Entanglement map · Established

Entanglement can be certified by witness operators

Proved, with a source.

A witness is an observable whose expectation value can only take certain values on separable states, so measuring beyond them certifies entanglement. A Bell inequality violation can be written formally as such a witness.

Connections

• Part of: Detection
• See also: A hierarchy of semidefinite tests detects every entangled state

Sources

• Separability of mixed states: necessary and sufficient conditions. M. Horodecki, P. Horodecki, R. Horodecki, 1996.
• Bell inequalities and the separability criterion. B. M. Terhal, 1999.
• Entanglement detection. O. Gühne, G. Tóth, 2008.

Checked 2026-10-30.