Semidefinite block-matrix relaxations for computing quantum correlations

• URL: http://arxiv.org/abs/2603.19388v1
• Date: Thu, 19 Mar 2026 18:25:31 GMT
• Title: Semidefinite block-matrix relaxations for computing quantum correlations
• Abstract summary: We propose a semidefinite relaxation methodology that can incorporate a breadth of constraints needed in various quantum correlation problems.<n>We showcase the methodology and its features by using it to address five different quantum information problems.<n>These include entanglement witnessing from imperfect measurement devices, certifying measurements from fidelity-constrained sources, benchmarking dimensionality for state preparation devices, and finding uncertainty relations for nearly anti-commuting observables.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Bounding the correlations predicted by quantum theory is an important challenge in quantum information science. Today's leading approach is semidefinite programming relaxations, but existing methods still cannot account for many relevant types of constraints. Here, we propose a semidefinite relaxation methodology that can incorporate a breadth of constraints needed in various quantum correlation problems, thereby generalising the seminal Navascués-Pironio-Acín hierarchy. It yields useful results at reasonable computational cost. We showcase the methodology and its features by using it to address five different quantum information problems. These are (i) entanglement witnessing from imperfect measurement devices, (ii) certifying measurements from fidelity-constrained sources, (iii) computing dimensionality in genuine multi-particle entangled states, (iv) benchmarking dimensionality for state preparation devices, and (v) finding uncertainty relations for nearly anti-commuting observables. These applications reflect both the usefulness and versatility of the methodology, as well as its potential for broader relevance in the field.

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