General Method for Classicality Certification in the Prepare and Measure Scenario

TL;DR

This paper introduces a general method to certify classicality in prepare and measure scenarios, enabling the distinction between classical and quantum behaviors based solely on observational data, with applications in quantum networks and randomness certification.

Contribution

It provides a novel, sufficient condition for certifying classicality of preparations and measurements in the prepare and measure scenario, advancing the ability to identify quantum versus classical behaviors.

Findings

Developed a general criterion for classicality certification.

Demonstrated non-classicality activation in prepare and measure scenarios.

Identified measurement sets that cannot produce non-classical behaviors.

Abstract

Preparation and measurement of physical systems are the operational building blocks of any physical experiment, and to describe them is the first purpose of any physical theory. It is remarkable that, in some situations, even when only preparation and measurement devices of a single system are present and they are uncharacterized, it is possible to distinguish between the behaviours of quantum and classical systems relying only on observational data. Certifying the physical origin of measurement statistics in the prepare and measure scenario is of primal importance for developing quantum networks, distributing quantum keys and certifying randomness, to mention a few applications, but, surprisingly, no general methods to do so are known. We progress on this problem by crafting a general, sufficient condition to certify that a given set of preparations can only generate classical statistics, for any number of generalized measurements. As an application, we employ the method to demonstrate non-classicality activation in the prepare and measure scenario, also considering its application in random access codes. Following that, we adapt our method to certify, again through a sufficient condition, whether a given set of measurements can never give rise to non-classical behaviors, irrespective of what preparations they may act upon. This, in turn, allows us to find a large set of incompatible measurements that cannot be used to demonstrate non-classicality, thus showing incompatibility is not sufficient for non-classicality in the prepare and measure scenario.