Bounding Large-Scale Bell Inequalities
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912427827789824 |
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| author | Mortimer, Luke |
| author_facet | Mortimer, Luke |
| contents | Bell inequalities are an important tool for studying non-locality, however quickly become computationally intractable as the system size grows. We consider a novel method for finding an upper bound for the quantum violation of such inequalities by combining the NPA hierarchy, the method of alternating projections, and the memory-efficient optimisation algorithm L-BFGS. Whilst our method may not give the tightest upper bound possible, it often does so several orders of magnitude faster than state-of-the-art solvers, with minimal memory usage, thus allowing solutions to problems that would otherwise be intractable. We benchmark using the well-studied I3322 inequality as well as a more general large-scale randomized inequality RXX22. For randomized inequalities with 130 inputs either side (a first-level moment matrix of size 261x261), our method is ~100x faster than both MOSEK and SCS whilst giving a bound only ~2% above the optimum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08532 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bounding Large-Scale Bell Inequalities Mortimer, Luke Quantum Physics Bell inequalities are an important tool for studying non-locality, however quickly become computationally intractable as the system size grows. We consider a novel method for finding an upper bound for the quantum violation of such inequalities by combining the NPA hierarchy, the method of alternating projections, and the memory-efficient optimisation algorithm L-BFGS. Whilst our method may not give the tightest upper bound possible, it often does so several orders of magnitude faster than state-of-the-art solvers, with minimal memory usage, thus allowing solutions to problems that would otherwise be intractable. We benchmark using the well-studied I3322 inequality as well as a more general large-scale randomized inequality RXX22. For randomized inequalities with 130 inputs either side (a first-level moment matrix of size 261x261), our method is ~100x faster than both MOSEK and SCS whilst giving a bound only ~2% above the optimum. |
| title | Bounding Large-Scale Bell Inequalities |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2412.08532 |