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.
|Pages (from-to)||062313-1 - 062312-13|
|Number of pages||13|
|Journal||Physical Review A - Atomic, Molecular, and Optical Physics|
|Publication status||Published - 2000|