{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"d23bd66078237accfa7964e767c1df340e23391528772bf4f73aff3e3ec9520e","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"a4f0a5ff65144bbe09654df2ab8f433c56a679c19d32b2064b9c9fc7c5195897","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"qi.quantum-shannon-theory.ppt-squared","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"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.","posed_since":"2012","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 $d \\ge 4$.","problem_ref":null,"references":"","settled_by":"A proof for all d, or an explicit pair of PPT channels whose composition is not entanglement breaking.","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 $d \\ge 4$.","title":"PPT-squared conjecture: is composing two PPT channels entanglement breaking","topic_ref":"66c5088d9a8eed6c4b6c5d401128245d915bf032a0cd5d9569f7f404a77d69c8"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"abeef5db0c354ad4a545105fb5bebeb398efde45a3697a21b1ca2eadd1b52354","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"b4d0558a7ab22599e23cc90316791f195c62c2ba7a062fac0950a994c1da07a9","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"36HIa-PfKkDZz03_Hz6yCurC5PYxjZkFR1DXJ_hlEhKwx-yds4201l5EIQmEBvdQHJdCwchD5Vf6O8Ms9lfXBA"},"schema":"pubphys.envelope/1"},"record_hash":"abeef5db0c354ad4a545105fb5bebeb398efde45a3697a21b1ca2eadd1b52354","leaf_index":2036}