{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AAU5Q2KOAG6XHUHIOSYAVH4BEO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a34f8085d749c8a029e2c3699a623819c60b24f183888a8c5fa980de056e7d09","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-03-28T00:24:15Z","title_canon_sha256":"12605da285251654372b4629c68e7b1151d4b57717e3ab0128f4c6547d98d1c9"},"schema_version":"1.0","source":{"id":"1903.11738","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.11738","created_at":"2026-07-04T23:51:40Z"},{"alias_kind":"arxiv_version","alias_value":"1903.11738v2","created_at":"2026-07-04T23:51:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.11738","created_at":"2026-07-04T23:51:40Z"},{"alias_kind":"pith_short_12","alias_value":"AAU5Q2KOAG6X","created_at":"2026-07-04T23:51:40Z"},{"alias_kind":"pith_short_16","alias_value":"AAU5Q2KOAG6XHUHI","created_at":"2026-07-04T23:51:40Z"},{"alias_kind":"pith_short_8","alias_value":"AAU5Q2KO","created_at":"2026-07-04T23:51:40Z"}],"graph_snapshots":[{"event_id":"sha256:4a40426c060af37df38e142cf810f370326dc9db09c9dea267f6db651cbe49cf","target":"graph","created_at":"2026-07-04T23:51:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1903.11738/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The trace distance between two quantum states, $\\rho$ and $\\sigma$, is an operationally meaningful quantity in quantum information theory. However, in general it is difficult to compute, involving the diagonalization of $\\rho - \\sigma$. In contrast, the Hilbert-Schmidt distance can be computed without diagonalization, although it is less operationally significant. Here, we relate the trace distance and the Hilbert-Schmidt distance with a bound that is particularly strong when either $\\rho$ or $\\sigma$ is low rank. Our bound is stronger than the bound one could obtain via the norm equivalence o","authors_text":"Lukasz Cincio, M. Cerezo, Patrick J. Coles","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-03-28T00:24:15Z","title":"Strong bound between trace distance and Hilbert-Schmidt distance for low-rank states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11738","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1911d9192296afa33f115ed3256ed5378b1df31e345aa70c8c2abfa828b40e96","target":"record","created_at":"2026-07-04T23:51:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a34f8085d749c8a029e2c3699a623819c60b24f183888a8c5fa980de056e7d09","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2019-03-28T00:24:15Z","title_canon_sha256":"12605da285251654372b4629c68e7b1151d4b57717e3ab0128f4c6547d98d1c9"},"schema_version":"1.0","source":{"id":"1903.11738","kind":"arxiv","version":2}},"canonical_sha256":"0029d8694e01bd73d0e874b00a9f8123aae6d7cc10c202d0378558186659abcd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0029d8694e01bd73d0e874b00a9f8123aae6d7cc10c202d0378558186659abcd","first_computed_at":"2026-07-04T23:51:40.769100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:51:40.769100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XrpMePQesJxI283izlhPuBzSi3XwPgQuQ3QS//jlul33KKwNjHSUHNliDQ1685KwkagyaoJR+h/q3BEIr1gbAA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:51:40.769523Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.11738","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1911d9192296afa33f115ed3256ed5378b1df31e345aa70c8c2abfa828b40e96","sha256:4a40426c060af37df38e142cf810f370326dc9db09c9dea267f6db651cbe49cf"],"state_sha256":"0016d1f1d24a9a7f46a48e8d9eeb7dcb7c1fe842abc8b38fdd999c469db6a7e7"}