Mixed state Pauli channel parameter estimation

TL;DR

This paper compares quantum correlated and independent state protocols for estimating the strength of a single qubit Pauli channel, showing that quantum correlations can improve accuracy even with mixed states and separable states.

Contribution

It demonstrates that quantum correlated states can outperform independent states in parameter estimation for mixed states, extending beyond pure state scenarios.

Findings

Quantum correlated states improve estimation accuracy over independent states.

Benefits persist even with separable states and no quantum discord.

Relevance to nuclear magnetic resonance measurements.

Abstract

The accuracy of any physical scheme used to estimate the parameter describing the strength of a single qubit Pauli channel can be quantified using standard techniques from quantum estimation theory. It is known that the optimal estimation scheme, with m channel invocations, uses initial states for the systems which are pure and unentangled and provides an uncertainty of O[1/m^(1/2)]. This protocol is analogous to a classical repetition and averaging scheme. We consider estimation schemes where the initial states available are not pure and compare a protocol involving quantum correlated states to independent state protocols analogous to classical repetition schemes. We show, that unlike the pure state case, the quantum correlated state protocol can yield greater estimation accuracy than any independent state protocol. We show that these gains persist even when the system states are separable and, in some cases, when quantum discord is absent after channel invocation. We describe the relevance of these protocols to nuclear magnetic resonance measurements.