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Based on the idea of teleportation and super-dense coding in quantum information theory, we exhibit the two $*$-isomorphisms $M_d(C^*(\\mathbb{F}_{d^2}))\\cong \\mathcal{B}_d\\rtimes \\mathbb{Z}_d\\rtimes \\mathbb{Z}_d$ and $M_d(\\mathcal{B}_d)\\cong C^*(\\mathbb{F}_{d^2})\\rtimes \\mathbb{Z}_d\\rtimes \\mathbb{Z}_d$, for certain actions of "},"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":"1709.02785","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-09-08T17:31:52Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"92313feaedb92ea32890d33ffdaf91ab0b34119257452fd9cf27c37857230367","abstract_canon_sha256":"2e1fe7b9bf1dfe90fba799262a898197fd2a954bbf466615a6fec2edaa2399a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:49.217577Z","signature_b64":"yKV6zVwjAFf+WTFonbK0NJVbFGU4jELgHJR7k7BX+9bKBYDGJQpBefLzZlbhXQkCPUOFgC/eCnhQHIOhCYMUAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8736b9772109c7dbb7e6bfa910275f725f4e6d01a891fc588a7e7b1df9dd5bc8","last_reissued_at":"2026-05-18T00:26:49.217036Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:49.217036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum Teleportation and Super-dense Coding in Operator Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.OA","authors_text":"Li Gao, Marius Junge, Samuel J. 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Based on the idea of teleportation and super-dense coding in quantum information theory, we exhibit the two $*$-isomorphisms $M_d(C^*(\\mathbb{F}_{d^2}))\\cong \\mathcal{B}_d\\rtimes \\mathbb{Z}_d\\rtimes \\mathbb{Z}_d$ and $M_d(\\mathcal{B}_d)\\cong C^*(\\mathbb{F}_{d^2})\\rtimes \\mathbb{Z}_d\\rtimes \\mathbb{Z}_d$, for certain actions of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02785","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1709.02785","created_at":"2026-05-18T00:26:49.217122+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.02785v2","created_at":"2026-05-18T00:26:49.217122+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02785","created_at":"2026-05-18T00:26:49.217122+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q43LS5ZBBHD5","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q43LS5ZBBHD5XN7G","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q43LS5ZB","created_at":"2026-05-18T12:31:37.085036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Q43LS5ZBBHD5XN7GX6URAJ27OJ","json":"https://pith.science/pith/Q43LS5ZBBHD5XN7GX6URAJ27OJ.json","graph_json":"https://pith.science/api/pith-number/Q43LS5ZBBHD5XN7GX6URAJ27OJ/graph.json","events_json":"https://pith.science/api/pith-number/Q43LS5ZBBHD5XN7GX6URAJ27OJ/events.json","paper":"https://pith.science/paper/Q43LS5ZB"},"agent_actions":{"view_html":"https://pith.science/pith/Q43LS5ZBBHD5XN7GX6URAJ27OJ","download_json":"https://pith.science/pith/Q43LS5ZBBHD5XN7GX6URAJ27OJ.json","view_paper":"https://pith.science/paper/Q43LS5ZB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.02785&json=true","fetch_graph":"https://pith.science/api/pith-number/Q43LS5ZBBHD5XN7GX6URAJ27OJ/graph.json","fetch_events":"https://pith.science/api/pith-number/Q43LS5ZBBHD5XN7GX6URAJ27OJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q43LS5ZBBHD5XN7GX6URAJ27OJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q43LS5ZBBHD5XN7GX6URAJ27OJ/action/storage_attestation","attest_author":"https://pith.science/pith/Q43LS5ZBBHD5XN7GX6URAJ27OJ/action/author_attestation","sign_citation":"https://pith.science/pith/Q43LS5ZBBHD5XN7GX6URAJ27OJ/action/citation_signature","submit_replication":"https://pith.science/pith/Q43LS5ZBBHD5XN7GX6URAJ27OJ/action/replication_record"}},"created_at":"2026-05-18T00:26:49.217122+00:00","updated_at":"2026-05-18T00:26:49.217122+00:00"}