{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:VNDQLDHAAZ3VNKC7LJTPJR5E36","short_pith_number":"pith:VNDQLDHA","canonical_record":{"source":{"id":"1010.1018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-10-05T20:45:38Z","cross_cats_sorted":[],"title_canon_sha256":"0f67623ccf2537defec3c11c8329a747aa108d7b45c7197d1a91f2bb7ff61f59","abstract_canon_sha256":"475ff1a6631f2058810ad9bfaf22c381856d9a4e20f05ffc95db8390ca457e1f"},"schema_version":"1.0"},"canonical_sha256":"ab47058ce0067756a85f5a66f4c7a4df9c5c80e5264ce2f3be66035e193a0601","source":{"kind":"arxiv","id":"1010.1018","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1018","created_at":"2026-05-18T04:39:49Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1018v1","created_at":"2026-05-18T04:39:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1018","created_at":"2026-05-18T04:39:49Z"},{"alias_kind":"pith_short_12","alias_value":"VNDQLDHAAZ3V","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VNDQLDHAAZ3VNKC7","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VNDQLDHA","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:VNDQLDHAAZ3VNKC7LJTPJR5E36","target":"record","payload":{"canonical_record":{"source":{"id":"1010.1018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-10-05T20:45:38Z","cross_cats_sorted":[],"title_canon_sha256":"0f67623ccf2537defec3c11c8329a747aa108d7b45c7197d1a91f2bb7ff61f59","abstract_canon_sha256":"475ff1a6631f2058810ad9bfaf22c381856d9a4e20f05ffc95db8390ca457e1f"},"schema_version":"1.0"},"canonical_sha256":"ab47058ce0067756a85f5a66f4c7a4df9c5c80e5264ce2f3be66035e193a0601","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:49.984986Z","signature_b64":"4P81WK+BeMYaOOnIn1jjXzBfbRvVZLRnvipO5oUvROuBiCOx5ypjFMr3c/ZrS9OujnFXLlv6Q4+Fe+VyPPL5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab47058ce0067756a85f5a66f4c7a4df9c5c80e5264ce2f3be66035e193a0601","last_reissued_at":"2026-05-18T04:39:49.984496Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:49.984496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.1018","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:39:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7fFAS/isdfKyNx5pIMHhDc4tAjK+HxU/rNaSFVt5/6sjMMRURBNMWWmFOpRM1O9S3Eq9o0d8v9/9v1C7LkZPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:07:14.834110Z"},"content_sha256":"22aa60c90c151d486d17d3461c74fb0d9852d549b6b66de4dbeff6b4a38bd68d","schema_version":"1.0","event_id":"sha256:22aa60c90c151d486d17d3461c74fb0d9852d549b6b66de4dbeff6b4a38bd68d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:VNDQLDHAAZ3VNKC7LJTPJR5E36","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Carl A. Miller, Eric Chitambar, Yaoyun Shi","submitted_at":"2010-10-05T20:45:38Z","abstract_excerpt":"In this brief report, we consider the equivalence between two sets of $m+1$ bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree $m$ matrix polynomials are unitarily equivalent; i.e. $UA_iV^\\dagger=B_i$ for $0\\leq i\\leq m$ where $U$ and $V$ are unitary and $(A_i, B_i)$ are arbitrary pairs of rectangular matrices. We present a randomized polynomial-time algorithm that solves this problem with an arbitrarily high success probability and outputs transforming matrices $U$ and $V$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1018","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:39:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RPJF4Ehxnuh2w8grw177IS7a2uBAcHSkrjtLuVl1w7Go+Rl0ya1ltWpHVkhwXegct64/kXZiTgBvo63c7mSXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:07:14.834478Z"},"content_sha256":"9f34f34661be11d823a5c2be7b4d2c47256a80576a5ca9fee34bbecf0911755b","schema_version":"1.0","event_id":"sha256:9f34f34661be11d823a5c2be7b4d2c47256a80576a5ca9fee34bbecf0911755b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VNDQLDHAAZ3VNKC7LJTPJR5E36/bundle.json","state_url":"https://pith.science/pith/VNDQLDHAAZ3VNKC7LJTPJR5E36/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VNDQLDHAAZ3VNKC7LJTPJR5E36/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T05:07:14Z","links":{"resolver":"https://pith.science/pith/VNDQLDHAAZ3VNKC7LJTPJR5E36","bundle":"https://pith.science/pith/VNDQLDHAAZ3VNKC7LJTPJR5E36/bundle.json","state":"https://pith.science/pith/VNDQLDHAAZ3VNKC7LJTPJR5E36/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VNDQLDHAAZ3VNKC7LJTPJR5E36/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VNDQLDHAAZ3VNKC7LJTPJR5E36","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":"475ff1a6631f2058810ad9bfaf22c381856d9a4e20f05ffc95db8390ca457e1f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-10-05T20:45:38Z","title_canon_sha256":"0f67623ccf2537defec3c11c8329a747aa108d7b45c7197d1a91f2bb7ff61f59"},"schema_version":"1.0","source":{"id":"1010.1018","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1018","created_at":"2026-05-18T04:39:49Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1018v1","created_at":"2026-05-18T04:39:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1018","created_at":"2026-05-18T04:39:49Z"},{"alias_kind":"pith_short_12","alias_value":"VNDQLDHAAZ3V","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VNDQLDHAAZ3VNKC7","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VNDQLDHA","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:9f34f34661be11d823a5c2be7b4d2c47256a80576a5ca9fee34bbecf0911755b","target":"graph","created_at":"2026-05-18T04:39:49Z","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"},"paper":{"abstract_excerpt":"In this brief report, we consider the equivalence between two sets of $m+1$ bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree $m$ matrix polynomials are unitarily equivalent; i.e. $UA_iV^\\dagger=B_i$ for $0\\leq i\\leq m$ where $U$ and $V$ are unitary and $(A_i, B_i)$ are arbitrary pairs of rectangular matrices. We present a randomized polynomial-time algorithm that solves this problem with an arbitrarily high success probability and outputs transforming matrices $U$ and $V$.","authors_text":"Carl A. Miller, Eric Chitambar, Yaoyun Shi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-10-05T20:45:38Z","title":"Deciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1018","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":"sha256:22aa60c90c151d486d17d3461c74fb0d9852d549b6b66de4dbeff6b4a38bd68d","target":"record","created_at":"2026-05-18T04:39:49Z","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":"475ff1a6631f2058810ad9bfaf22c381856d9a4e20f05ffc95db8390ca457e1f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-10-05T20:45:38Z","title_canon_sha256":"0f67623ccf2537defec3c11c8329a747aa108d7b45c7197d1a91f2bb7ff61f59"},"schema_version":"1.0","source":{"id":"1010.1018","kind":"arxiv","version":1}},"canonical_sha256":"ab47058ce0067756a85f5a66f4c7a4df9c5c80e5264ce2f3be66035e193a0601","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab47058ce0067756a85f5a66f4c7a4df9c5c80e5264ce2f3be66035e193a0601","first_computed_at":"2026-05-18T04:39:49.984496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:49.984496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4P81WK+BeMYaOOnIn1jjXzBfbRvVZLRnvipO5oUvROuBiCOx5ypjFMr3c/ZrS9OujnFXLlv6Q4+Fe+VyPPL5DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:49.984986Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.1018","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22aa60c90c151d486d17d3461c74fb0d9852d549b6b66de4dbeff6b4a38bd68d","sha256:9f34f34661be11d823a5c2be7b4d2c47256a80576a5ca9fee34bbecf0911755b"],"state_sha256":"55d3137d40012029a725c3e7a35204806663efa8c297b2d089fab6b942f4dffb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rXvh8D+IkZdduXriZtfUpN1zIZJiHWz+jrMXIPBhnSYjqkp6+caNCJPUIZjddHD51epCIrPNCW3M8PrUE1wWAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T05:07:14.836437Z","bundle_sha256":"9e4f43e8ce7124802a727181c90452525e24b9bdba19a6cb703d7be055311767"}}