Entanglement map · Conjectured

Is the composition of two PPT maps always entanglement breaking?

Widely expected, not proved in general.

Equivalently: can two PPT entangled links ever generate entanglement between their ends through entanglement swapping? The conjecture says no.

Still unknown

It has been proved in dimension 3 and for Gaussian channels. Higher finite dimensions remain open.

Connections

• Part of: Detection
• See also: Bound entanglement exists

Sources

• When do composed maps become entanglement breaking?. M. Christandl, A. Müller-Hermes, M. M. Wolf, 2018.
• The positive partial transpose conjecture for n=3. L. Chen, Y. Yang, W. Tang, 2018.
• Beyond the positive partial transpose squared conjecture: the qutrit case. J. An, S. Lee, 2026.

Checked 2026-10-30.