{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"04db6f2514e1b3d3f67214f40b22d3a8019a9c0f501b4cf428ac2f5422377ad5","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011","739762f12407ed0e7d7603081db99791c540b8c9c650118d7c95395904b30d49"],"salt":"ad8f7133a0d05c12ddcf6fcb1f11e5cfd63769a5c1b7cef3cd5a56e291c2f181","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"qi.quantum-shannon-theory.werner-two-copy","kind":"well-posed","literature_status":"open","n":"1","parents":[{"note":"","parent_revision":"739762f12407ed0e7d7603081db99791c540b8c9c650118d7c95395904b30d49","relation":"special_case"}],"plain":"A sharper test case: one specific entangled state of two four-level systems. The task is to show that even two copies of it cannot be processed into an entangled pair.","posed_since":"2022","precise":"Show that the $d = 4$ Werner state $\\rho(4, -1/2)$ is not 2-copy distillable: for all rank-2 projectors P, Q acting on two copies of each party's space, $\\left(P\\,\\operatorname{tensor}\\,Q\\right)\\left[(\\rho^\\Gamma)^{\\operatorname{tensor} 2}\\right]\\left(P\\,\\operatorname{tensor}\\,Q\\right)$ has no negative eigenvalue; or exhibit P, Q giving a negative eigenvalue. Its partial transpose is proportional to a unitary (Problem 5 of Horodecki, Rudnicki and Zyczkowski 2022).","problem_ref":null,"references":"","settled_by":"A proof of positivity over all rank-2 projector pairs, or explicit projectors giving a negative eigenvalue.","status_note":"","title":"Two-copy distillability of the two-ququart Werner state at $\\alpha = -1/2$","topic_ref":"66c5088d9a8eed6c4b6c5d401128245d915bf032a0cd5d9569f7f404a77d69c8"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"c71320a93fc88493638591e2dc26f61f9a11aad2484a5916d3845d7b1f97ea5a","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"f66cf6941ac087f9b90573d2e0a58257c8ae0a80a0c737ce0ebe7c4b9ea0e83e","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"xamzJ835-TF8S_OB_z7Rievrg40pQTkvXo0JPmOkRMMGSU7GIXgdMCVgAcZoZ-XQ6M6CJT7txiCTO1rMIA4WDA"},"schema":"pubphys.envelope/1"},"record_hash":"c71320a93fc88493638591e2dc26f61f9a11aad2484a5916d3845d7b1f97ea5a","leaf_index":2038}