{
  "abstract": "Given Hermitian observable $A$, the variance of $A$ is given by the difference of expectations $\\langle A^2\\rangle - \\langle A\\rangle^2$, where the expectation of an observable implicitly assumes a choice of state for the underlying system. As a sub-case of a general lower bound for the sum of variances for finitely many arbitrary elements in a $C^*$-algebra, we prove that the sum of the variances for $d$ observables $A_1, \\dots , A_d$ is greater than some expression in the expectations $\\langle i[A_j,A_k]\\rangle$ for $j\\neq k$ plus the square of the smallest singular value of the associated localizer. In special cases, this expression is just a root mean square average. Our technique also derives a general containment between the Clifford pseudospectra and quadratic pseudospectra for $d$ observables.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32014",
  "author_total": 3,
  "authors": [
    {
      "name": "Alexander Cerjan"
    },
    {
      "name": "Lara Ismert"
    },
    {
      "name": "Terry A. Loring"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b3j5cdke9bbwz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32014",
  "fulltext_url": null,
  "id": "b3j5cdke9bbwz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32014",
  "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",
      "math.OA"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7223686554",
  "pdf_url": "https://arxiv.org/pdf/2610.32014",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b3j5cdke9bbwz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:15Z",
      "native_id": "2610.32014",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32014"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Additive uncertainty relations via pseudospectral methods",
  "title_text": "Additive uncertainty relations via pseudospectral methods",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/b3j5cdke9bbwz",
  "venue": "arXiv",
  "versions": []
}