Entanglement map · Established

A hierarchy of semidefinite tests detects every entangled state

Proved, with a source.

Separable states have symmetric extensions to more parties. Searching for such an extension is a semidefinite program, and any entangled state fails at some finite level of the hierarchy. The first level is the partial transpose test.

Connections

• Part of: Detection
• Relies on: Every separable state has a positive partial transpose
• See also: Entanglement can be certified by witness operators
• See also: Deciding separability is NP-hard

Sources

• A complete family of separability criteria. A. C. Doherty, P. A. Parrilo, F. M. Spedalieri, 2003.

Checked 2026-10-30.