Towards Grothendieck Constants and LHV Models in Quantum Mechanics

TL;DR

This paper introduces a continuous model to estimate Grothendieck constants, deriving an explicit analytical formula for lower bounds that enhance previous estimates and refine nonlocality thresholds for two-qubit Werner states.

Contribution

It provides a new continuous model and an explicit analytical formula for lower bounds of Grothendieck constants, improving upon previous bounds and refining nonlocality thresholds.

Findings

Derived explicit lower bounds for Grothendieck constants of arbitrary orders.

Improved previous bounds on Grothendieck constants.

Refined the threshold for nonlocality of two-qubit Werner states.

Abstract

We adopt a continuous model to estimate the Grothendieck constants. An analytical formula to compute the lower bounds of Grothendieck constants has been explicitly derived for arbitrary orders, which improves previous bounds. Moreover, our lower bound of the Grothendieck constant of order three gives a refined bound of the threshold value for the nonlocality of the two-qubit Werner states.