Entanglement-Free Parameter Estimation of Generalized Pauli Channels

TL;DR

This paper introduces a practical, entanglement-free protocol for estimating parameters of generalized Pauli channels using product states and measurements, with error mitigation techniques that preserve estimation accuracy.

Contribution

It presents a novel parameter estimation method that avoids entanglement, simplifies measurements, and incorporates error mitigation for generalized Pauli channels.

Findings

Method achieves mean square error scaling comparable to entanglement-based schemes.

Measurement errors due to Pauli noise can be effectively modeled and mitigated.

Protocol scales linearly with the dimension of the Hilbert space.

Abstract

We propose a parameter estimation protocol for generalized Pauli channels acting on $d$-dimensional Hilbert space. The salient features of the proposed method include product probe states and measurements, the number of measurement configurations linear in $d$, minimal post-processing, and the scaling of the mean square error comparable to that of the entanglement-based parameter estimation scheme for generalized Pauli channels. We also show that while measuring generalized Pauli operators the errors caused by the Pauli noise can be modeled as measurement errors. This makes it possible to utilize the measurement error mitigation framework to mitigate the errors caused by the generalized Pauli channels. We use this result to mitigate noise on the probe states and recover the scaling of the noiseless probes, except with a noise strength-dependent constant factor. This method of modeling Pauli channel as measurement noise can also be of independent interest in other NISQ tasks, e.g., state tomography problems, variational quantum algorithms, and other channel estimation problems where Pauli measurements have the central role.