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How entangled are bound entangled states?

Wei, Tzu-Chieh; Altepeter, Josseph B.; Goldbart, Paul M.; Munro, William J.

HPL-2003-239

Keyword(s): bound entanglement; quantum entanglement; entanglement measures

Abstract: 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 to start with. To date, no analytic results reveal the entanglement content of these strange states. Here, the entanglement of two distinct multipartite bound entangled states is determined analytically in terms of geometric measure of entanglement and a related quantity. The results are compared with those for the relative entropy of entanglement and the negativity, and plausible lower bounds on the entanglement of formation are given. Along the way, an intriguing example emerges, in which a bipartite mixed state, associated with Smolin's bound entangled state, can be reversibly converted into a bipartite Bell state, and vice versa. Furthermore, for any N-qubit state that is PPT for all bipartite partitionings, there is no violation of the two-setting, three-setting, and functional Bell inequalities. Notes: Tzu-Chieh Wei, Joseph B. Altepeter and Paul M. Goldbart, Department of Physics, University of Illinois at Urbana- Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080 USA

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