A generalized Grothendieck inequality and entanglement in XOR games

2009/01/14 by Briët, Jop, Buhrman, Harry, Toner, Ben · 1 citation
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.0901.2009

Abstract

Suppose Alice and Bob make local two-outcome measurements on a shared entangled state. For any d, we show that there are correlations that can only be reproduced if the local dimension is at least d. This resolves a conjecture of Brunner et al. Phys. Rev. Lett. 100, 210503 (2008) and 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 the first lower bounds on a new generalization of Grothendieck's constant.

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