Entanglement map · Established

PPT entangled states exist in 3×3 and 2×4

Proved, with a source.

One dimension past the solved cases, the equivalence fails: there are entangled states the partial transpose test cannot see. Explicit examples come from a separate criterion based on the range of the density matrix.

Connections

• Part of: Detection
• See also: In 2×2 and 2×3 systems, PPT is equivalent to separability
• See also: Bound entanglement exists
• Needed by: Bound entanglement exists

Sources

• Separability criterion and inseparable mixed states with positive partial transposition. P. Horodecki, 1997.

Checked 2026-10-30.