Characterizing Quantum Properties of a Measurement Apparatus: Insights from the Retrodictive Approach

TL;DR

This paper uses the retrodictive approach to quantum physics to characterize measurement apparatuses, revealing their quantum properties and introducing estimators relevant for quantum information protocols.

Contribution

It introduces a retrodictive framework to fully characterize quantum measurement devices and defines new estimators for their properties, advancing understanding of quantum measurement behavior.

Findings

Retrodicted states effectively characterize detector quantum properties.

Non-classicality and non-Gaussianity of measurements are analyzed.

New estimators like projectivity and fidelity are introduced for measurement assessment.

Abstract

Using the retrodictive approach of quantum physics, we show that the state retrodicted from the response of a measurement apparatus is a convenient tool to fully characterize its quantum properties. We translate in terms of this state some interesting aspects of the quantum behavior of a detector, such as the non-classicality or the non-gaussian character of its measurements. We also introduce estimators - the projectivity, the ideality, the fidelity or the detectivity of measurements perfomed by the apparatus - which directly follow from the retrodictive approach. Beyond their fundamental significance for describing general quantum measurements, these properties are crucial in several protocols, in particular in the conditional preparation of non-classical states of light or in measurement-driven quantum information processing.