A Generalized Grothendieck Inequality and Nonlocal Correlations that Require High Entanglement

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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. © 2011 The Author(s).

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Briët, J., Buhrman, H., & Toner, B. (2011). A Generalized Grothendieck Inequality and Nonlocal Correlations that Require High Entanglement. Communications in Mathematical Physics, 305(3), 827–843. https://doi.org/10.1007/s00220-011-1280-3

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