Witnesses of causal nonseparability: an introduction and a few case studies.

Cyril Branciard

doi:10.1038/srep26018

Abstract

It was recently realised that quantum theory allows for so-called causally nonseparable processes, which are incompatible with any definite causal order. This was first suggested on a rather abstract level by the formalism of process matrices, an extension of the quantum formalism which only assumes that quantum theory holds locally in some observers’ laboratories, but does not impose a global causal structure; it was then shown, on a more practical level, that the quantum switch—a new, already implementable resource for quantum computation that goes beyond causally ordered circuits—provided precisely a physical example of a causally nonseparable process. To demonstrate that a given process is causally nonseparable, the concept of witnesses of causal nonseparability was introduced. Here we present a shorter introduction to this concept, and concentrate on some explicit examples—by considering in particular different noise models for the quantum switch—to show how to construct and use such witnesses in practice.

Highlights

In our common understanding of the world, we typically perceive events as happening one after another, in a given order
This viewpoint is ingrained for instance in the circuit model for computation or information processing, where operations are performed by gates that are applied in a definite order
In this paper we have given an introduction to witnesses of causal nonseparability[2], and illustrated this concept on a few explicit examples

Summary

Introduction

In our common understanding of the world, we typically perceive events as happening one after another, in a given order. A concrete physical example of a causally nonseparable process was later exhibited[2,3]: namely, the recently proposed quantum switch, a new resource for quantum computation where the order of operations is controlled by a qubit in a superposition of two different states—which does not fit in the standard framework of causally ordered quantum circuits[4]. To ensure that this notion of causal nonseparability has any practical meaning, one needs to be able to verify that a given process is causally nonseparable. We showed in particular that a witness can be efficiently constructed for any causally nonseparable process

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Methods

Conclusion