No-signalling-projection-invariant Bell inequalities

TL;DR

This paper introduces a canonical form of Bell inequalities that remains invariant under no-signalling projections, simplifying analysis and computation for device-independent quantum information tasks.

Contribution

It presents a general closed-form formula for no-signalling projections of Bell data and demonstrates their invariance, aiding device-independent quantum applications.

Findings

Projection leaves Bell violation unchanged

Derived a simple computational formula

Generalized to non-standard projections

Abstract

In this paper, we highlight how any Bell inequality for a configuration involving $n$ parties each performing one of $m$ binary-outcome measurements has a canonical form that is no-signalling-projection invariant. Specifically, the $L^2$-projection of weakly signalling data onto the no-signalling polytope leaves the violation of this canonical Bell inequality unchanged. Our methods allow us to derive a general closed formula for the projection and present a substantially more computationally simple procedure for its evaluation. We also show this can be generalised to non-standard projections of potential interest for certain applications. No-signalling projections serve as a preliminary step before undertaking any device-independent application involving Bell experiment data, such as hypothesis testing against local realism, random number generation and entanglement detection.