Multi-time correlators in continuous measurement of qubit observables

TL;DR

This paper derives a factorization method for multi-time correlators in continuous qubit measurement, validated by experiments, simplifying analysis of complex quantum measurement signals.

Contribution

It introduces a novel factorization approach for multi-time correlators in continuous qubit measurement under unital evolution, supported by experimental validation.

Findings

Multi-time correlators can be factorized into two-time correlators for even N.

For odd N, correlators factorize with an additional single-time average.

Experimental results confirm theoretical predictions for non-commuting observables.

Abstract

We consider multi-time correlators for output signals from linear detectors, continuously measuring several qubit observables at the same time. Using the quantum Bayesian formalism, we show that for unital (symmetric) evolution in the absence of phase backaction, an $N$-time correlator can be expressed as a product of two-time correlators when $N$ is even. For odd $N$, there is a similar factorization, which also includes a single-time average. Theoretical predictions agree well with experimental results for two detectors, which simultaneously measure non-commuting qubit observables.