Revisiting dynamics of quantum causal structures -- when can causal order evolve?

TL;DR

This paper challenges previous claims that causal order in quantum processes cannot change under continuous, reversible dynamics, showing that causal structures can indeed evolve when considering the full quantum-mechanical framework.

Contribution

It demonstrates that the causal order in quantum processes can evolve under certain conditions, contradicting earlier theorems, and clarifies the limitations of the higher-order process framework.

Findings

Causal order can change under specific reversible dynamics.

The higher-order process framework may not always reflect physical evolution.

Reconciliation with entanglement processing clarifies the evolution of causal structures.

Abstract

Recently, there has been substantial interest in studying the dynamics of quantum theory beyond that of states, in particular, the dynamics of channels, measurements, and higher-order transformations. Ref. [Phys. Rev. X 8(1), 011047 (2018)] pursues this using the process-matrix formalism, together with a definition of the possible dynamics of such process matrices, and focusing especially on the question of evolution of causal structures. One of its major conclusions is a strong theorem saying that within the formalism, under continuous and reversible transformations, the causal order between operations must be preserved. Our result here challenges that of Ref. [Phys. Rev. X 8(1), 011047 (2018)]: if one is to take into account a full picture of the physical evolution of operations within the standard quantum-mechanical formalism, then the conclusion of Ref. [Phys. Rev. X 8(1), 011047 (2018)] does not hold. That is, we show that under certain continuous and reversible dynamics, the causal order between operations is not necessarily preserved. We moreover identify and analyse the root of this apparent contradiction, specifically, that the commonly accepted and widely applied framework of higher-order processes, whilst mathematically sound, is not always appropriate for drawing conclusions on physical dynamics. Finally, we show how to reconcile the elements of the whole picture following the intuition based on entanglement processing by local operations and classical communication.