Two-copy sufficiency and exact regularized entanglement of purification

Determine whether two copies suffice to violate additivity for the two-qubit Werner states treated in the paper, and determine the exact regularized entanglement of purification for those states.

Background

The paper establishes a strict separation between single-copy and regularized entanglement of purification for two-qubit Werner states with singlet weight in the interval 1/64 ≤ f < f*, where f* is approximately 0.017086. The argument proves that some finite-copy violation exists but does not identify the required number of copies, and it supplies an achievable asymptotic upper bound rather than the exact regularized value.

References

Several questions remain open. Our argument guarantees a finite-copy violation of additivity without identifying the required number of copies. It remains to determine whether two copies suffice and to find the exact regularized value.

— Entanglement of purification for Werner states: canonical purification and nonadditivity  (2610.03630 - Khanian et al., 2 Oct 2026) in Section 6, Discussion