Certified bounds on optimization problems in quantum theory

• URL: http://arxiv.org/abs/2512.17713v1
• Date: Fri, 19 Dec 2025 15:44:15 GMT
• Title: Certified bounds on optimization problems in quantum theory
• Authors: Younes Naceur, Jie Wang, Victor Magron, Antonio Acín,
• Abstract summary: We introduce a rigorous framework for extracting exact rational optimization on non-commutative problems from numerical data.<n>An extension to sparsity and symmetry-adapted semidefinite relaxations is also provided compared to the general scheme.
• Score: 2.8417851789786686
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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