Evidence for bound entangled states with negative partial transpose

Journal article (2000)

Authors

David P. Divincenzo IBM Thomas J. Watson Research Centre
Peter W. Shor Florham Park
John A. Smolin IBM Thomas J. Watson Research Centre
B.M. Terhal IBM Thomas J. Watson Research Centre
Ashish V. Thapliyal University of California
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Published Date

2000

Language

English

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Abstract

We exhibit a two-parameter family of bipartite mixed states [Formula Presented] in a [Formula Presented] Hilbert space, which are negative under partial transposition (NPT), but for which we conjecture that no maximally entangled pure states in [Formula Presented] can be distilled by local quantum operations and classical communication (LQ+CC). Evidence for this undistillability is provided by the result that, for certain states in this family, we cannot extract entanglement from any arbitrarily large number of copies of [Formula Presented] using a projection on [Formula Presented] These states are canonical NPT states in the sense that any bipartite mixed state in any dimension with NPT can be reduced by LQ+CC operations to a NPT state of the [Formula Presented] form. We show that the main question about the distillability of mixed states can be formulated as an open mathematical question about the properties of composed positive linear maps.