{"paper":{"title":"Quantum Advantage in Storage and Retrieval of Isometry Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Quantum strategies store unknown isometry channels using only the square root as many queries as classical estimation.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jisho Miyazaki, Mio Murao, Satoshi Yoshida","submitted_at":"2025-07-14T20:18:12Z","abstract_excerpt":"Storage and retrieval refer to the task of encoding an unknown quantum channel $\\Lambda$ into a quantum state, known as the program state, such that the channel can later be retrieved. There are two strategies for this task: classical and quantum strategies. The classical strategy uses multiple queries to $\\Lambda$ to estimate $\\Lambda$ and retrieves the channel based on the estimate represented in classical bits. The classical strategy turns out to offer the optimal performance for the storage and retrieval of unitary channels. In this work, we analyze the asymptotic performance of the classi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The optimal fidelity for isometry estimation is F = 1 - d(D-d)/n + O(n^{-2}), showing classical strategy requires n = Θ(ε^{-1}) while the proposed quantum strategy achieves n = Θ(1/√ε) for diamond-norm error ε.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The analysis assumes multiple independent queries to the fixed but unknown isometry channel are available and that the large-n asymptotic regime governs the error scaling.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Quantum strategy stores isometry channels with n = Θ(1/√ε) queries for error ε, quadratic improvement over classical n = Θ(ε^{-1}).","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Quantum strategies store unknown isometry channels using only the square root as many queries as classical estimation.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"302e5d94a44ef796d3e49a0fc1f609f2a5cceecc307d4a2e3a0b6309ddba339e"},"source":{"id":"2507.10784","kind":"arxiv","version":4},"verdict":{"id":"3703d7ca-d931-4c08-a085-e6808b316ca3","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T04:15:59.906761Z","strongest_claim":"The optimal fidelity for isometry estimation is F = 1 - d(D-d)/n + O(n^{-2}), showing classical strategy requires n = Θ(ε^{-1}) while the proposed quantum strategy achieves n = Θ(1/√ε) for diamond-norm error ε.","one_line_summary":"Quantum strategy stores isometry channels with n = Θ(1/√ε) queries for error ε, quadratic improvement over classical n = Θ(ε^{-1}).","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The analysis assumes multiple independent queries to the fixed but unknown isometry channel are available and that the large-n asymptotic regime governs the error scaling.","pith_extraction_headline":"Quantum strategies store unknown isometry channels using only the square root as many queries as classical estimation."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.10784/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":101,"sample":[{"doi":"","year":null,"title":"Isometry operatorV∈V iso(d, D) is defined by ad×Dcomplex matrix satisfyingV †V=1 d, which is given byd 2 independent conditions on real param- eters","work_id":"79cf4c45-2461-408b-8cf0-cc0bbab4622d","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":",|v d⟩} ⊂C D","work_id":"554e302e-04a3-424e-be28-77fb2826969a","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Definition of the Young diagrams 6","work_id":"80c3fd4b-ae07-437a-a151-5343bf789919","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Schur-Weyl duality 7","work_id":"9fdad4d0-ff5d-463b-845f-f2574389efc3","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Review on quantum testers 10","work_id":"2ce1167d-7818-46e8-8262-104a450cf81c","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":101,"snapshot_sha256":"5655c8eb20aacc1c0b303b307e8fdafe7c94cec63c17869d3c45cd2ae56df944","internal_anchors":37},"formal_canon":{"evidence_count":2,"snapshot_sha256":"28af680455d3e030ffd5cec5267d7529fe265ad393596bc137081e37caa53ec9"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}