Quantum superposition of the order of parties as a communication resource

TL;DR

This paper demonstrates that quantum superpositions of communication order can enhance success probabilities in distributed tasks, providing a new resource beyond entanglement and classical communication, and offers semi-device-independent certification of indefinite causal order.

Contribution

It introduces the concept of using quantum superpositions of communication order as a resource, showing advantages in a specific tripartite task and establishing semi-device-independent certification of indefinite causal order.

Findings

Quantum superpositions of communication order improve success probability.

A tripartite task demonstrates advantage over fixed communication order.

First semi-device-independent certification of indefinite causal order.

Abstract

In a variant of communication complexity tasks, two or more separated parties cooperate to compute a function of their local data, using a limited amount of communication. It is known that communication of quantum systems and shared entanglement can increase the probability for the parties to arrive at the correct value of the function, compared to classical resources. Here we show that quantum superpositions of the direction of communication between parties can also serve as a resource to improve the probability of success. We present a tripartite task for which such a superposition provides an advantage compared to the case where the parties communicate in a fixed order. In a more general context, our result also provides the first semi-device-independent certification of the absence of a definite order of communication.