Pith Number

pith:INB6AA6E

pith:2026:INB6AA6EE7ZRJYMVABLLY43T56

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Strict Hierarchy for Quantum Channel Certification to Unitary

Kean Chen, Qisheng Wang, Zhicheng Zhang

The query complexity for certifying a quantum channel as a target unitary forms a strict hierarchy across three access models.

arxiv:2604.26900 v1 · 2026-04-29 · quant-ph · cs.CC · cs.DS

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3 Author claim open · sign in to claim

4 Citations 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

We show that (i) Θ(d/ε²) queries suffice for incoherent access model, matching the lower bound due to Fawzi et al. (COLT 2023); (ii) Θ(d/ε) queries suffice for coherent access model, matching Regev and Schiff (ICALP 2008); (iii) Θ(√d/ε) queries suffice for source-code access model, matching Jeon and Oh (npj Quantum Inf. 2026).

C2weakest assumption

The analysis assumes the standard diamond norm as the distance measure and that the target is exactly a unitary channel; if the distance measure or the notion of 'unitary' changes, the query bounds may not hold.

C3one line summary

Optimal algorithms achieve query complexities Θ(d/ε²) for incoherent access, Θ(d/ε) for coherent access, and Θ(√d/ε) for source-code access in quantum channel certification to unitary, exactly matching prior lower bounds.

References

35 extracted · 35 resolved · 3 Pith anchors

[1] Quantum algorithmic measurement 2022 · doi:10.1038/s41467-021-27922-0

[2] Entanglement is necessary for optimal quantum property testing 2020 · doi:10.1109/focs46700.2020.00070

[3] Quantum amplitude amplification and estimation 2002 · doi:10.1090/conm/305/05215

[4] VC dimension and distribution-free sample-based testing 2021 · doi:10.1145/3406325.3451109

[5] Quantum state certification 2019 · doi:10.1145/3313276.3316344

Receipt and verification

First computed	2026-07-03T01:17:55.365816Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4343e003c427f314e1950056bc7373efb145a62d2918e84db0a4e9ae622d06f3

Aliases

arxiv: 2604.26900 · arxiv_version: 2604.26900v1 · doi: 10.48550/arxiv.2604.26900 · pith_short_12: INB6AA6EE7ZR · pith_short_16: INB6AA6EE7ZRJYMV · pith_short_8: INB6AA6E

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/INB6AA6EE7ZRJYMVABLLY43T56 \
  | 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: 4343e003c427f314e1950056bc7373efb145a62d2918e84db0a4e9ae622d06f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c21754e47c0622e02b8f995ca9df02aa435434a5aede31a966b928e140cc9819",
    "cross_cats_sorted": [
      "cs.CC",
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-04-29T17:10:34Z",
    "title_canon_sha256": "69e51c982eebaa9d7860a6cbddd2a22e275d9f3533a2fbd89349521735b1d2b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.26900",
    "kind": "arxiv",
    "version": 1
  }
}