A preprint posted to arXiv — not yet peer-reviewed — reports two main advances in the theory of entanglement distillation under PPT (positive-partial-transpose-preserving) channels, the class of operations that remain completely positive when composed with partial transposition. Working in the asymptotic regime of vanishing but non-zero error, the authors derive a regularised formula for the PPT distillable entanglement expressed via a measured-relative-entropy-like quantity, and establish two independent single-letter upper bounds: one built from operator quadratic forms, and a second that draws on Hirschman's strengthening of the classical Hadamard three-line theorem from complex analysis.
The sharper of these converses settles an open question posed by Regula and collaborators in 2019: the PPT distillable entanglement can be strictly smaller than the regularised Rains bound, a quantity previously considered the tightest known PPT-based ceiling. The gap is demonstrated concretely for 3×3 Werner states at antisymmetric weight 25/26, where the authors certify an upper bound of approximately 0.621 ebits against a Rains bound of roughly 0.648 ebits — a modest but unambiguous separation.
On the lower-bound side, the regularised formula yields a quantitative relationship between PPT distillable entanglement and the entanglement negativity, strengthening the qualitative result that any NPT state is PPT distillable. As with all arXiv preprints, these claims await independent peer review, and the significance of the techniques — particularly the analytic interpolation method via Hirschman's theorem — will require further scrutiny by the community.