{"paper":{"title":"A classification of incomparable states","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Spmshubhro Bandyopadhyay, Ujjwal Sen, Vwani P. Roychowdhury","submitted_at":"2001-03-23T13:51:22Z","abstract_excerpt":"Let (\\{| \\psi> ,| \\phi>}) be an incomparable pair of states ((| \\psi \\nleftrightarrow | \\phi>)), \\emph, i.e., (| \\psi>) and (| \\phi>) cannot be transformed to each other with probability one by local transformations and classical communication (LOCC). We show that incomparable states can be multiple-copy transformable, \\emph, i.e., there can exist a \\emph{k}, such that (| \\psi> ^{\\otimes k+1}\\to | \\phi> ^{\\otimes k+1}), i.e., (k+1) copies of (| \\psi>) can be transformed to (k+1) copies of (| \\phi>) with probability one by LOCC but (| \\psi> ^{\\otimes n}\\nleftrightarrow | \\phi> ^{\\otimes n} \\for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0103131","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"}