Operationally classical simulation of quantum states

TL;DR

This paper introduces classical models that can simulate certain quantum states through stochastic coordination, providing a framework to distinguish quantum coherence from classical mimicry and exploring implications for quantum information.

Contribution

It develops systematic methods for simulating quantum states classically and certifying quantum coherence, including exact noise thresholds for full quantum state space simulation.

Findings

Classical models can simulate many non-commuting quantum states.

Exact noise rates for classical simulation of quantum state space are determined.

Connections between classicality, joint measurability, and EPR steering are revealed.

Abstract

A classical state-preparation device cannot generate states in relative superposition. We introduce classical models in which devices that are individually unable to generate states with relative superposition can be stochastically coordinated to simulate sets of quantum states. These models have natural operational interpretation in prepare-and-measure scenarios and they can account for many non-commuting quantum state sets. We develop systematic methods both for classically simulating quantum sets and for showing that no such simulation exists, thereby certifying quantum coherence. In particular, we determine the exact noise rates required to classically simulate the entire state space of quantum theory. We also reveal connections between the operational classicality of sets and the well-known fundamental concepts of joint measurability and Einstein-Podolsky-Rosen steering. Here, we present an avenue to understand how and to what extent quantum states defy generic models based on classical devices, which also has relevant implications for quantum information applications.