{"paper":{"title":"The PPT square conjecture holds generically for some classes of independent states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Beno\\^it Collins, Ping Zhong, Zhi Yin","submitted_at":"2018-03-01T00:21:38Z","abstract_excerpt":"Let $|\\psi\\rangle\\langle \\psi|$ be a random pure state on $\\mathbb{C}^{d^2}\\otimes \\mathbb{C}^s$, where $\\psi$ is a random unit vector uniformly distributed on the sphere in $\\mathbb{C}^{d^2}\\otimes \\mathbb{C}^s$. Let $\\rho_1$ be random induced states $\\rho_1=Tr_{\\mathbb{C}^s}(|\\psi\\rangle\\langle \\psi |)$ whose distribution is $\\mu_{d^2,s}$; and let $\\rho_2$ be random induced states following the same distribution $\\mu_{d^2,s}$ independent from $\\rho_1$. Let $\\rho$ be a random state induced by the entanglement swapping of $\\rho_1$ and $\\rho_2$. We show that the empirical spectrum of $\\rho- {1\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00143","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}