Quantum Liang Information Flow as Causation Quantifier

TL;DR

This paper extends Liang information flow, a classical causation measure, to quantum networks using von-Neumann entropy, enabling the assessment of node influence in quantum network dynamics.

Contribution

It introduces a quantum version of Liang information flow and demonstrates its application to small quantum networks for causality analysis.

Findings

Quantum Liang information flow quantifies causality in quantum networks.

The method identifies influential nodes in quantum network dynamics.

Application to small quantum networks illustrates practical utility.

Abstract

Liang information flow is a quantity widely used in classical network theory to quantify causation, and has been applied widely, for example, to finance and climate. The most striking aspect here is to freeze/subtract a certain node of the network to ascertain its causal influence to other nodes of the network. Such an approach is yet to be applied to quantum network dynamics. Here we generalize Liang information flow to the quantum domain using the von-Neumann entropy. Using that we propose to assess the relative importance of various nodes of a network to causally influence a target node. We exemplify the application by using small quantum networks.