Evidence for Bound Entangled States with Negative Partial Transpose

Details Evidence for Bound Entangled States with Negative Partial Transpose Evidence for Bound Entangled States with Negative Partial Transpose

1999-10-06

arxiv.org/abs/quant-ph/9910026v3

Phys. Rev. A 61, 062312 (2000)

Physics

Quantum Physics

Revtex, 19 pages, 2 eps figures. v2,3: very minor changes, submitted to Phys. Rev. A. v4: minor typos corrected

Scientific paper

10.1103/PhysRevA.61.062312

We exhibit a two-parameter family of bipartite mixed states $\rho_{bc}$, in a $d\otimes d$ Hilbert space, which are negative under partial transposition (NPT), but for which we conjecture that no maximally entangled pure states in $2\otimes 2$ 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 $\rho_{bc}$ using a projection on $2\otimes 2$. 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 $\rho_{bc}$ 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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