dorsal/arxiv
View SchemaBounds on Quantum Correlations in Bell Inequality Experiments
| Authors | Yeong-Cherng Liang, Andrew C. Doherty |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0608128 |
| URL | https://arxiv.org/abs/quant-ph/0608128 |
| DOI | 10.1103/PhysRevA.75.042103 |
| Journal | Physical Review A, vol. 75, art. 042103 (2007) |
Abstract
Bell inequality violation is one of the most widely known manifestations of entanglement in quantum mechanics; indicating that experiments on physically separated quantum mechanical systems cannot be given a local realistic description. However, despite the importance of Bell inequalities, it is not known in general how to determine whether a given entangled state will violate a Bell inequality. This is because one can choose to make many different measurements on a quantum system to test any given Bell inequality and the optimization over measurements is a high-dimensional variational problem. In order to better understand this problem we present algorithms that provide, for a given quantum state, both a lower bound and an upper bound on the maximal expectation value of a Bell operator. Both bounds apply techniques from convex optimization and the methodology for creating upper bounds allows them to be systematically improved. In many cases these bounds determine measurements that would demonstrate violation of the Bell inequality or provide a bound that rules out the possibility of a violation. Examples are given to illustrate how these algorithms can be used to conclude definitively if some quantum states violate a given Bell inequality.
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"abstract": "Bell inequality violation is one of the most widely known manifestations of\nentanglement in quantum mechanics; indicating that experiments on physically\nseparated quantum mechanical systems cannot be given a local realistic\ndescription. However, despite the importance of Bell inequalities, it is not\nknown in general how to determine whether a given entangled state will violate\na Bell inequality. This is because one can choose to make many different\nmeasurements on a quantum system to test any given Bell inequality and the\noptimization over measurements is a high-dimensional variational problem. In\norder to better understand this problem we present algorithms that provide, for\na given quantum state, both a lower bound and an upper bound on the maximal\nexpectation value of a Bell operator. Both bounds apply techniques from convex\noptimization and the methodology for creating upper bounds allows them to be\nsystematically improved. In many cases these bounds determine measurements that\nwould demonstrate violation of the Bell inequality or provide a bound that\nrules out the possibility of a violation. Examples are given to illustrate how\nthese algorithms can be used to conclude definitively if some quantum states\nviolate a given Bell inequality.",
"arxiv_id": "quant-ph/0608128",
"authors": [
"Yeong-Cherng Liang",
"Andrew C. Doherty"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.75.042103",
"journal_ref": "Physical Review A, vol. 75, art. 042103 (2007)",
"title": "Bounds on Quantum Correlations in Bell Inequality Experiments",
"url": "https://arxiv.org/abs/quant-ph/0608128"
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