{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6W2HQACBPZ5DNBO75R6D3KI6V3","short_pith_number":"pith:6W2HQACB","canonical_record":{"source":{"id":"1612.06410","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-12-19T21:10:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"12bbd65345c9e8af78bb1417760a08bd8167a61e38c0b5b2ff1870a01724e44b","abstract_canon_sha256":"3ae47c30e5aec70ade1c7e608631ec1bcd7774b4697411f97032a4736309b876"},"schema_version":"1.0"},"canonical_sha256":"f5b47800417e7a3685dfec7c3da91eaefcb22d9cefa803ae3991210b47756bf0","source":{"kind":"arxiv","id":"1612.06410","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06410","created_at":"2026-05-18T00:31:13Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06410v2","created_at":"2026-05-18T00:31:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06410","created_at":"2026-05-18T00:31:13Z"},{"alias_kind":"pith_short_12","alias_value":"6W2HQACBPZ5D","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6W2HQACBPZ5DNBO7","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6W2HQACB","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6W2HQACBPZ5DNBO75R6D3KI6V3","target":"record","payload":{"canonical_record":{"source":{"id":"1612.06410","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-12-19T21:10:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"12bbd65345c9e8af78bb1417760a08bd8167a61e38c0b5b2ff1870a01724e44b","abstract_canon_sha256":"3ae47c30e5aec70ade1c7e608631ec1bcd7774b4697411f97032a4736309b876"},"schema_version":"1.0"},"canonical_sha256":"f5b47800417e7a3685dfec7c3da91eaefcb22d9cefa803ae3991210b47756bf0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:13.531777Z","signature_b64":"0n8gkLM1MFcteJ0ZVdRrRcI2Ax6mgHe7lfYCa1bX0oKXkLgE6m4SsKCGilMgbfXnOfF5He4FVMxKsQcFiw3RDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5b47800417e7a3685dfec7c3da91eaefcb22d9cefa803ae3991210b47756bf0","last_reissued_at":"2026-05-18T00:31:13.531056Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:13.531056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.06410","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HwyPDrc4Q+cUI/Ms7ohzsy75YXNKs1R8Zp8t0YvyXMUtXM8QZyriMij2wSJnf31eRcUTSQLeAym72kYfec5yBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T04:00:18.847026Z"},"content_sha256":"592ac06ddf817628f42ba609c87558ac2769c2a818959b8dd51df5f519ea4499","schema_version":"1.0","event_id":"sha256:592ac06ddf817628f42ba609c87558ac2769c2a818959b8dd51df5f519ea4499"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6W2HQACBPZ5DNBO75R6D3KI6V3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric characterization of mixed quantum states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Hoshang Heydari","submitted_at":"2016-12-19T21:10:57Z","abstract_excerpt":"Characterization of mixed quantum states represented by density operator is one of the most important task in quantum information processing. In this work we will present a geometric approach to characterize the density operator in terms of fiber bundle over a quantum phase space. The geometrical structure of the quantum phase space of an isospectral mixed quantum states can be realized as a co-adjoint orbit of a Lie group equipped with a specific K\\\"{a}hler structure.\n  In particular we will briefly discuss the construction of a fiber bundle over the quantum phase space based on symplectic re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06410","kind":"arxiv","version":2},"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":"2026-05-18T00:31:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fPBmmdXfkee17hyEzZris0MhiY2t/YkFZdcUQMjc37pxvAJSc1lbVdo2fqcRlf9NtO9IsK/4hqzeChKq6XzLCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T04:00:18.847719Z"},"content_sha256":"1222cae7586fca043135d43941228cdc8cabc4a080c6f5cc06fbdc130d92d348","schema_version":"1.0","event_id":"sha256:1222cae7586fca043135d43941228cdc8cabc4a080c6f5cc06fbdc130d92d348"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6W2HQACBPZ5DNBO75R6D3KI6V3/bundle.json","state_url":"https://pith.science/pith/6W2HQACBPZ5DNBO75R6D3KI6V3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6W2HQACBPZ5DNBO75R6D3KI6V3/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":"2026-05-30T04:00:18Z","links":{"resolver":"https://pith.science/pith/6W2HQACBPZ5DNBO75R6D3KI6V3","bundle":"https://pith.science/pith/6W2HQACBPZ5DNBO75R6D3KI6V3/bundle.json","state":"https://pith.science/pith/6W2HQACBPZ5DNBO75R6D3KI6V3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6W2HQACBPZ5DNBO75R6D3KI6V3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6W2HQACBPZ5DNBO75R6D3KI6V3","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":"3ae47c30e5aec70ade1c7e608631ec1bcd7774b4697411f97032a4736309b876","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-12-19T21:10:57Z","title_canon_sha256":"12bbd65345c9e8af78bb1417760a08bd8167a61e38c0b5b2ff1870a01724e44b"},"schema_version":"1.0","source":{"id":"1612.06410","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06410","created_at":"2026-05-18T00:31:13Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06410v2","created_at":"2026-05-18T00:31:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06410","created_at":"2026-05-18T00:31:13Z"},{"alias_kind":"pith_short_12","alias_value":"6W2HQACBPZ5D","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6W2HQACBPZ5DNBO7","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6W2HQACB","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:1222cae7586fca043135d43941228cdc8cabc4a080c6f5cc06fbdc130d92d348","target":"graph","created_at":"2026-05-18T00:31:13Z","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":"Characterization of mixed quantum states represented by density operator is one of the most important task in quantum information processing. In this work we will present a geometric approach to characterize the density operator in terms of fiber bundle over a quantum phase space. The geometrical structure of the quantum phase space of an isospectral mixed quantum states can be realized as a co-adjoint orbit of a Lie group equipped with a specific K\\\"{a}hler structure.\n  In particular we will briefly discuss the construction of a fiber bundle over the quantum phase space based on symplectic re","authors_text":"Hoshang Heydari","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-12-19T21:10:57Z","title":"Geometric characterization of mixed quantum states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06410","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":"sha256:592ac06ddf817628f42ba609c87558ac2769c2a818959b8dd51df5f519ea4499","target":"record","created_at":"2026-05-18T00:31:13Z","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":"3ae47c30e5aec70ade1c7e608631ec1bcd7774b4697411f97032a4736309b876","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-12-19T21:10:57Z","title_canon_sha256":"12bbd65345c9e8af78bb1417760a08bd8167a61e38c0b5b2ff1870a01724e44b"},"schema_version":"1.0","source":{"id":"1612.06410","kind":"arxiv","version":2}},"canonical_sha256":"f5b47800417e7a3685dfec7c3da91eaefcb22d9cefa803ae3991210b47756bf0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5b47800417e7a3685dfec7c3da91eaefcb22d9cefa803ae3991210b47756bf0","first_computed_at":"2026-05-18T00:31:13.531056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:13.531056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0n8gkLM1MFcteJ0ZVdRrRcI2Ax6mgHe7lfYCa1bX0oKXkLgE6m4SsKCGilMgbfXnOfF5He4FVMxKsQcFiw3RDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:13.531777Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06410","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:592ac06ddf817628f42ba609c87558ac2769c2a818959b8dd51df5f519ea4499","sha256:1222cae7586fca043135d43941228cdc8cabc4a080c6f5cc06fbdc130d92d348"],"state_sha256":"38f157d83d645dc3c75f8e8e75e199ef2e6551151059cbf1255f176af74a6492"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hW03zVgSWuzzg+gp9bQbVxHEvs/9R3ujI6SAfDqNrshAFHfPqMB8UdZwkbuPLuY2wmnyxaKot4d9WQVqEPWGCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T04:00:18.851295Z","bundle_sha256":"a48f052eb6401f41e1c2931c4757a798304bbb0cfbbee2dfe4daceb6156ed721"}}