Quantifying Quantum Causal Influences

TL;DR

This paper introduces a quantum version of the average causal effect to quantify how interventions influence quantum systems, with applications in quantum computing and insights into entanglement's role in causality.

Contribution

It develops a quantum causality measure, the quantum ACE, applicable to various quantum systems and algorithms, extending classical causality concepts into the quantum realm.

Findings

Quantum ACE quantifies causality in two-qubit gates.

Entangled states show greater causal influence than separable states.

Causality measures can optimize quantum algorithms.

Abstract

Causal influences are at the core of any empirical science, the reason why its quantification is of paramount relevance for the mathematical theory of causality and applications. Quantum correlations, however, challenge our notion of cause and effect, implying that tools and concepts developed over the years having in mind a classical world, have to be reevaluated in the presence of quantum effects. Here, we propose the quantum version of the most common causality quantifier, the average causal effect (ACE), measuring how much a target quantum system is changed by interventions on its presumed cause. Not only it offers an innate manner to quantify causation in two-qubit gates but also in alternative quantum computation models such as the measurement-based version, suggesting that causality can be used as a proxy for optimizing quantum algorithms. Considering quantum teleportation, we show that any pure entangled state offers an advantage in terms of causal effects as compared to separable states. This broadness of different uses showcases that, just as in the classical case, the quantification of causal influence has foundational and applied consequences and can lead to a yet totally unexplored tool for quantum information science.