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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"quant-ph/0103131","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2001-03-23T13:51:22Z","cross_cats_sorted":[],"title_canon_sha256":"3dcbacbc87876137064867057e6d46fb0e70c5cb3cd5d338c323f9b9902327a4","abstract_canon_sha256":"eb1b0b3edaec5cda12a7074a4220c94657b0630a4ae6c326086fd8f2805f0ce2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:20.563528Z","signature_b64":"Vf2makpa49jj5RWWR9lbTC2N2m1VeKuXYFrKac4DaJ3PCktd/Xeu+znAaa9cQfBe3cQ0JWvogctKSEabnjhnAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"932bfb9671e78c3bd84897db724a78c7b30e27347d25403aca41344ec7f272fc","last_reissued_at":"2026-05-18T03:24:20.563042Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:20.563042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A classification of incomparable states","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Spmshubhro Bandyopadhyay, Ujjwal Sen, Vwani P. 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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"},"aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0103131","created_at":"2026-05-18T03:24:20.563116+00:00"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0103131v1","created_at":"2026-05-18T03:24:20.563116+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0103131","created_at":"2026-05-18T03:24:20.563116+00:00"},{"alias_kind":"pith_short_12","alias_value":"SMV7XFTR46GD","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_16","alias_value":"SMV7XFTR46GDXWCI","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_8","alias_value":"SMV7XFTR","created_at":"2026-05-18T12:25:50.845339+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SMV7XFTR46GDXWCIS7NXESTYY6","json":"https://pith.science/pith/SMV7XFTR46GDXWCIS7NXESTYY6.json","graph_json":"https://pith.science/api/pith-number/SMV7XFTR46GDXWCIS7NXESTYY6/graph.json","events_json":"https://pith.science/api/pith-number/SMV7XFTR46GDXWCIS7NXESTYY6/events.json","paper":"https://pith.science/paper/SMV7XFTR"},"agent_actions":{"view_html":"https://pith.science/pith/SMV7XFTR46GDXWCIS7NXESTYY6","download_json":"https://pith.science/pith/SMV7XFTR46GDXWCIS7NXESTYY6.json","view_paper":"https://pith.science/paper/SMV7XFTR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=quant-ph/0103131&json=true","fetch_graph":"https://pith.science/api/pith-number/SMV7XFTR46GDXWCIS7NXESTYY6/graph.json","fetch_events":"https://pith.science/api/pith-number/SMV7XFTR46GDXWCIS7NXESTYY6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SMV7XFTR46GDXWCIS7NXESTYY6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SMV7XFTR46GDXWCIS7NXESTYY6/action/storage_attestation","attest_author":"https://pith.science/pith/SMV7XFTR46GDXWCIS7NXESTYY6/action/author_attestation","sign_citation":"https://pith.science/pith/SMV7XFTR46GDXWCIS7NXESTYY6/action/citation_signature","submit_replication":"https://pith.science/pith/SMV7XFTR46GDXWCIS7NXESTYY6/action/replication_record"}},"created_at":"2026-05-18T03:24:20.563116+00:00","updated_at":"2026-05-18T03:24:20.563116+00:00"}