Entanglement map · Established

Entanglement manipulation under LOCC is irreversible

Proved, with a source.

Creating a bound entangled state costs entanglement, yet none can be distilled back. Every entangled state has strictly positive entanglement cost, so this happens for all non-distillable entangled states.

Connections

• Part of: Conversion
• Relies on: Bound entanglement exists
• See also: Entanglement cost equals regularised entanglement of formation
• See also: Catalysis cannot distill PPT bound entanglement

Sources

• Irreversibility in asymptotic manipulations of entanglement. G. Vidal, J. I. Cirac, 2001.
• Irreversibility for all bound entangled states. D. Yang, M. Horodecki, R. Horodecki, B. Synak-Radtke, 2005.

Checked 2026-10-30.