General quantum constraints on detector noise in continuous linear measurements

TL;DR

This paper derives fundamental quantum constraints on detector noise in continuous linear measurements, revealing new equalities at the quantum limit and illustrating them with cavity QED setups involving qubits and mechanical oscillators.

Contribution

It establishes new quantum equalities constraining detector noise at the quantum limit in continuous measurements, extending the understanding of measurement backaction and imprecision.

Findings

Quantum noise obeys a Heisenberg-like uncertainty relation.

At the quantum limit, new equalities relate noise components and correlations.

Illustrations include dispersive qubit readout and mechanical sideband measurements.

Abstract

In quantum sensing and metrology, an important class of measurement is the continuous linear measurement, in which the detector is coupled to the system of interest linearly and continuously in time. One key aspect involved is the quantum noise of the detector, arising from quantum fluctuations in the detector input and output. It determines how fast we acquire information about the system and also influences the system evolution in terms of measurement backaction. We therefore often categorize it as the so-called imprecision noise and quantum backaction noise. There is a general Heisenberg-like uncertainty relation that constrains the magnitude of and the correlation between these two types of quantum noise. The main result of this paper is to show that, when the detector becomes ideal, i.e., at the quantum limit with minimum uncertainty, not only does the uncertainty relation takes the equal sign as expected, but also there are two new equalities. This general result is illustrated by using the typical cavity QED setup with the system being either a qubit or a mechanical oscillator. Particularly, the dispersive readout of a qubit state, and the measurement of mechanical motional sideband asymmetry are considered.