{"ID":2827169,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.17713","arxiv_id":"2512.17713","title":"Certified bounds on optimization problems in quantum theory","abstract":"Semidefinite relaxations of polynomial optimization have become a central tool for addressing the non-convex optimization problems over non-commutative operators that are ubiquitous in quantum information theory and, more in general, quantum physics. Yet, as these global relaxation methods rely on floating-point methods, the bounds issued by the semidefinite solver can - and often do - exceed the global optimum, undermining their certifiability. To counter this issue, we introduce a rigorous framework for extracting exact rational bounds on non-commutative optimization problems from numerical data, and apply it to several paradigmatic problems in quantum information theory. An extension to sparsity and symmetry-adapted semidefinite relaxations is also provided and compared to the general dense scheme. Our results establish rational post-processing as a practical route to reliable certification, pushing semidefinite optimization toward a certifiable standard for quantum information science.","short_abstract":"Semidefinite relaxations of polynomial optimization have become a central tool for addressing the non-convex optimization problems over non-commutative operators that are ubiquitous in quantum information theory and, more in general, quantum physics. Yet, as these global relaxation methods rely on floating-point method...","url_abs":"https://arxiv.org/abs/2512.17713","url_pdf":"https://arxiv.org/pdf/2512.17713v1","authors":"[\"Younes Naceur\",\"Jie Wang\",\"Victor Magron\",\"Antonio Acín\"]","published":"2025-12-19T15:44:15Z","proceeding":"quant-ph","tasks":"[\"quant-ph\",\"cs.SC\",\"math.OC\"]","methods":"[]","has_code":false}