Improved Semidefinite Programming Upper Bound on Distillable Entanglement

TL;DR

This paper introduces a new SDP-based entanglement measure that provides a tighter upper bound on distillable entanglement than the logarithmic negativity, with exact characterizations for certain states.

Contribution

A novel additive SDP entanglement measure is proposed, improving bounds on distillable entanglement and offering a simple characterization for one-copy PPT distillation.

Findings

New SDP measure is always less than or equal to logarithmic negativity.

The measure is strictly smaller than the logarithmic negativity in general.

Identifies a state where bounds coincide with actual distillable entanglement.

Abstract

A new additive and semidefinite programming (SDP) computable entanglement measure is introduced to upper bound the amount of distillable entanglement in bipartite quantum states by operations completely preserving the positivity of partial transpose (PPT). This quantity is always smaller than or equal to the logarithmic negativity, the previously best known SDP bound on distillable entanglement, and the inequality is strict in general. Furthermore, a succinct SDP characterization of the one-copy PPT deterministic distillable entanglement for any given state is also obtained, which provides a simple but useful lower bound on the PPT distillable entanglement. Remarkably, there is a genuinely mixed state of which both bounds coincide with the distillable entanglement while being strictly less than the logarithmic negativity.