Depolarizing channel parameter estimation using noisy initial states

TL;DR

This paper investigates how to improve the estimation of depolarizing channel parameters in qubits using noisy initial states, demonstrating that correlated states can outperform product states under certain conditions.

Contribution

It introduces protocols comparing product and correlated states for parameter estimation, revealing advantages of correlated states with mixed initial states.

Findings

Correlated states can provide higher estimation accuracy than product states.

Using more than two qubits and channel invocations can be beneficial.

Correlated states outperform pure initial states in some scenarios.

Abstract

We consider estimating the parameter associated with the qubit depolarizing channel when the available initial states that might be employed are mixed. We use quantum Fisher information as a measure of the accuracy of estimation to compare protocols which use collections of qubits in product states to one in which the qubits are in a correlated state. We show that, for certain parameter values and initial states, the correlated state protocol can yield a greater accuracy per channel invocation than the product state protocols. We show that, for some parameters and initial states, using more than two qubits and channel invocations is advantageous. These results stand in contrast to the known optimal case that uses pure initial states and a single channel invocation on a pair of entangled qubits.