Bridging the gap between general probabilistic theories and the device-independent framework for nonlocality and contextuality

TL;DR

This paper compares general probabilistic theories and the device-independent framework to unify approaches in quantum foundations, enhancing understanding of quantum correlations and theory characterization.

Contribution

It bridges the gap between two major frameworks in quantum foundations, enabling mutual insights and advancing the study of quantum correlations and theory characterization.

Findings

Identifies connections between the two frameworks.

Provides methods to translate concepts across frameworks.

Highlights potential for unified approaches in quantum foundations.

Abstract

Characterizing quantum correlations in terms of information-theoretic principles is a popular chapter of quantum foundations. Traditionally, the principles adopted for this scope have been expressed in terms of conditional probability distributions, specifying the probability that a black box produces a certain output upon receiving a certain input. This framework is known as "device-independent". Another major chapter of quantum foundations is the information-theoretic characterization of quantum theory, with its sets of states and measurements, and with its allowed dynamics. The different frameworks adopted for this scope are known under the umbrella term "general probabilistic theories". With only a few exceptions, the two programmes on characterizing quantum correlations and characterizing quantum theory have so far proceeded on separate tracks, each one developing its own methods and its own agenda. This paper aims at bridging the gap, by comparing the two frameworks and illustrating how the two programmes can benefit each other.