Violations of Bell inequalities from random pure states
(2015) Physical Review A — Vol. 92, n° 1, p. 12331 (2015)
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- Abstract
- We consider the expected violations of Bell inequalities from random pure states. More precisely, we focus on a slightly generalized version of the Collins-Gisin-Linden-Massar-Popescu inequality, which concerns Bell experiments of two parties, two measurement options, and N outcomes, and analyze their expected quantum violations from random pure states for varying N, assuming the conjectured optimal measurement operators. It is seen that for small N the Bell inequality is not violated on average, while for larger N it is. Both ensembles of unstructured as well as structured random pure states are considered. Using techniques from random matrix theory this is obtained analytically for small and large N and numerically for intermediate N. The results show a beautiful interplay of different aspects of random matrix theory, ranging from the Marchenko-Pastur distribution and fixed-trace ensembles to the O(n) model.
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Atkin, M. R., & Zohren, S. (2015). Violations of Bell inequalities from random pure states. Physical Review A, 92(1), 12331. https://doi.org/10.1103/physreva.92.012331 (Original work published 2015)