Single-letter one-way distillable entanglement for non-degradable states

TL;DR

This paper identifies conditions under which the one-way distillable entanglement of certain non-degradable, non-PPT states remains single-letter, simplifying its computation and linking it to quantum channel capacity additivity.

Contribution

It introduces new conditions and stability results that ensure additivity and single-letter formulas for one-way distillable entanglement beyond known classes.

Findings

Single-letter formulas for non-degradable, non-PPT states

Additivity guaranteed by regularized less-noisy and informationally degradable conditions

Stability of single-letter property under orthogonal mixture

Abstract

The one-way distillable entanglement is a central operational measure of bipartite entanglement, quantifying the optimal rate at which maximally entangled pairs can be extracted by one-way LOCC. Despite its importance, it is notoriously hard to compute, since it is defined by a regularized optimization over many copies and adaptive one-way protocols. At present, single-letter formulas are only known for (conjugate) degradable and PPT states. More generally, it has remained unclear when one-way distillable entanglement can still be additive beyond degradability and PPT settings, and how such additivity relates to additivity questions of quantum capacity of channels. In this paper, we address this gap by identifying three explicit families of non-degradable and non-PPT states whose one-way distillable entanglement is nevertheless single-letter. First, we introduce two weakened degradability-type conditions--regularized less-noisy and informationally degradable--and prove that each guarantees additivity and hence a single-letter formula. Second, we show a stability result for orthogonally flagged mixtures: when one component has orthogonal support on Alice's system and zero one-way distillable entanglement, the mixture remains single-letter, even though degradability is typically lost under such mixing. Finally, we propose a generalized spin-alignment principle for entropy minimization in tensor-product settings, which we establish in several key cases, including a complete R\'enyi-2 result. As an application, we obtain additivity results for generalized direct-sum channels and their corresponding Choi states.