Comment on "Revisiting dynamics of quantum causal structures --when can causal order evolve?''

TL;DR

This paper clarifies misconceptions about the ability of higher order transformations to change causal order in quantum processes, demonstrating that previous claims of limitations are unfounded and that certain examples are compatible with established frameworks.

Contribution

It refutes claims that higher order transformations cannot change causal order, showing existing examples are consistent with prior formalism.

Findings

Higher order transformations cannot change causal order as previously claimed.

Certain examples of causal order change are compatible with existing frameworks.

The critique of the formalism in prior work is unfounded.

Abstract

In the last few years, there has been increasing interest in quantum processes with indefinite causal order. Process matrices are a convenient framework to study such processes. Ref. [1] defines higher order transformations from process matrices to process matrices and shows that no continuous and reversible transformation can change the causal order of a process matrix. Ref. [2] argues, based on a set of examples, that there are situations where a process can change its causal order over time. Ref. [2] claims that the formalism of higher order transformations is not general enough to capture its examples. Here we show that this claim is incorrect. Moreover, a crucial example of Ref. [2] has already been explicitly considered in Ref. [1] and shown to be compatible with its results.