A map of indefinite causal order

TL;DR

This paper provides an overview of indefinite causal order in quantum mechanics, exploring its conceptual foundations, key frameworks like the quantum switch, and ongoing debates, serving as a guide for researchers in the field.

Contribution

It offers a comprehensive map of the concept of indefinite causal order, connecting various approaches and frameworks for understanding causality in quantum theory.

Findings

Introduction of the quantum switch as an example of indefinite causal order

Discussion of the process matrices framework

Commentary on ongoing debates in the field

Abstract

In this "map" we are going to present the concept of indefinite causal order and make a quick journey through its different flavours. We will start with a broad conceptual motivation for studying indefinite causal order, based on the approach of Lucien Hardy to quantum gravity. Then, we will introduce the quantum switch, which is a particular instance of indefinite causal order, followed by the process matrices framework and the superposition of causal structures. Finally, we will comment on some ongoing debates within the field. This document started as an excerpt of the author's PhD Thesis and is intended as a map of indefinite causal order, which can be used to guide the trip of any explorer in the field.