{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HHPAFLLWE3QIJBF2TXR4JOCSBG","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":"fc6f1e45c6db00bdcdfc32074b1038668c93ec6d9505a3c2d123312b98217d78","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-08-03T07:50:28Z","title_canon_sha256":"e7e2659144962617d03840defce3776e96aaa727caf02215f2d42273d647dab3"},"schema_version":"1.0","source":{"id":"2608.01841","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.01841","created_at":"2026-08-04T02:07:26Z"},{"alias_kind":"arxiv_version","alias_value":"2608.01841v1","created_at":"2026-08-04T02:07:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.01841","created_at":"2026-08-04T02:07:26Z"},{"alias_kind":"pith_short_12","alias_value":"HHPAFLLWE3QI","created_at":"2026-08-04T02:07:26Z"},{"alias_kind":"pith_short_16","alias_value":"HHPAFLLWE3QIJBF2","created_at":"2026-08-04T02:07:26Z"},{"alias_kind":"pith_short_8","alias_value":"HHPAFLLW","created_at":"2026-08-04T02:07:26Z"}],"graph_snapshots":[{"event_id":"sha256:bf57e5cb996b2329a8230ef3755aa2023690bd71705a6453081a3ccee34d7d62","target":"graph","created_at":"2026-08-04T02:07:26Z","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/2608.01841/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the trace distance \\[D_{\\mathrm{tr}}(\\rho,\\sigma)\n  =\\frac12\\|\\rho-\\sigma\\|_1,\n  \\rho=\\bigotimes_{i=1}^n\\rho_i,\\quad\n  \\sigma=\\bigotimes_{i=1}^n\\sigma_i, \\] when the two exponentially large states are specified by their local factors. We give a deterministic approximation within a universal constant factor for rational product inputs. Its running time is polynomial in the number of factors, the local dimension, and the input bit length. In the opposite direction, exact computation is $\\#\\mathsf P$-hard even for diagonal qubit states, by the corresponding hardness of total variation di","authors_text":"Dimitrios Myrisiotis, Junhong Nie, Kun He, Zongqi Wan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-08-03T07:50:28Z","title":"Approximating the Trace Distance Between Product Quantum States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.01841","kind":"arxiv","version":1},"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":"sha256:8b20651863c39a1cfbf2dce772f6720cb428196d71538ea3532565ba1a68de8c","target":"record","created_at":"2026-08-04T02:07:26Z","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":"fc6f1e45c6db00bdcdfc32074b1038668c93ec6d9505a3c2d123312b98217d78","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-08-03T07:50:28Z","title_canon_sha256":"e7e2659144962617d03840defce3776e96aaa727caf02215f2d42273d647dab3"},"schema_version":"1.0","source":{"id":"2608.01841","kind":"arxiv","version":1}},"canonical_sha256":"39de02ad7626e08484ba9de3c4b85209be468f8019b03c098ba237f9181b5a22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39de02ad7626e08484ba9de3c4b85209be468f8019b03c098ba237f9181b5a22","first_computed_at":"2026-08-04T02:07:26.570333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T02:07:26.570333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SMScLKwHJZkwt2ox5Ut6hS7IhT3g/3i/3c00ecUmVsynLFbxvb4eD56d2Ix5Fht3wX7JmIYwcg6brc7LUCl5AQ==","signature_status":"signed_v1","signed_at":"2026-08-04T02:07:26.571911Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.01841","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b20651863c39a1cfbf2dce772f6720cb428196d71538ea3532565ba1a68de8c","sha256:bf57e5cb996b2329a8230ef3755aa2023690bd71705a6453081a3ccee34d7d62"],"state_sha256":"518a88b6c5a03fa000900134947b20e30ac99ee0baaa90e3f4bbdf937b210546"}