Cyclic quantum causal models

Abstract

Causal reasoning is essential to science, yet quantum theory challenges it. Quantum correlations violating Bell inequalities defy satisfactory causal explanations within the framework of classical causal models. What is more, a theory encompassing quantum systems and gravity is expected to allow causally nonseparable processes featuring operations in indefinite causal order, defying that events be causally ordered at all. The first challenge has been addressed through the recent development of intrinsically quantum causal models, allowing causal explanations of quantum processes – provided they admit a definite causal order, i.e. have an acyclic causal structure. This work addresses causally nonseparable processes and offers a causal perspective on them through extending quantum causal models to cyclic causal structures. Among other applications of the approach, it is shown that all unitarily extendible bipartite processes are causally separable and that for unitary processes, causal nonseparability and cyclicity of their causal structure are equivalent.

Consequences of preserving reversibility in quantum superchannels

“…1 is independently obtained in Ref. [28] by Barrett et al They present it as a main result and use the same fact as Thm. 4 in their proof.…”

“…[27] proving the decomposition of the reversibility preserving superchannels and Ref. [28] on one of our implications on the equivalence between causal separability and unitarily extendibility of bipartite processes. Reference [27] exploits the decomposition derived in Ref.…”

“…Related results are recently presented in Ref [27]. and Ref [28]. byBarrett et al using different proof techniques.…”

Routed quantum circuits

“…The second is the existence of parallel compositions of 1 This has to be distinguished from the recent surge in interest in indefinite causal order (ICO) [6,7,8,9], which also goes beyond standard quantum circuits in a different way. Even though the framework presented here would have natural applications to the study of ICO [10], it is important to emphasise that the features that differentiate it from standard quantum circuits are not of the same kind as those that give rise to ICO; all the constructions under study in the present work display a definite causal order.…”

“…A second line of research, that of causal decompositions [29,30,31,10] (described more comprehensively in Section 2.2), aims at probing the equivalence between the compatibility of a unitary channel with a given causal structure, and the existence of a decomposition for this channel along a given unitary circuit in which this causal structure is made obvious. In this context, it was found that, in order to prove such an equivalence in some cases, one has to consider decompositions in which some of the unitary channels satisfy sectorial constraints and are parallelly composed in a non-trivial way.…”