Entanglement map · Established

Bound entanglement exists

Proved, with a source.

A distillable state must violate the partial transpose test, so PPT entangled states cannot be distilled. There are two kinds of entanglement: free and bound.

Connections

• Part of: Conversion
• Relies on: PPT entangled states exist in 3×3 and 2×4
• See also: PPT entangled states exist in 3×3 and 2×4
• See also: Is the composition of two PPT maps always entanglement breaking?
• Needed by: Bound entanglement can improve teleportation
• See also: Do bound entangled states with a negative partial transpose exist?
• See also: Bell nonlocality implies distillability (the Peres conjecture)
• Needed by: Entanglement manipulation under LOCC is irreversible

Sources

• Mixed-state entanglement and distillation: is there a "bound" entanglement in nature?. M. Horodecki, P. Horodecki, R. Horodecki, 1998.

Checked 2026-10-30.