Pith Number

pith:46XFAD7A

pith:2026:46XFAD7AIRY37Q3U5VUQULYLUC

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Unitary invariance of Connes spectral distances of quantum states

Bing-Sheng Lin, Ji-Hong Wang, Zhi-Kang You

Connes spectral distances between quantum states remain unchanged under unitary transformations in finite spectral triples.

arxiv:2605.13014 v1 · 2026-05-13 · math-ph · math.MP

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Claims

C1strongest claim

We also explicitly construct some spectral triples in which the Connes spectral distances between quantum states are exactly the quantum trace distances.

C2weakest assumption

The assumption that the chosen finite-dimensional matrix algebra representations and spectral triples are sufficient to capture the relevant geometric and distance properties of general quantum states.

C3one line summary

Connes spectral distances are unitarily invariant and can be constructed to equal quantum trace distances in certain finite spectral triples.

References

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[1] Connes,Noncommutative geometry(Academic Press, New York, 1994) 1994

[2] Compact metric spaces, Fredholm modules and hyperfinite- ness 1989

[3] Distances on a lattice from non- commutative geometry 1994

[4] Connes’ distance of one-dimensional lattices: general cases 2001

[5] The spectral dis- tance on the Moyal plane 2011

Formal links

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Receipt and verification

First computed	2026-05-18T03:09:00.189969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7ae500fe04471bfc374ed690a2f0ba09340e70e65e172020fbe138e4b1cd047

Aliases

arxiv: 2605.13014 · arxiv_version: 2605.13014v1 · doi: 10.48550/arxiv.2605.13014 · pith_short_12: 46XFAD7AIRY3 · pith_short_16: 46XFAD7AIRY37Q3U · pith_short_8: 46XFAD7A

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/46XFAD7AIRY37Q3U5VUQULYLUC \
  | 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: e7ae500fe04471bfc374ed690a2f0ba09340e70e65e172020fbe138e4b1cd047

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b52cc305ec75d6729fdcb9cf4291ed20ab0008b8d717a4b27f23832427609b46",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-05-13T05:08:52Z",
    "title_canon_sha256": "bd5522dd2cb463f144f707ae489d644b0a5923d4ee0abcdffa07573d5400da3f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13014",
    "kind": "arxiv",
    "version": 1
  }
}