Correlators in simultaneous measurement of non-commuting qubit observables

TL;DR

This paper derives analytical expressions for the correlations in simultaneous measurements of non-commuting qubit observables, demonstrating their application in parameter estimation and calibration correction.

Contribution

It introduces a quantum Bayesian approach to analytically describe correlators in simultaneous qubit measurements, validated by experimental data.

Findings

Analytical correlator expressions match experimental results

Correlators can be used for parameter estimation

Residual Hamiltonian inferred from correlator analysis

Abstract

We consider the simultaneous and continuous measurement of qubit observables $\sigma_z$ and $\sigma_z\cos\varphi + \sigma_x\sin\varphi$, focusing on the temporal correlations of the two output signals. Using quantum Bayesian theory, we derive analytical expressions for the correlators, which we find to be in very good agreement with experimentally measured output signals. We further discuss how the correlators can be applied to parameter estimation, and use them to infer a small residual qubit Hamiltonian arising from calibration inaccuracy in the experimental data.