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Nonadditivity of Bipartite Distillable Entanglement follows from Conjecture on Bound Entangled Werner States

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arxiv quant-ph/0010054 v2 pith:AAZNUUS4 submitted 2000-10-13 quant-ph

Peter W. Shor , John A. Smolin , Barbara M. Terhal This is my paper · ORCID
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keywords distillableentanglementstatesbipartiteboundconjectureentangledproduct
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Assuming the validity of a conjecture in quant-ph/9910026 and quant-ph/9910022 we show that the distillable entanglement for two bipartite states, each of which individually has zero distillable entanglement, can be nonzero. We show that this also implies that the distillable entanglement is not a convex function. Our example consists of the tensor product of a bound entangled state based on an unextendible product basis with a Werner state which lies in the class of conjectured undistillable states.

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  1. A partial-trace matrix inequality and Werner-state distillability

    quant-ph 2026-07 accept novelty 7.0 of 10

    Every rank-at-most-two bipartite matrix satisfies a partial-trace inequality that implies two-copy undistillability of NPT Werner states for all local dimensions when α ≥ −1/2.

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