Entanglement map · Topic

Detection

Given a density matrix, is it entangled? The definition asks us to search over every possible mixture of product states, so the branch looks for tests we can actually run, and asks how far they can reach.

Connections

• Part of: Entanglement
• Includes: Every separable state has a positive partial transpose
• Includes: In 2×2 and 2×3 systems, PPT is equivalent to separability
• Includes: PPT entangled states exist in 3×3 and 2×4
• Includes: Entanglement can be certified by witness operators
• Includes: The cross norm and realignment criterion
• Includes: A hierarchy of semidefinite tests detects every entangled state
• Includes: Deciding separability is NP-hard
• Includes: Is the composition of two PPT maps always entanglement breaking?
• Includes: How powerful are two unentangled quantum proofs?

Sources

• Entanglement detection. O. Gühne, G. Tóth, 2008.

Checked 2026-10-30.