How many systems can be dephased before the quantum switch becomes causally definite?

TL;DR

This paper investigates how dephasing quantum systems affects the causal nonseparability of quantum processes, revealing conditions under which causal nonseparability persists or vanishes.

Contribution

It provides a detailed analysis of the impact of dephasing on causal nonseparability in bipartite and multipartite quantum processes, especially within quantum circuits with quantum control.

Findings

Dephasing all systems or only the future system makes processes causally separable.

Causal nonseparability persists if any non-future system remains undephased.

Results apply to bipartite and multipartite quantum processes, including QC-QCs.

Abstract

Quantum processes with indefinite causal order -- so-called causally nonseparable processes -- can exhibit various advantages over quantum circuits with a fixed or a well-defined causal structure. A natural question is how much nonclassicality is required for a process to display causal nonseparability. Here we address this by investigating how many systems can be dephased (or decohered) before this property vanishes. First, for bipartite processes with open past and future we show that if all systems are dephased, or if only the future system is kept undephased, then the process becomes causally separable. However, if any single system other than the future system remains undephased, then there exist processes that retain causal nonseparability. Next, we demonstrate a similar behaviour in the multipartite case, when restricted to the physically motivated class of quantum circuits with quantum control (QC-QCs). Namely, dephasing all systems or keeping only the future system undephased renders any QC-QC causally separable; while causal nonseparability can persist if any non-future system is left undephased.