Quantum to classical transitions in causal relations

TL;DR

This paper explores the complex landscape of quantum causal relations, studying how different types of quantum coherence in causal mechanisms transition and degrade under noise, both theoretically and experimentally.

Contribution

It provides a comprehensive analysis of quantum-to-classical causal transitions, including experimental validation of coherence degradation in quantum causal mixtures.

Findings

Coherence in causal pathways degrades under noise as predicted.

Quantum-coherent mixtures can be experimentally realized and studied.

Transitions between causal relation classes are characterized and confirmed experimentally.

Abstract

The landscape of causal relations that can hold among a set of systems in quantum theory is richer than in classical physics. In particular, a pair of time-ordered systems can be related as cause and effect or as the effects of a common cause, and each of these causal mechanisms can be coherent or not. Furthermore, one can combine these mechanisms in different ways: by probabilistically realizing either one or the other or by having both act simultaneously (termed a physical mixture). In the latter case, it is possible for the two mechanisms to be combined quantum-coherently. Previous work has shown how to experimentally realize one example of each class of possible causal relations. Here, we make a theoretical and experimental study of the transitions between these classes. In particular, for each of the two distinct types of coherence that can exist in mixtures of common-cause and cause-effect relations--coherence in the individual causal pathways and coherence in the way the causal relations are combined--we determine how it degrades under noise and we confirm these expectations in a quantum-optical experiment.