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We give a necessary and sufficient condition for the vanishing of the concurrence $C_{1(2...n)}$. The condition implies that the concurrence $% C_{1(2...n)}$ is always positive for any entangled states while the $n$% -tangle vanishes for some entangled states. We argue that for even $n$\\ qubits, the concurrence $C_{1(2...n)}$\\ is equal to or greater than the $n$% "},"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":"1003.4774","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"quant-ph","submitted_at":"2010-03-24T23:10:41Z","cross_cats_sorted":[],"title_canon_sha256":"6628b72a9ecf0058f21de15e9ed0f02ea5bb566d2637a384ca04f16c1cb816c9","abstract_canon_sha256":"a6f93d952cc97c76733f6b039698f84a756f32fd77b40c7c3ea32197e49e6d21"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:30.708908Z","signature_b64":"SwxdugssVWQm8AzAOti+F1erOoxgXrBKXYIUBw5/a4nf358suX4n8PeBTnXMEavdOLytCoOL4toiS2Ls2OVxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb813b2680aef0cbdf661a8bed7bfa438c20d1ff720d4ea19466df1fb16f3e66","last_reissued_at":"2026-05-18T04:40:30.708167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:30.708167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Relationship between the n-tangle and the residual entanglement of even n qubits","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"D. Li, X. Li","submitted_at":"2010-03-24T23:10:41Z","abstract_excerpt":"We show that $n$-tangle, the generalization of the 3-tangle to even $n$ qubits, is the square of the SLOCC polynomial invariant of degree 2. We find that the $n$-tangle is not the residual entanglement for any even $n\\geq 4$\\ qubits. We give a necessary and sufficient condition for the vanishing of the concurrence $C_{1(2...n)}$. The condition implies that the concurrence $% C_{1(2...n)}$ is always positive for any entangled states while the $n$% -tangle vanishes for some entangled states. 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