Entanglement map · Refuted

Relative entropy of entanglement is additive

The statement shown is false.

The relative entropy of entanglement measures distance to the separable set. Vollbrecht and Werner found a counterexample to its additivity, which is why the regularised version is the quantity that appears in asymptotic theorems.

Connections

• Part of: Measures
• See also: The generalised quantum Stein's lemma, and reversibility under asymptotically non-entangling operations

Sources

• Entanglement measures and purification procedures. V. Vedral, M. B. Plenio, 1997.
• Entanglement measures under symmetry. K. G. H. Vollbrecht, R. F. Werner, 2000.

Checked 2026-10-30.