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Convex optimization on moment polytopes: Hadamard mirror descent and efficient algorithms for quantum functionals and other tensor parameters — arXiv:2609.06633

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.06633
License (as archived): CC0-1.0
Archived: 2026-10-16T14:29:55.212Z
SHA-256 of the archived text: bfd73eb9f1c3fcc62d3ab66962268db17246e4c4d6d4f81524e35a57d2d57284
Stable URL of this page: https://metraipolis.com/documento/dc_4ba970dcc703

How to cite

Convex optimization on moment polytopes: Hadamard mirror descent and efficient algorithms for quantum functionals and other tensor parameters — arXiv:2609.06633 — arXiv (en), https://arxiv.org/abs/2609.06633 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_4ba970dcc703 (Metraipolis archive dc_4ba970dcc703, sha256 bfd73eb9f1c3fcc62d3ab66962268db17246e4c4d6d4f81524e35a57d2d57284)

BibTeX

@misc{dc4ba970dcc703,
  title = {Convex optimization on moment polytopes: Hadamard mirror descent and efficient algorithms for quantum functionals and other tensor parameters — arXiv:2609.06633},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.06633},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_4ba970dcc703; sha256 bfd73eb9f1c3fcc62d3ab66962268db17246e4c4d6d4f81524e35a57d2d57284},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.06633. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Convex optimization on polytopes arises in many areas of science. When the polytope is given implicitly or has exponentially many vertices and facets, standard methods may not apply or be ineffective. This is the case for moment polytopes, such as the entanglement polytopes, which play a foundational role in quantum information and algebraic complexity. They give rise to important entanglement measures and tensor parameters such as the quantum functionals, yet general effective methods for computing these quantities have been elusive. In this paper we address this challenge. We develop a first-order framework called Hadamard mirror descent to optimize suitable convex functions over moment polytopes and, more generally, the gradient sets of geodesically convex functions. It operates locally and does not rely on any explicit description of the polytope. Our framework extends mirror descent, an effective and widely used framework for convex optimization, from the Euclidean setting to Hadamard manifolds, and is motivated by a recent work by Hirai, which we interpret as a Hadamard version of mirror flow. Applying the framework to entanglement polytopes yields the first efficient first-order algorithms to compute the quantum functionals, the symmetric quantum functional, and the G-stable ranks, as well as a new direct algorithm for the non-commutative rank.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-09 in math.OC).
Categorie arXiv: Computational Complexity (cs.CC) ; Mathematical Physics (math-ph); Optimization and Control (math.OC); Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2609.06633 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T14:09:21.748Z dalla pagina https://arxiv.org/catchup/math.OC/2026-09-09?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).