{
  "abstract": "We present a variational--adjoint interpretation of quantum mechanics in which the interaction between forward and adjoint wavefunctions defines a general sensitivity kernel of the system. This Fréchet interaction density quantifies how perturbations in the wavefunction (or system parameters) influence a chosen observable. The familiar Born probability density appears as a special case when the adjoint wavefunction is chosen as the complex conjugate of the forward wavefunction, for which the interaction density becomes real and non-negative. Within this framework, probability is a particular positive-definite form of sensitivity described by the Fréchet interaction density. In general, the variational--adjoint interpretation also produces Fréchet sensitivity kernels associated with other quantum observables, including momentum, energy, and spin. This suggests that the Born probability density belongs to a broader class of Fréchet sensitivity kernels associated with quantum observables. The proposed interpretation also provides a connection with time-symmetric interpretations of quantum mechanics and possible future applications in quantum control and quantum metrology.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.23191",
  "author_total": 1,
  "authors": [
    {
      "name": "Rafael Abreu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/67tr4cg6chj5r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.23191",
  "fulltext_url": null,
  "id": "67tr4cg6chj5r",
  "issns": [],
  "landing_url": "https://hal.science/hal-05802219v1",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.phys"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7204169117",
  "pdf_url": "https://arxiv.org/pdf/2608.23191",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/67tr4cg6chj5r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:58Z",
      "native_id": "hal-05802219",
      "source": "hal",
      "url": "https://hal.science/hal-05802219v1"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3107|Quantum Mechanics and Applications",
      "subfield": "amo"
    }
  ],
  "title": "Quantum observables as Fréchet sensitivity kernels",
  "title_text": "Quantum observables as Fréchet sensitivity kernels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:58Z",
  "url": "https://research.draconitic.com/paper/67tr4cg6chj5r",
  "venue": "HAL",
  "versions": []
}