{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"1c58922b76a67aa1f27bdd5723a980093660ed20f1e7649c4e18487c53e1e98c","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"3d91aef6d5287694c8f7e9808c7c5dd3de3a9757cba28e4cc1087184fd444450","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qi.quantum-shannon-theory.npt-bound-entanglement","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Some entangled states cannot be purified into perfect entangled pairs, no matter how many copies are used. All known examples pass a simple test called positive partial transpose, and it is open whether states that fail the test can also be impossible to purify.","posed_since":"2000","precise":"Does there exist a bipartite state $\\rho$ on $C^{d}\\,\\operatorname{tensor}\\,C^{d}$, $d \\ge 3$, with negative partial transpose $\\rho^{\\Gamma}$ that is not distillable, i.e. for every n and all rank-2 projectors P, Q on the n-copy spaces, $(P\\,\\operatorname{tensor}\\,Q)(\\rho^{\\Gamma})^{\\operatorname{tensor}\\,n}(P\\,\\operatorname{tensor}\\,Q) \\ge 0$? It suffices to decide this for Werner states $\\rho(d, \\alpha) = (1 + \\alpha V)/(d^{2} + \\alpha d)$, $V$ the swap operator, with $-1/2 \\le \\alpha < -1/d$ (for $\\alpha < -1/2$ the state is already 1-copy distillable).","problem_ref":null,"references":"","settled_by":"A proof that some NPT Werner state is n-copy undistillable for all n, or a distillation protocol for every NPT state.","status_note":"Listed as open with a prize in 2022 (Horodecki, Rudnicki and Zyczkowski, PRX Quantum 3, 010101).","title":"Do bound entangled states with negative partial transpose exist","topic_ref":"66c5088d9a8eed6c4b6c5d401128245d915bf032a0cd5d9569f7f404a77d69c8"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"739762f12407ed0e7d7603081db99791c540b8c9c650118d7c95395904b30d49","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"1256c13ededf79ec9baf1fbfaa85117dacbe055a2177be7401e8871dcf86ecb5","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"mBitzpeIBHNB3v-791LCW0oyJGgifuYvJe3woi4G7Qo5OxIEuJ69s2ilsaD2QzEurXUnhg_EBQ7mSLLnYAbyDw"},"schema":"pubphys.envelope/1"},"record_hash":"739762f12407ed0e7d7603081db99791c540b8c9c650118d7c95395904b30d49","leaf_index":2035}