Quantum dynamics under simultaneous and continuous measurement of noncommutative observables

TL;DR

This paper generalizes the Arthurs-Kelly model for simultaneous, continuous measurement of noncommutative observables, deriving a Lindblad-form master equation and proposing a feedback control scheme for a two-level system.

Contribution

It extends the measurement model to noncommutative observables with non-c-number commutators and develops a feedback control scheme based on continuous measurements.

Findings

Master equation reduces to Lindblad form in the continuous limit

No cross term appears in the master equation for the two measurements

Proposes a feedback control scheme for state preparation of a two-level system

Abstract

We consider simultaneous and continuous measurement of two noncommutative observables of the system whose commutator is not necessarily a $c$-number. We revisit the Arthurs-Kelly model and generalize it to describe the simultaneous measurement of two observables of the system. Using this generalized model, we continuously measure the system by following the scheme proposed by Scott and Milburn [Scott and Milburn, Phys. Rev. A 63, 042101 (2001)]. We find that the unconditioned master equation reduces to the Lindblad form in the continuous limit. In addition, we find that the master equation does not contain a cross term of these two measurements. Finally, we propose a scheme to prepare the state of a two-level system in an external field by feedback control based on the simultaneous, continuous measurement of the two observables.