Single Shot Quantum State Estimation via a Continuous Measurement in the Strong Backaction Regime

TL;DR

This paper introduces a maximum likelihood quantum state estimator based on continuous measurement records, accounting for measurement backaction, and demonstrates its effectiveness in single-qubit tomography with dynamical control.

Contribution

It develops a novel estimator that incorporates measurement backaction in continuous quantum measurement, improving state estimation accuracy over previous methods.

Findings

Estimator achieves near-optimal fidelity in single-qubit tomography.

Inclusion of backaction significantly improves estimation accuracy.

Method outperforms estimators ignoring backaction.

Abstract

We study quantum tomography based on a stochastic continuous-time measurement record obtained from a probe field collectively interacting with an ensemble of identically prepared systems. In comparison to previous studies, we consider here the case in which the measurement-induced backaction has a nonnegligible effect on the dynamical evolution of the ensemble. We formulate a maximum likelihood estimate for the initial quantum state given only a single instance of the continuous diffusive measurement record. We apply our estimator to the simplest problem -- state tomography of a single pure qubit, which, during the course of the measurement, is also subjected to dynamical control. We identify a regime where the many-body system is well approximated at all times by a separable pure spin coherent state, whose Bloch vector undergoes a conditional stochastic evolution. We simulate the results of our estimator and show that we can achieve close to the upper bound of fidelity set by the optimal POVM. This estimate is compared to, and significantly outperforms, an equivalent estimator that ignores measurement backaction.