Experimentally determining the incompatibility of two qubit measurements

TL;DR

This paper presents an experimental method to quantify the incompatibility of two qubit measurements using a state discrimination task, demonstrating its practical feasibility with an optical setup.

Contribution

It introduces an experimental procedure to assess measurement incompatibility via success statistics, aligning upper bounds with true robustness for certain qubit measurements.

Findings

Successfully implemented the method in an optical setup.

Achieved direct access to incompatibility through refined control of measurement parameters.

Validated the practical applicability of a theoretical incompatibility detection method.

Abstract

We describe and realize an experimental procedure for assessing the incompatibility of two qubit measurements. The experiment consists in a state discrimination task where either measurement is used according to some partial intermediate information. The success statistics of the task provides an upper bound for the amount of incompatibility of the two measurements, as it is quantified by means of their incompatibility robustness. For a broad class of unbiased and possibly noisy qubit measurements, one can make this upper bound coincide with the true value of the robustness by suitably tuning the preparation of the experiment. We demonstrate this fact in an optical setup, where the qubit states are encoded into the photons' polarization degrees of freedom, and incompatibility is directly accessed by virtue of a refined control on the amplitude, phase and purity of the final projection stage of the measurements. Our work thus establishes the practical feasibility of a recently proposed method for the detection of quantum incompatibility.