure of entanglement to its convex roof Linking a distance measure of entanglement to its convex roof

2010-06-15

arxiv.org/abs/1006.3077v2

New J. Phys. 12 123004 (2010)

Physics

Quantum Physics

11 pages, 4 figures

Scientific paper

10.1088/1367-2630/12/12/123004

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.

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