Device-Independent Tests of Entropy

TL;DR

This paper introduces two methods for device-independent testing of message entropy in prepare-and-measure scenarios, demonstrating quantum communication's advantage in requiring lower entropy than classical communication.

Contribution

It develops two novel techniques for lower-bounding communication entropy without trusting device details, advancing device-independent quantum information analysis.

Findings

Quantum communication requires lower entropy than classical for the same data.

Two methods successfully bound entropy in device-independent scenarios.

Quantum advantage in entropy efficiency demonstrated.

Abstract

We show that the entropy of a message can be tested in a device-independent way. Specifically, we consider a prepare-and-measure scenario with classical or quantum communication, and develop two different methods for placing lower bounds on the communication entropy, given observable data. The first method is based on the framework of causal inference networks. The second technique, based on convex optimization, shows that quantum communication provides an advantage over classical, in the sense of requiring a lower entropy to reproduce given data. These ideas may serve as a basis for novel applications in device-independent quantum information processing.