Unbounded violations of bipartite Bell Inequalities via Operator Space theory

TL;DR

This paper demonstrates that bipartite quantum states can significantly violate Bell inequalities using operator space theory, leading to improved dimension witnesses and noise resistance.

Contribution

It establishes a connection between Bell inequality violations and operator space theory, providing new bounds and insights into quantum nonlocality.

Findings

Violations scale as √n (up to log factors) with local dimension n.

Enhanced Hilbert space dimension witnesses.

Improved resistance to noise in Bell inequality violations.

Abstract

In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order $\sqrt{n}$ (up to a logarithmic factor) when observables with n possible outcomes are used. A central tool in the analysis is a close relation between this problem and operator space theory and, in particular, the very recent noncommutative $L_p$ embedding theory. As a consequence of this result, we obtain better Hilbert space dimension witnesses and quantum violations of Bell inequalities with better resistance to noise.