{
  "abstract": "We describe a family of convex uniformly continuous functions $E^λ_F$, $λ>0$, on the set of states of a bipartite quantum system (consisting of finite-dimensional or infinite-dimensional subsystems), which monotonically increase and converge pointwise to the Entanglement of Formation (EoF) as $λ\\to0$. These functions are \"nonselective\" entanglement monotones defined in a way close to the construction of the Moreau-Yosida regularization (the Moreau envelope) of a convex function on a convex set used in the modern convex analysis. So, we call the functions $E^λ_F$ the Moreau-Yosida approximations of the EoF and describe their equivalent definitions and basic properties. The semicontinuity bounds for the EoF (presented in [Lob.J.Math., 46(6), 2632-2658]) allow us to obtain easily computable upper bounds on the difference $E_F(ρ)-E^λ_F(ρ)$ for a given state $ρ$. These bounds give easily computable bounds on the rate of uniform convergence of the function $E^λ_F$ to the EoF as $λ\\to0^+$ on the sets of states with bounded rank/energy of one of the marginal states. We also discuss sufficient conditions for the coincidence of $E_F(ρ)$ and $E^λ_F(ρ)$ at a given state $ρ$ for all $λ$ small enough and consider several classes of states for which such coincidence takes place. The conjectured selective LOCC-monotonicity of the functions $E^λ_F$ and a possible way to prove it are briefly discussed. Secondary parts of the article are written with the help of ChatGPT-5.6.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30246",
  "author_total": 1,
  "authors": [
    {
      "name": "M. E. Shirokov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/600v8v3h5kj85.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30246",
  "fulltext_url": null,
  "id": "600v8v3h5kj85",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30246",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7214322388",
  "pdf_url": "https://arxiv.org/pdf/2609.30246",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/600v8v3h5kj85.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2609.30246",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30246"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The Moreau-Yosida approximation of the Entanglement of Formation: basic properties and accuracy estimates",
  "title_text": "The Moreau-Yosida approximation of the Entanglement of Formation: basic properties and accuracy estimates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/600v8v3h5kj85",
  "venue": "arXiv",
  "versions": []
}