Evidence for Bound Entangled States with Negative Partial Transpose

1999/10/31 by David P. DiVincenzo, Peter W. Shor, John A. Smolin +2 · 2 citations
Physics and Astronomy · #quant-ph

paper · pdf · doi:10.1103/physreva.61.062312

published as Phys. Rev. A 61, 062312 (2000) · Revtex, 19 pages, 2 eps figures. v2,3: very minor changes, submitted to Phys. Rev. A. v4: minor typos corrected

arxiv created 2000/10/27 · arxiv updated 2009/12/01

Abstract

We exhibit a two-parameter family of bipartite mixed states ρ_bc, in a d⊗ d Hilbert space, which are negative under partial transposition (NPT), but for which we conjecture that no maximally entangled pure states in 2⊗ 2 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 ρ_bc using a projection on 2⊗ 2. 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 an NPT state of the ρ_bc 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.

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