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Accepted · first revision · record

Title: PPT-squared conjecture: is composing two PPT channels entanglement breaking
Plain: Some noisy channels are so weak at carrying entanglement that their partial transpose stays positive. The conjecture says that applying two such channels in a row always destroys all entanglement.
Precise: For all quantum channels $\Phi_1, \Phi_2$ on d x d matrices whose Choi matrices have positive partial transpose, is $\Phi_2$ composed with $\Phi_1$ entanglement breaking? Proved for $d \le 3$ (2018-2019) and in an asymptotic form under repeated composition; open for $d \ge 4$.
Settled by: A proof for all d, or an explicit pair of PPT channels whose composition is not entanglement breaking.
Kind: well-posed
Answer type: proof
References: (empty)
Literature status: partially-resolved
Status note: A 2026 preprint proves that every PPT channel has finite entanglement-breaking index (arXiv:2608.13551); the two-fold statement remains open for $d \ge 4$.
Posed since: 2012