Ordering the processes with indefinite causal order

TL;DR

This paper presents a method to describe processes with indefinite causal order using a definite causal order framework, emphasizing the role of superposition and addressing the limitations of classical language in quantum contexts.

Contribution

It introduces a relabeling technique to represent ICO processes within a definite causal order, linking superposition to causal nonseparability and discussing language limitations.

Findings

Causal nonseparability can be represented with definite causal order through relabeling.

Superposition plays a key role in creating ICO paradoxes.

Current language structures are incompatible with quantum logic.

Abstract

We show a method of describing processes with indefinite causal order (ICO) by a definite causal order. We do so by relabeling the processes that take place in the circuit in accordance with the basis of measurement of control qubit. Causal nonseparability is alleviated at a cost of nonlocality of the acting processes. This result highlights the key role of superposition in creating the paradox of ICO. We also draw attention to the issue of growing incompatibility of language in its current form (especially the logical structures it embodies) with the quantum logic.