Measuring unconventional causal structures in monitored dynamics

TL;DR

This paper investigates the complex causal structures in monitored quantum dynamics, introducing a new measure to quantify causal influence, revealing exotic causal phenomena, and linking the arrow of time to entropy in quantum systems.

Contribution

It proposes the cross-entropy quantum causal influence measure and demonstrates its ability to detect unconventional causal structures in quantum processes.

Findings

Exotic causal structures like inverted light cones can be simulated.

The new measure can be experimentally implemented on current quantum platforms.

A theoretical link between time arrow and entropy is established in quantum models.

Abstract

Causality underpins all logical reasoning. However, the causal structure in quantum processes can be far from intuitive, often differing from its classical counterpart in relativity, which is defined by the light cone. In particular, in systems with measurement and post-selection, causal influence can occur between spacelike separated regions. In this work, we study the causal structure and emergent "arrow of time" in monitored quantum dynamics, particularly their dependence on initial and final states. We propose a new measure, the cross-entropy quantum causal influence, to quantify the extent of causal influence, whose simulation demonstrates exotic causal structures, such as inverted light cones. This quantity can be measured in current quantum computing platforms. Additionally, we provide an analytical understanding of the relation between time arrow and entropy by studying two types of models that are analytically tractable: a quantum Brownian evolution model and a dual-unitary circuit model.