Pith Number

pith:BMCXOTJK

pith:2026:BMCXOTJKO7DA2IQBYRWTIL5HH4

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Worst-Case Sample Complexity Bounds for Distributed Inner Product Estimation with Local Randomized Measurements

Kun Wang, Ping Xu, Zhenyuan Huang

Local Clifford measurements achieve O(√(4.5^n)) worst-case sample complexity for distributed inner product estimation on n-qubit states.

arxiv:2605.14256 v1 · 2026-05-14 · quant-ph

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Record completeness

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4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

62 extracted · 62 resolved · 0 Pith anchors

[1] 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) 2020

[2] J. Eisert, D. Hangleiter, N. Walk, I. Roth, D. Markham, R. Parekh, U. Chabaud, and E. Kashefi, Nature Reviews Physics2,382(2020) 2020

[3] M. Kliesch and I. Roth, PRX Quantum2,010201(2021) 2021

[4] Distributed quantum information processing: A review of recent progress 2025

[5] 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 2022 · doi:10.1038/s41467-022-34279-5(2022

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:10.526009Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b05774d2a77c60d2201c46d342fa73f368cc0ceaeb4c6fca7e285a4c99aefef

Aliases

arxiv: 2605.14256 · arxiv_version: 2605.14256v1 · doi: 10.48550/arxiv.2605.14256 · pith_short_12: BMCXOTJKO7DA · pith_short_16: BMCXOTJKO7DA2IQB · pith_short_8: BMCXOTJK

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BMCXOTJKO7DA2IQBYRWTIL5HH4 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0b05774d2a77c60d2201c46d342fa73f368cc0ceaeb4c6fca7e285a4c99aefef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28087bded4c5d64fcee81984467731f1f1318cfe8acb88d34801a11975bf54de",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-14T01:48:14Z",
    "title_canon_sha256": "4e14ef8e355f02869cdf75fbe92296480f09bea816f610cdcd3a0e7f8ad61e08"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14256",
    "kind": "arxiv",
    "version": 1
  }
}