Entanglement map · Established

In 2×2 and 2×3 systems, PPT is equivalent to separability

Proved, with a source.

In these two smallest cases the partial transpose test is both necessary and sufficient. Separability is settled by one eigenvalue calculation.

Connections

• Part of: Detection
• Relies on: Every separable state has a positive partial transpose
• See also: PPT entangled states exist in 3×3 and 2×4

Sources

• Separability of mixed states: necessary and sufficient conditions. M. Horodecki, P. Horodecki, R. Horodecki, 1996.

Checked 2026-10-30.