- A Generalized Grothendieck Inequality and Nonlocal Correlations that Require High Entanglement
- Communications in Mathematical Physics
- Volume | Issue number
- 305 | 3
- Pages (from-to)
- Number of pages
- Document type
- Interfacultary Research Institutes
- Institute for Logic, Language and Computation (ILLC)
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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