{
  "abstract": "This survey introduces the role of frame phase retrieval in pure-state identification and information preservation by quantum channels. For unit vectors, the lift $x\\mapsto xx^*$ identifies vectors that differ only by a global phase with the same rank-one quantum state, converts frame intensities into linear functionals of the lifted state, and makes the adjoint pullback of output observables an operator-valued measurement on the input system. From this viewpoint, a channel is phase retrievable exactly when it is injective on pure states. We develop this correspondence through Choi-rank-two linear combinations of Kraus operators, higher-rank relative spectra, structural obstructions, and constructions with prescribed Choi rank. We distinguish injective identification from full tomography, perfect one-shot discrimination, zero-error classical communication, and exact quantum correction. Twirling channels then provide a structured setting in which commutants, irreducible dimensions, multiplicities, orbit-frame orthogonality, coding indices, and phase-retrievable subspaces can be read from group representations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30006",
  "author_total": 2,
  "authors": [
    {
      "name": "Deguang Han"
    },
    {
      "name": "Kai Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6msq43h932kwk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30006",
  "fulltext_url": null,
  "id": "6msq43h932kwk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30006",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7204929383",
  "pdf_url": "https://arxiv.org/pdf/2608.30006",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6msq43h932kwk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2608.30006",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30006"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Frame phase retrievability and state distinguishability of quantum channels",
  "title_text": "Frame phase retrievability and state distinguishability of quantum channels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/6msq43h932kwk",
  "venue": "arXiv",
  "versions": []
}