Computable upper bounds for PPT distillable entanglement

Construct a convergent computable family of upper bounds that certifies arbitrarily accurate values of the PPT distillable entanglement for every finite-dimensional bipartite state.

Background

The paper establishes a computable increasing sequence of lower bounds converging to the PPT distillable entanglement, but the separation from the regularised Rains bound prevents the authors from obtaining computability through that upper-bound framework. A complementary computable sequence of upper bounds would provide two-sided effective approximations and settle the computability question for the PPT distillable entanglement.

References

Our separation rules out that identification, but does not rule out computability by another method; the existence of a convergent computable family of upper bounds remains open.

— On PPT entanglement distillation  (2610.12454 - Lami, 8 Oct 2026) in Section 3, subsection “A regularised formula”

The main problem left open is to calculate the PPT distillable entanglement by means of a single-letter formula, or at least to decide whether it is computable at all for general states.

— On PPT entanglement distillation  (2610.12454 - Lami, 8 Oct 2026) in Section 8, “Conclusion”