{"paper":{"title":"Worst-Case Sample Complexity Bounds for Distributed Inner Product Estimation with Local Randomized Measurements","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"Local Clifford measurements achieve O(√(4.5^n)) worst-case sample complexity for distributed inner product estimation on n-qubit states.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Kun Wang, Ping Xu, Zhenyuan Huang","submitted_at":"2026-05-14T01:48:14Z","abstract_excerpt":"We study distributed inner product estimation for $n$-qubit states using local randomized measurements, for which rigorous worst-case guarantees are less understood. We first reduce the minimax kernel optimization to Hamming-distance kernels. Within this class, unbiasedness fixes a unique kernel. For this kernel under local Clifford sampling, we prove a sharp fourth-moment bound using the single-qubit Clifford commutant. This yields worst-case sample complexity $\\mathcal{O}(\\sqrt{4.5^n})$, attained by identical pure product stabilizer states. For the same kernel under local Haar sampling, we p"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For this kernel under local Clifford sampling, we prove a sharp fourth-moment bound using the single-qubit Clifford commutant. This yields worst-case sample complexity O(√(4.5^n)), attained by identical pure product stabilizer states.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The reduction of the minimax kernel optimization to Hamming-distance kernels, together with the claim that unbiasedness fixes a unique kernel within this class.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The work proves a worst-case sample complexity of O(sqrt(4.5^n)) for distributed inner product estimation with local Clifford sampling on n-qubit states, with a conjectured O(sqrt(3.6^n)) for Haar sampling.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Local Clifford measurements achieve O(√(4.5^n)) worst-case sample complexity for distributed inner product estimation on n-qubit states.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a1f727aaba18679ef5231c65eb6bf92e2752a56d6f2ae8f3e0c954ede6ee9709"},"source":{"id":"2605.14256","kind":"arxiv","version":1},"verdict":{"id":"34956ff4-12ec-4b05-9a0c-1a1ac23db93d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:41:57.813954Z","strongest_claim":"For this kernel under local Clifford sampling, we prove a sharp fourth-moment bound using the single-qubit Clifford commutant. This yields worst-case sample complexity O(√(4.5^n)), attained by identical pure product stabilizer states.","one_line_summary":"The work proves a worst-case sample complexity of O(sqrt(4.5^n)) for distributed inner product estimation with local Clifford sampling on n-qubit states, with a conjectured O(sqrt(3.6^n)) for Haar sampling.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The reduction of the minimax kernel optimization to Hamming-distance kernels, together with the claim that unbiasedness fixes a unique kernel within this class.","pith_extraction_headline":"Local Clifford measurements achieve O(√(4.5^n)) worst-case sample complexity for distributed inner product estimation on n-qubit states."},"references":{"count":62,"sample":[{"doi":"","year":2020,"title":"A. Elben, B. Vermersch, R. van Bijnen, C. Kokail, T. Bry- dges, C. Maier, M. K. Joshi, R. Blatt, C. F. Roos, and P . Zoller, Physical Review Letters124,010504(2020)","work_id":"0958467f-b544-4cb3-a47b-c1723c0f0533","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"J. Eisert, D. Hangleiter, N. Walk, I. Roth, D. Markham, R. Parekh, U. Chabaud, and E. Kashefi, Nature Reviews Physics2,382(2020)","work_id":"549f198f-38c9-4c56-a2bd-28e8b1dc561a","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"M. Kliesch and I. Roth, PRX Quantum2,010201(2021)","work_id":"fa97cf24-222c-4beb-83d0-2489ae24a73f","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Distributed quantum information processing: A review of recent progress","work_id":"8f1ceac6-d03e-4520-bd8b-fc3796cd0778","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1038/s41467-022-34279-5(2022","year":2022,"title":"D. Zhu, Z. P . Cian, C. Noel, A. Risinger, D. Biswas, L. Egan, Y. Zhu, A. M. Green, C. H. Alderete, N. H. Nguyen, Q. Wang, A. Maksymov, Y. Nam, M. Cetina, N. M. Linke, M. Hafezi, and C. Monroe, Nature","work_id":"6d8de622-abc8-480a-959a-8f2fba5677fa","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":62,"snapshot_sha256":"4cc78a78fcbbf2f66e744082b25bbe1c452bf7f3356cefcd7388dd4e90087732","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"01365b82c2e62865c44e82988a9dc4b56b41e76e378ba55ad61d8cf1d60ff451"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}