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107881 |
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|a Yin, Z.
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|a Massachusetts Institute of Technology. Center for Theoretical Physics
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|a Massachusetts Institute of Technology. Department of Physics
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|a Harrow, Aram W
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|a Horodecki, M.
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|a Marciniak, M.
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|a Rutkowski, A.
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|a Harrow, Aram W
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|a Saturation of the Tsirelson bound for the Clauser-Horne-Shimony-Holt inequality with random and free observables
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|b American Physical Society,
|c 2017-04-05T16:22:44Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/107881
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|a Maximal violation of the CHSH-Bell inequality is usually said to be a feature of anticommuting observables. In this work we show that even random observables exhibit near-maximal violations of the CHSH-Bell inequality. To do this, we use the tools of free probability theory to analyze the commutators of large random matrices. Along the way, we introduce the notion of "free observables," which can be thought of as infinite-dimensional operators that reproduce the statistics of random matrices as their dimension tends towards infinity. We also study the fine-grained uncertainty of a sequence of free or random observables and use this to construct a steering inequality with a large violation.
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|a European Research Council (Advanced Grant QOLAPS)
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|a European Union (Grant RAQUEL)
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|a Foundation for Polish Science (TEAM Project)
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|a National Science Foundation (U.S.) (Grants CCF-1111382 and CCF-1452616)
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|a United States. Army Research Office (Contract W911NF-12-1-0486)
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|a Leverhulme Trust (Visiting Professorship VP2-2013-041)
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|a en
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|a Article
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|t Physical Review A
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