Computability of LOCC distillable entanglement

Determine whether the LOCC distillable entanglement of a finite-dimensional bipartite state is Turing computable.

Background

The paper contrasts PPT operations, which admit semidefinite-program descriptions, with the mathematically more complicated class of LOCC operations. Even for simple mixed states, the authors state that the computational status of the LOCC distillable entanglement is unresolved. This problem concerns whether the asymptotic operational quantity can be computed by any Turing machine, rather than merely whether a particular numerical method is efficient.

References

As far as the author is aware, it is even unclear whether $E_{d,\,LOCC}(\rho)$ is Turing computable at all.

— On PPT entanglement distillation  (2610.12454 - Lami, 8 Oct 2026) in Section 1, subsection “Background”