Pith Number

pith:QPDM6JAZ

pith:2025:QPDM6JAZJGNKHYGFLUNH4AVJQ6

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Metrics on completely positive maps via noncommutative geometry

Are Austad, Erik B\'edos, Jonas Eidesen, Nadia S. Larsen, Tron Omland

Seminorms from noncommutative geometry induce metrics on unital completely positive maps that satisfy stability and chaining.

arxiv:2512.10842 v3 · 2025-12-11 · math.OA · math.FA · quant-ph

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Claims

C1strongest claim

Under suitable conditions, the induced metrics satisfy the quantum information theoretic properties of stability and chaining. Moreover, we show how to generate such metrics using constructions native to noncommutative geometry, by for example using external Kasparov products of spectral triples.

C2weakest assumption

The development of an infinite-dimensional C*-algebraic analogue of the Choi-Jamiołkowski isomorphism holds and the seminorms arising in noncommutative geometry induce well-defined metrics on the set of unital completely positive maps.

C3one line summary

Develops metrics on unital completely positive maps via noncommutative geometry seminorms and a C*-algebraic Choi-Jamiołkowski analogue that satisfy stability and chaining under suitable conditions.

References

17 extracted · 17 resolved · 0 Pith anchors

[1] The Podle´ s sphere as a spectral metric space 2018

[2] Quantum metrics on crossed products with groups of polynomial growth 2025

[3] Transmission distance in the space of quantum channels 2008

[4] Matricial Wasserstein-1 distance 2017

[5] A dual formula for the spectral distance in noncommutative geometry 2021

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

The Bures metric and the quantum metric on the density space of a C*-algebra: the non-unital case

Receipt and verification

First computed	2026-05-18T02:45:12.164363Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83c6cf2419499aa3e0c55d1a7e02a987a0bc54340b435322cc1c14579fe1369e

Aliases

arxiv: 2512.10842 · arxiv_version: 2512.10842v3 · doi: 10.48550/arxiv.2512.10842 · pith_short_12: QPDM6JAZJGNK · pith_short_16: QPDM6JAZJGNKHYGF · pith_short_8: QPDM6JAZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QPDM6JAZJGNKHYGFLUNH4AVJQ6 \
  | 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: 83c6cf2419499aa3e0c55d1a7e02a987a0bc54340b435322cc1c14579fe1369e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a635810b27c596769a1e883cab4e838a940e1d01e45eac48b9ea063ff5878fd0",
    "cross_cats_sorted": [
      "math.FA",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2025-12-11T17:31:18Z",
    "title_canon_sha256": "05bf8563ce493ef42639e70c4290a5366918bea139bbe3775c2d3c912cb92d09"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.10842",
    "kind": "arxiv",
    "version": 3
  }
}