Pith Number

pith:J3PQBABH

pith:2025:J3PQBABHOERNW54BOFQKOBQFFW

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Performance Guarantees for Quantum Neural Estimation of Entropies

Mark M. Wilde, Sreejith Sreekumar, Ziv Goldfeld

Quantum neural estimators achieve O(d/ε²) copy complexity for measured Rényi relative entropies when density pairs have bounded Thompson metric.

arxiv:2511.19289 v2 · 2025-11-24 · quant-ph · cs.IT · cs.LG · math.IT

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Claims

C1strongest claim

For an appropriate sub-class of density operator pairs on a space of dimension d with bounded Thompson metric, our theory establishes a copy complexity of O(|Θ(U)|d/ε²) for QNE with a quantum circuit parameter set Θ(U), which has minimax optimal dependence on the accuracy ε.

C2weakest assumption

The central bounds rely on the density operator pairs having bounded Thompson metric (or being permutation invariant); without this restriction the stated copy complexity no longer holds and the analysis does not apply.

C3one line summary

Quantum neural estimators achieve minimax-optimal copy complexity O(|Θ(U)| d / ε²) with sub-Gaussian concentration for measured Rényi relative entropies on density pairs with bounded Thompson metric.

References

95 extracted · 95 resolved · 1 Pith anchors

[1] J. von Neumann, “Thermodynamik quantenmechanischer gesamtheiten,”Nachrichten von der Gesellschaft der Wis- senschaften zu G ¨ottingen, Mathematisch-Physikalische Klasse, vol. 1927, pp. 273–291, 1927 1927

[2] A mathematical theory of communication 1948

[3] On measures of entropy and information, 1961

[4] On information and sufficiency, 1951

[5] Conditional expectations in an operator algebra IV (entropy and information), 1962

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:04.609184Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4edf0080277122db77817160a706052dbbfb4dca56e7088fc0b47d7263bcf2ab

Aliases

arxiv: 2511.19289 · arxiv_version: 2511.19289v2 · doi: 10.48550/arxiv.2511.19289 · pith_short_12: J3PQBABHOERN · pith_short_16: J3PQBABHOERNW54B · pith_short_8: J3PQBABH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/J3PQBABHOERNW54BOFQKOBQFFW \
  | 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: 4edf0080277122db77817160a706052dbbfb4dca56e7088fc0b47d7263bcf2ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49ec455f458cfb8913998f5a12cf3bde4c7a907154ce0a6029cac29ca78c29f1",
    "cross_cats_sorted": [
      "cs.IT",
      "cs.LG",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-11-24T16:36:06Z",
    "title_canon_sha256": "7b4f6fae66912667e032cb30bfa54fa0bcff1c3d55e7529d3d1788d8534cc213"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.19289",
    "kind": "arxiv",
    "version": 2
  }
}