{
  "abstract": "Quantum contrastive, metric, and self-supervised learning often expose encoded quantum states to the learner through transition probabilities, especially fidelity. Quantum states are known to possess higher-order relational invariants, but their consequences for learned representations remain unclear. Here we show that a transition-probability-only learning interface can possess exact continuous blind directions in certain quantum-state families. We recover this missing information with a batch operator, built from coherent overlap amplitudes and negative masking, where its second moment $q_-$ retains four-state interference. Moreover, $q_-$ is directly measurable through two-copy interference and can enter variational learning via methods like parameter shift. In relational quartets derived from toric-code and double-semion states, this fidelity-blind signal encodes inequivalent modular data despite identical pairwise fidelities. Finally, in a four-photon benchmark with preparation drift, augmenting all six pairwise fidelities at two orthogonal probes with the corresponding normalized $q_-$ reduces the mean out-of-distribution phase error by $86\\%$ at equal total shot budget. These results establish multistate relational observables as measurable, trainable, and physically consequential signals for quantum representation learning beyond pairwise fidelity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01797",
  "author_total": 2,
  "authors": [
    {
      "name": "Junpeng Hou"
    },
    {
      "name": "Changbin Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3yy2q0gesh9zr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01797",
  "fulltext_url": null,
  "id": "3yy2q0gesh9zr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01797",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7207697390",
  "pdf_url": "https://arxiv.org/pdf/2609.01797",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3yy2q0gesh9zr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2609.01797",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01797"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Representation Learning Beyond Pairwise Fidelity",
  "title_text": "Quantum Representation Learning Beyond Pairwise Fidelity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:16Z",
  "url": "https://research.draconitic.com/paper/3yy2q0gesh9zr",
  "venue": "arXiv",
  "versions": []
}