Generalized phase estimation in noisy quantum gates

TL;DR

This paper investigates the ultimate precision limits in quantum metrology when estimating parameters encoded by noisy quantum gates, focusing on how noise affects the Quantum Fisher Information over multiple gate applications.

Contribution

It introduces a framework for analyzing the robustness of quantum metrology under noise, extending beyond unitary gates to include dephasing and tilting noise models.

Findings

QFI growth is non-monotonic with the number of gate applications.

Maximum QFI occurs at an optimal number of steps.

Noise introduces a peak in QFI, unlike the quadratic growth in noiseless cases.

Abstract

We examine metrological scenarios where the parameter of interest is encoded onto a quantum state through the action of a noisy quantum gate and investigate the ultimate bound to precision by analyzing the behaviour of the Quantum Fisher Information (QFI). We focus on qubit gates and consider the possibility of employing successive applications of the gate. We go beyond the trivial case of unitary gates and characterize the robustness of the metrological procedure introducing noise in the performed quantum operation, looking at how this affects the QFI at different steps (gate applications). We model the dephasing and tilting noise affecting qubit rotations as classical fluctuations governed by a Von Mises-Fisher distribution. Compared to the noiseless case, in which the QFI grows quadratically with the number of steps, we observe a non monotonic behavior, and the appearance of a maximum in the QFI, which defines the ideal number of steps that should be performed in order to precisely characterize the action of the gate.