Noisy initial-state qubit-channel metrology with additional undesirable noisy evolution

TL;DR

This paper compares single-qubit and multi-qubit protocols for estimating parameters in noisy unital qubit channels, analyzing their performance via quantum Fisher information and effects of additional noise.

Contribution

It extends previous work by including additional noisy evolution in the multi-qubit protocol and provides criteria for when multi-qubit strategies outperform single-qubit ones.

Findings

The $n$-qubit protocol can be superior or inferior depending on the noise type.

Simple algebraic expressions determine the protocol's effectiveness.

A technique is proposed to mitigate certain noise effects.

Abstract

We consider protocols for estimating the parameter in a single-parameter unital qubit channel, assuming that the available initial states are highly mixed with very low purity. We compare two protocols, each invoking the channel once, via their quantum Fisher informations. One uses $n$ qubits prepared in a particular correlated input state and subsequently queries the channel on one qubit. The other uses a single qubit. We extend the results of Collins [1] by allowing for additional noisy evolution on the spectator qubits in the $n$-qubit protocol. We provide simple algebraic expressions that will determine when the $n$-qubit protocol is superior. We provide a technique that can alleviate certain types of noise. We show that for certain types of noisy evolution the $n$-qubit protocol will be inferior but for others it will be superior.