Correlators exceeding one in continuous measurements of superconducting qubits

TL;DR

This paper investigates how phase backaction affects correlators in continuous superconducting qubit measurements, revealing conditions where correlators exceed one and validating a generalized calculation method with experimental data.

Contribution

It introduces a generalized collapse recipe for calculating multi-time correlators under phase backaction and validates it with experiments on transmon qubits.

Findings

Correlators can exceed 1 due to phase backaction.

The generalized recipe accurately predicts experimental results.

Phase backaction can be used for calibration of measurement setups.

Abstract

We consider the effect of phase backaction on the correlator $\langle I(t)\, I(t+\tau )\rangle$ for the output signal $I(t)$ from continuous measurement of a qubit. We demonstrate that the interplay between informational and phase backactions in the presence of Rabi oscillations can lead to the correlator becoming larger than 1, even though $|\langle I\rangle|\leq 1$. The correlators can be calculated using the generalized "collapse recipe" which we validate using the quantum Bayesian formalism. The recipe can be further generalized to the case of multi-time correlators and arbitrary number of detectors, measuring non-commuting qubit observables. The theory agrees well with experimental results for continuous measurement of a transmon qubit. The experimental correlator exceeds the bound of 1 for a sufficiently large angle between the amplified and informational quadratures, causing the phase backaction. The demonstrated effect can be used to calibrate the quadrature misalignment.