More non-locality with less entanglement

TL;DR

This paper presents a simple Bell inequality example where the maximal violation is achieved without using maximally entangled states, challenging assumptions about entanglement and nonlocality.

Contribution

It provides an explicit, elementary example demonstrating that maximal Bell violation does not require maximally entangled states, even with unlimited entanglement resources.

Findings

Maximal violation achieved without maximally entangled states

Explicit example with 3 settings and 2 outcomes per site

Shows nonlocality can be stronger than entanglement

Abstract

We provide an explicit example of a Bell inequality with 3 settings and 2 outcomes per site for which the largest violation is not obtained by the maximally entangled state, even if its dimension is allowed to be arbitrarily large. This complements recent results by Junge and Palazuelos (arXiv:1007.3042) who show, employing tools from operator space theory, that such inequalities do exist. Our elementary example provides arguably the simplest setting in which it can be demonstrated that even an infinite supply of EPR pairs is not the strongest possible nonlocal resource.