Entanglement map · Established

Every separable state has a positive partial transpose

Proved, with a source.

Transpose one subsystem of a separable state and the result still has no negative eigenvalues. A negative eigenvalue is therefore proof of entanglement, and this test is stronger than Bell inequalities.

Connections

• Part of: Detection
• Needed by: In 2×2 and 2×3 systems, PPT is equivalent to separability
• Needed by: A hierarchy of semidefinite tests detects every entangled state
• Needed by: Negativity and log-negativity can be computed for any state

Sources

• Separability criterion for density matrices. A. Peres, 1996.

Checked 2026-10-30.