Causally nonseparable processes admitting a causal model

TL;DR

This paper demonstrates the existence of bipartite causally nonseparable quantum processes that admit a causal model, providing algorithms and evidence of their properties and behaviors under noise and extensions.

Contribution

It is the first to show bipartite causally nonseparable processes with a causal model and offers an algorithm to generate such processes.

Findings

Existence of bipartite causally nonseparable processes with a causal model.

Processes can stop violating causal inequalities yet remain causally nonseparable.

Causally nonseparable processes can have a causal model even with shared entanglement.

Abstract

A recent framework of quantum theory with no global causal order predicts the existence of "causally nonseparable" processes. Some of these processes produce correlations incompatible with any causal order (they violate so-called "causal inequalities" analogous to Bell inequalities) while others do not (they admit a "causal model" analogous to a local model). Here we show for the first time that bipartite causally nonseparable processes with a causal model exist, and give evidence that they have no clear physical interpretation. We also provide an algorithm to generate processes of this kind and show that they have nonzero measure in the set of all processes. We demonstrate the existence of processes which stop violating causal inequalities but are still causally nonseparable when mixed with a certain amount of "white noise". This is reminiscent of the behavior of Werner states in the context of entanglement and nonlocality. Finally, we provide numerical evidence for the existence of causally nonseparable processes which have a causal model even when extended with an entangled state shared among the parties.