Simulating quantum measurements without using superposition

TL;DR

This paper explores whether quantum measurements can be simulated with classical devices lacking superposition, providing models, noise thresholds, and operational implications for such classical representations.

Contribution

It introduces classical measurement models that bridge commutative measurements and joint measurability, analyzing their thresholds and operational consequences.

Findings

All projective measurements in $d$-dimensional quantum theory admit a classical model at specific noise rates.

Methods for constructing and falsifying classical models for finite quantum measurement sets are developed.

Classical models imply that quantum measurements with side-information can be implemented sequentially without disturbance.

Abstract

Superposition is the core feature that sets quantum theory apart from classical physics. Here, we investigate whether sets of quantum measurements can be modelled by using only devices that are operationally classical, in the sense that they have no superposition properties. This leads us to propose classical measurement models, which we show to be intermediate between the notion of commutative measurements and joint measurability. We determine both the exact depolarisation noise rate and the measurement loss rate at which all the projective measurements in $d$-dimensional quantum theory admit a classical model. For finite sets of quantum measurements we develop methods both for constructing classical models and for falsifying the existence of such model via prepare-and-measure setups. Furthermore, we show that this concept also has operational implications. For that, we consider whether quantum measurements with classical side-information can be implemented in sequence without causing a disturbance and we show that classical models imply an affirmative answer. Our work sheds light on superposition as a resource for quantum measurement devices.