Theory Seminar: Tropical contraction of tensor networks as a Bell inequality optimization toolset

Jordi Tura (University of Leiden): We show that finding the classical bound of broad families of Bell inequalities can be naturally framed as the contraction of an associated tensor network, but in tropical algebra, where the sum is replaced by the minimum and the product is replaced by the arithmetic addition.

Jordi Tura i Brugués (University of Leiden)
Group Seminar via zoom
Wed, 22 June 2022, 10:30 am (MEZ)

Abstract:

We show that finding the classical bound of broad families of Bell inequalities can be naturally framed as the contraction of an associated tensor network, but in tropical algebra, where the sum is replaced by the minimum and the product is replaced by the arithmetic addition. We illustrate our method with paradigmatic examples and we discuss its implications in terms of computational complexity. We showcase how the method extends unto the thermodynamic limit via a renormalization procedure for some translationally invariant systems. This allows us to establish a connection between the optimal local deterministic strategies that saturate a Bell inequality and the notion of tropical eigenvector and tropical spectral radius. We also provide a recursive tropical contraction method for many-outcome inequalities, such as the CGLMP and generalizations thereof. In the talk I will also cover the basic concepts of tropical algebra, their motivation and interpretation.

If you would like to participate in the seminar, please contact us.