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We investigate the properties of three W-like states named as $|\\vartheta ^{\\prime }\\rangle $, $|\\eta ^{\\prime }\\rangle $ and $|\\xi ^{\\prime }\\rangle $. We point out that $|\\vartheta ^{\\prime }\\rangle $ (resp. $|\\eta ^{\\prime }\\rangle $ and $|\\xi ^{\\prime }\\rangle $) has the maximal von Neumann entanglement entropy (vNEE) $S(\\rho _{A})=\\ln 2$ (resp. $S(\\r"},"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":"2607.13223","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-07-14T19:31:39Z","cross_cats_sorted":[],"title_canon_sha256":"fd31b1d243f1f24f9ee791ed25d89bcf2aa45624c697b5fe08f02b9feeaffad0","abstract_canon_sha256":"3cbd4b95d3bb0bd24c3a85472471e88d7a0de7087cddb9b78b232ccd2e8f0cef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T00:22:03.706096Z","signature_b64":"4ZyBfvVKfy1WJzbgtbrOblnsQ+LBs5qGMsSA3CRk/XeRAAYJ4VqkRJ9+ADye8SNYvCeXnpzRyQMBGuI7hGdcBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24648ade66a6f06f3ffac3257629a625d5b34e6803e5dea9673ce974f188da9a","last_reissued_at":"2026-07-16T00:22:03.705288Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T00:22:03.705288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Comparing the three W-like states with the W state","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dafa Li","submitted_at":"2026-07-14T19:31:39Z","abstract_excerpt":"In [Phy. Rev. Lett., 98, 260501 (2007)] and previous papers, the W-like states were used in many quantum communication schemes, distillation, teleportation and superdense coding. So far, no one has compared the W-like states with the W state. We investigate the properties of three W-like states named as $|\\vartheta ^{\\prime }\\rangle $, $|\\eta ^{\\prime }\\rangle $ and $|\\xi ^{\\prime }\\rangle $. We point out that $|\\vartheta ^{\\prime }\\rangle $ (resp. $|\\eta ^{\\prime }\\rangle $ and $|\\xi ^{\\prime }\\rangle $) has the maximal von Neumann entanglement entropy (vNEE) $S(\\rho _{A})=\\ln 2$ (resp. $S(\\r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13223","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.13223/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2607.13223","created_at":"2026-07-16T00:22:03.705709+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.13223v1","created_at":"2026-07-16T00:22:03.705709+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13223","created_at":"2026-07-16T00:22:03.705709+00:00"},{"alias_kind":"pith_short_12","alias_value":"ERSIVXTGU3YG","created_at":"2026-07-16T00:22:03.705709+00:00"},{"alias_kind":"pith_short_16","alias_value":"ERSIVXTGU3YG6P72","created_at":"2026-07-16T00:22:03.705709+00:00"},{"alias_kind":"pith_short_8","alias_value":"ERSIVXTG","created_at":"2026-07-16T00:22:03.705709+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/ERSIVXTGU3YG6P72YMSXMKNGEX","json":"https://pith.science/pith/ERSIVXTGU3YG6P72YMSXMKNGEX.json","graph_json":"https://pith.science/api/pith-number/ERSIVXTGU3YG6P72YMSXMKNGEX/graph.json","events_json":"https://pith.science/api/pith-number/ERSIVXTGU3YG6P72YMSXMKNGEX/events.json","paper":"https://pith.science/paper/ERSIVXTG"},"agent_actions":{"view_html":"https://pith.science/pith/ERSIVXTGU3YG6P72YMSXMKNGEX","download_json":"https://pith.science/pith/ERSIVXTGU3YG6P72YMSXMKNGEX.json","view_paper":"https://pith.science/paper/ERSIVXTG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.13223&json=true","fetch_graph":"https://pith.science/api/pith-number/ERSIVXTGU3YG6P72YMSXMKNGEX/graph.json","fetch_events":"https://pith.science/api/pith-number/ERSIVXTGU3YG6P72YMSXMKNGEX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ERSIVXTGU3YG6P72YMSXMKNGEX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ERSIVXTGU3YG6P72YMSXMKNGEX/action/storage_attestation","attest_author":"https://pith.science/pith/ERSIVXTGU3YG6P72YMSXMKNGEX/action/author_attestation","sign_citation":"https://pith.science/pith/ERSIVXTGU3YG6P72YMSXMKNGEX/action/citation_signature","submit_replication":"https://pith.science/pith/ERSIVXTGU3YG6P72YMSXMKNGEX/action/replication_record"}},"created_at":"2026-07-16T00:22:03.705709+00:00","updated_at":"2026-07-16T00:22:03.705709+00:00"}