Quantifying Causality in Quantum and General Models

TL;DR

This paper establishes axioms for quantifying causality in various models, especially quantum, and introduces measures based on quantum capacities to assess quantum causality and signaling.

Contribution

It proposes a comprehensive set of axioms for causality measures and develops quantum causality quantifiers using one-shot quantum capacities.

Findings

Axioms for causality measures applicable to broad probabilistic theories

Introduction of quantum causality measures based on quantum capacities

Quantification of quantum signaling and causality in operational models

Abstract

In studies of entanglement, finding out if a state is entangled and quantifying the amount of entanglement contained in a state are related but different questions. Similarly in studies of causality, finding out the causal structures compatible with a model and quantifying the causal strengths are related but different questions. Recently much research have been directed towards the first question but considerably less attention is paid to the second one. In this paper we propose axioms for all reasonable quantitative measures of causality to obey. The axioms apply to a broad family of operational probabilistic theories with and without definite causal structure. For quantum models, we study causality measures based on one-shot quantum capacities in detail. These measures are used to define the notions of quantum signalling and quantum causality measures in order to quantify quantum causality.