{
  "abstract": "We develop a mixing time method for estimating the sample complexity of quantum state discrimination. We start with considering the minimum-error discrimination of geometrically uniform pure state ensembles, and prove that its sample complexity has a tight estimate given by a quantum homogeneous mixing time [George et al., 2026] and a quantum version of the generalized Dobrushin coefficient [Wolfer, 2020]. This quantum mixing time further reduces to a classical one when the generating group $G$ forms a Gelfand pair with the stabilizer subgroup $H$ of the generator state. In this case the generalized Dobrushin coefficient can be fully expressed by representation-theoretic quantities of the commutative Hecke algebra $\\operatorname{End}_G(\\mathbb C[G/H])$. In particular, this method reduces the sample complexity estimation of learning quantum coupon collector states [Arunachalam et al., 2020] and learning phase states to classical mixing time problems. We apply this framework to answer the open problems of learning degree-$d$ phase states over $\\mathbb F_q$ in [Alrabiah et al., 2026] and generalized Boolean phase states over $\\mathbb Z_q$ [Arunachalam et al., 2023]. The framework also applies to hypergraph state ensembles, giving estimates expressed fully in terms of hypergraph data and recovering estimates for graph state ensembles in [Montanaro and Shao, 2022]. Finally, we extend the discussion to arbitrary mixed state ensembles with uniform priors, prove a sandwiched bound for minimum-error discrimination sample complexity by a quantum weakly mixing time, and provide a tight estimate for the minimax discrimination sample complexity from [D'Ariano et al., 2005] by a Dobrushin-type coefficient. We also discuss the method of strengthened data processing inequality [Gao and Rouz{é}, 2022] and give an upper bound in terms of a strengthened data processing inequality constant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40182",
  "author_total": 2,
  "authors": [
    {
      "name": "Juntai Zhou"
    },
    {
      "name": "Felix Leditzky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8kyv32dzb3c6b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40182",
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  "id": "8kyv32dzb3c6b",
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  "landing_url": "https://arxiv.org/abs/2609.40182",
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      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
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  "openalex": "W7215118531",
  "pdf_url": "https://arxiv.org/pdf/2609.40182",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8kyv32dzb3c6b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.40182",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40182"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A mixing time method for estimating the sample complexity of quantum state discrimination",
  "title_text": "A mixing time method for estimating the sample complexity of quantum state discrimination",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/8kyv32dzb3c6b",
  "venue": "arXiv",
  "versions": []
}