Measurement dependent locality

TL;DR

This paper explores measurement dependence in Bell tests, characterizing the measurement dependent local polytope, analyzing its properties, and developing inequalities to better understand nonlocal correlations under relaxed assumptions.

Contribution

It provides a full characterization of the measurement dependent local polytope for bipartite binary scenarios and introduces methods to derive inequalities for multiple parties and inputs.

Findings

Partially entangled states are more robust under measurement dependence.

The measurement dependent local set forms a polytope describable by linear inequalities.

A method to transform Bell inequalities into measurement dependent inequalities.

Abstract

The demonstration and use of Bell-nonlocality, a concept that is fundamentally striking and is at the core of applications in device independent quantum information processing, relies heavily on the assumption of measurement independence, also called the assumption of free choice. The latter cannot be verified or guaranteed. In this paper, we consider a relaxation of the measurement independence assumption. We briefly review the results of Phys. Rev. Lett. 113, 190402 (2014), which show that with our relaxation, the set of so-called measurement dependent local (MDL) correlations is a polytope, i.e. it can be fully described using a finite set of linear inequalities. Here we analyze this polytope, first in the simplest case of 2 parties with binary inputs and outputs, for which we give a full characterization. We show that partially entangled states are preferable to the maximally entangled state when dealing with measurement dependence in this scenario. We further present a method which transforms any Bell-inequality into an MDL inequality and give valid inequalities for the case of arbitrary number of parties as well as one for arbitrary number of inputs. We introduce the assumption of independent sources in the measurement dependence scenario and give a full analysis for the bipartite scenario with binary inputs and outputs. Finally, we establish a link between measurement dependence and another strong hindrance in certifying nonlocal correlations: nondetection events.