Von Neumann additivity for classical two-qubit states

Determine whether entanglement of purification is additive for classical two-qubit states at the von Neumann entropy order.

Background

The paper proves nonadditivity of the von Neumann entanglement of purification for separable two-qubit Werner states. This complements earlier Rényi nonadditivity results for classical two-qubit states, but the Werner states considered here are not diagonal in a local product basis. Consequently, the analogous additivity question for classical two-qubit states at Rényi order one remains unresolved.

References

These states are not diagonal in a local product basis, so the corresponding von Neumann question for classical states remains open.

— Entanglement of purification for Werner states: canonical purification and nonadditivity  (2610.03630 - Khanian et al., 2 Oct 2026) in Section 1, Introduction; Section 6, Discussion