Saturation of the Tsirelson bound for the Clauser-Horne-Shimony-Holt inequality with random and free observables
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PhysRevA.95.032101.pdf
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Author(s)
Yin, Z.
Horodecki, M.
Marciniak, M.
Rutkowski, A.
Harrow, Aram W
Date Issued
March 2017
Journal
Physical Review A
Publisher
American Physical Society
Citation
Yin, Z. et al. “Saturation of the Tsirelson Bound for the Clauser-Horne-Shimony-Holt Inequality with Random and Free Observables.” Physical Review A 95.3 (2017): n. pag. © 2017 American Physical Society
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevA.95.032101
