Optimal parameter estimation of Pauli channels

TL;DR

This paper determines the optimal measurement setup for estimating parameters of qubit and generalized Pauli channels, maximizing Fisher information, and proposes an efficient method for estimating channel directions with simulations confirming its effectiveness.

Contribution

It identifies the optimal measurement configuration for Pauli channels and introduces a computationally efficient estimation method for channel directions.

Findings

Optimal configuration uses three von Neumann measurements and pure input states.

The proposed estimation method has variance of order 1/N.

Simulations confirm the method's efficiency and accuracy.

Abstract

The optimal measurement configuration, i.e., the optimal input quantum state and measurement in the form of a POVM with two elements, is investigated in this paper for qubit and generalized Pauli channels. The channel directions are defined as the contracting directions of the channel with an arbitrary fixed basis of Pauli- matrices. In the qubit Pauli channel case with known channel directions it is shown that the optimal configuration that maximizes the Fisher information of the estimated parameters consists of three von Neumann measurements together with pure input states directed to the appropriate channel directions. Extensions of these results for generalized Pauli channels are also given. Furthermore, a computationally efficient estimation method is proposed for estimating the channel directions in the qubit Pauli channel case. The efficiency of this method is illustrated by simulations: it is shown that its variance is of order 1/N, where N is the number of used measurements.