A Generalized Grothendieck Inequality and Nonlocal Correlations that Require High Entanglement |
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Authors: | Jop Briët Harry Buhrman Ben Toner |
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Institution: | (1) Department of Physics, University of Toronto, M5S 1A7 Toronto, ON, Canada;(2) Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, 61801-3080 Urbana, IL, USA;(3) U.C. Berkeley, 366 Leconte Hall, 94720-7300 Berkeley, CA, USA |
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Abstract: | Suppose that Alice and Bob make local two-outcome measurements on a shared entangled quantum state. We show that, for all
positive integers d, there exist correlations that can only be reproduced if the local Hilbert-space dimension is at least d. This establishes that the amount of entanglement required to maximally violate a Bell inequality must depend on the number
of measurement settings, not just the number of measurement outcomes. We prove this result by establishing a lower bound on
a new generalization of Grothendieck’s constant. |
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Keywords: | |
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