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These bounds are also known to be tight, as explicit constructions exist for $n=4^m-1$ and $n=2^m-1$ for quantum and classical codes respectively. We generalize (Q)RACs to a scheme encoding $n$ $d$-levels into $m$ (qu)-$d$-levels such that any $d$-level can be recovered with the probability for"},"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":"1607.02667","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-07-09T21:26:12Z","cross_cats_sorted":[],"title_canon_sha256":"0a820d1bfbcd97798b983a8334c3e4297ac0c49ad3119996f0017973af61c55f","abstract_canon_sha256":"38f4fae513f5fe3ef0af9bb133cdab66ba1664a0841a40a3f8613c896685aecb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:24.600663Z","signature_b64":"JA8HvAqe3K7kKjctChB9T1Pt5z9bybZrxeS/ScE6MfUH0zAk9Bv+TSy88zEJ37qvhyY0M9Dm8RuagsnXXHyzBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"506b5bfdad84aac912ce197b5b7fff403fec9bf4b470ad71974b09d6b7e64acd","last_reissued_at":"2026-05-18T00:44:24.600200Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:24.600200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved Classical and Quantum Random Access Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Ola Liab{\\o}tr{\\o}","submitted_at":"2016-07-09T21:26:12Z","abstract_excerpt":"A (Quantum) Random Access Code ((Q)RAC) is a scheme that encodes $n$ bits into $m$ (qu)bits such that any of the $n$ bits can be recovered with a worst case probability $p>\\frac{1}{2}$. Such a code is denoted by the triple $(n,m,p)$. It is known that $n<4^m$ for all QRACs and $n<2^m$ for classical RACs. These bounds are also known to be tight, as explicit constructions exist for $n=4^m-1$ and $n=2^m-1$ for quantum and classical codes respectively. We generalize (Q)RACs to a scheme encoding $n$ $d$-levels into $m$ (qu)-$d$-levels such that any $d$-level can be recovered with the probability for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02667","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":"1607.02667","created_at":"2026-05-18T00:44:24.600275+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.02667v2","created_at":"2026-05-18T00:44:24.600275+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02667","created_at":"2026-05-18T00:44:24.600275+00:00"},{"alias_kind":"pith_short_12","alias_value":"KBVVX7NNQSVM","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"KBVVX7NNQSVMSEWO","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"KBVVX7NN","created_at":"2026-05-18T12:30:25.849896+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/KBVVX7NNQSVMSEWODF5VW777IA","json":"https://pith.science/pith/KBVVX7NNQSVMSEWODF5VW777IA.json","graph_json":"https://pith.science/api/pith-number/KBVVX7NNQSVMSEWODF5VW777IA/graph.json","events_json":"https://pith.science/api/pith-number/KBVVX7NNQSVMSEWODF5VW777IA/events.json","paper":"https://pith.science/paper/KBVVX7NN"},"agent_actions":{"view_html":"https://pith.science/pith/KBVVX7NNQSVMSEWODF5VW777IA","download_json":"https://pith.science/pith/KBVVX7NNQSVMSEWODF5VW777IA.json","view_paper":"https://pith.science/paper/KBVVX7NN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.02667&json=true","fetch_graph":"https://pith.science/api/pith-number/KBVVX7NNQSVMSEWODF5VW777IA/graph.json","fetch_events":"https://pith.science/api/pith-number/KBVVX7NNQSVMSEWODF5VW777IA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KBVVX7NNQSVMSEWODF5VW777IA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KBVVX7NNQSVMSEWODF5VW777IA/action/storage_attestation","attest_author":"https://pith.science/pith/KBVVX7NNQSVMSEWODF5VW777IA/action/author_attestation","sign_citation":"https://pith.science/pith/KBVVX7NNQSVMSEWODF5VW777IA/action/citation_signature","submit_replication":"https://pith.science/pith/KBVVX7NNQSVMSEWODF5VW777IA/action/replication_record"}},"created_at":"2026-05-18T00:44:24.600275+00:00","updated_at":"2026-05-18T00:44:24.600275+00:00"}