Quantum parameter estimation on coherently superposed noisy channels

TL;DR

This paper investigates how superposing noisy quantum channels can enhance phase estimation, showing that a control qubit can effectively estimate phases even under strong noise, outperforming traditional methods.

Contribution

It introduces a novel superposed channel framework for quantum parameter estimation, demonstrating robustness against noise and the ability to measure the control qubit independently.

Findings

Control qubit can estimate phase without direct interaction with the unitary.

Superposed channel remains effective under strong noise, including depolarizing noise.

Outperforms conventional and switched channels in noisy environments.

Abstract

A generic qubit unitary operator affected by quantum noise is duplicated and inserted in a coherently superposed channel, superposing two paths offered to a probe qubit across the noisy unitary, and driven by a control qubit. A characterization is performed of the transformation realized by the superposed channel on the joint state of the probe-control qubit pair. The superposed channel is then specifically analyzed for the fundamental metrological task of phase estimation on the noisy unitary, with the performance assessed by the Fisher information, classical or quantum. A comparison is made with conventional estimation techniques and also with a quantum switched channel with indefinite causal order recently investigated for a similar task of phase estimation. In the analysis here, a first important observation is that the control qubit of the superposed channel, although it never directly interacts with the unitary being estimated, can nevertheless be measured alone for effective estimation, while discarding the probe qubit that interacts with the unitary. This property is also present with the switched channel but is inaccessible with conventional techniques. The optimal measurement of the control qubit here is characterized in general conditions. A second important observation is that the noise plays an essential role in coupling the control qubit to the unitary, and that the control qubit remains operative for phase estimation at very strong noise, even with a fully depolarizing noise, whereas conventional estimation and the switched channel become inoperative in these conditions. The results extend the analysis of the capabilities of coherently controlled channels which represent novel devices exploitable for quantum signal and information processing.