{
  "abstract": "This paper gives a categorical interpretation of Baumeler \\& Wolf's logically consistent non-causal circuits, connecting them to postselected quantum teleportation. Looped feedback is represented by a trace in the category of non-negative matrices, and it is shown that the traced process is stochastic precisely when the induced loop transition matrix has trace $1$ for every external input, a condition shown to be equivalent to a unique fixed point for the loop for each input to a deterministic circuit. A classical non-causal circuit is represented by a measure-and-prepare quantum channel with an internal register utilising a maximally entangled Bell-state with postselection. The main result is that classical logical consistency is equivalent to the postselected Bell outcome having, for loop dimension $d$, probability exactly $1/d^2$ for each classical input distribution. The subsequent normalised conditional output then agrees exactly with the classical categorical trace. This work identifies a class of quantum Bell-postselection constructions whose conditional evolution maintains linear dependence on classical input distributions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08716",
  "author_total": 1,
  "authors": [
    {
      "name": "Mark Carney"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cxryb6hgyhkcq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08716",
  "fulltext_url": null,
  "id": "cxryb6hgyhkcq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08716",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7212057772",
  "pdf_url": "https://arxiv.org/pdf/2609.08716",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cxryb6hgyhkcq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.08716",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08716"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Tracing the Loop: Non-Causal Computation, Partial Traces, & Postselected Entanglement",
  "title_text": "Tracing the Loop: Non-Causal Computation, Partial Traces, & Postselected Entanglement",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/cxryb6hgyhkcq",
  "venue": "arXiv",
  "versions": []
}