Local hidden variable values without optimization procedures

Abstract

The problem of computing the local hidden variable (LHV) value of a Bell inequality plays a central role in the study of quantum nonlocality. In particular, this problem is the first step towards characterizing the LHV polytope of a given scenario. In this work, we establish a relation between the LHV value of bipartite Bell inequalities and the mathematical notion of excess of a matrix. Inspired by the well developed theory of excess, we derive several results that directly impact the field of quantum nonlocality. We show infinite families of bipartite Bell inequalities for which the LHV value can be computed exactly, without needing to solve any optimization problem, for any number of measurement settings. We also find tight Bell inequalities for a large number of measurement settings.

14 pages. Comments are very welcome! Accepted in Quantum (January 9, 2023)

References in corpus (7)

• Device-independent security of quantum cryptography against collective attacks
• Secure device-independent quantum key distribution with causally independent measurement devices
• Private Randomness Expansion With Untrusted Devices
• Classifying 50 years of Bell inequalities
• Qutrit witness from the Grothendieck constant of order four
• Bell nonlocality with a single shot
• Characterising the Performance of XOR Games and the Shannon Capacity of Graphs