{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"8b21a79a0ecc1ef498fe09a3da26455eaae319f91ac061c9c773646de5658efc","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["c71320a93fc88493638591e2dc26f61f9a11aad2484a5916d3845d7b1f97ea5a","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"f91c31e09f54d8cf2cef2e731525724368cf605e3285e262b381cf3b3cb812de","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":"2","parents":[],"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, $\\left(P\\,\\otimes\\,Q\\right)\\left[(\\rho^\\Gamma)^{\\otimes 2}\\right]\\left(P\\,\\otimes\\,Q\\right)$ 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":"c71320a93fc88493638591e2dc26f61f9a11aad2484a5916d3845d7b1f97ea5a","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":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"61b48b898d700a817aac3ef99b905398e04a8fd2fba5904a34ae1651caae181a","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"0f6badb0cdb15034796ba72b92ac14c846fd076b5f351122825469f90a0306af","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"w42RKc8SgEynOYH9uNx8-xuWYidmFMcLiPACnbKF5qDMui9eJ5qZ8XGhFo1Lf_MDFg7Gv4NsBfysyDHa0uDDAA"},"schema":"pubphys.envelope/1"},"record_hash":"61b48b898d700a817aac3ef99b905398e04a8fd2fba5904a34ae1651caae181a","leaf_index":3748}