TY - JOUR

T1 - Evidence for bound entangled states with negative partial transpose

AU - DiVincenzo, David P.

AU - Shor, Peter W.

AU - Smolin, John A.

AU - Terhal, Barbara M.

AU - Thapliyal, Ashish V.

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85035299498&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.61.062312

DO - 10.1103/PhysRevA.61.062312

M3 - Article

AN - SCOPUS:85035299498

VL - 61

SP - 062313-1 - 062312-13

JO - Physical Review A (Atomic, Molecular and Optical Physics)

JF - Physical Review A (Atomic, Molecular and Optical Physics)

SN - 1050-2947

IS - 6

M1 - 062312

ER -