Fidelity estimation between two finite ensembles of unknown pure equatorial qubit states

TL;DR

This paper investigates optimal methods for estimating the fidelity between two finite ensembles of unknown pure equatorial qubit states, proposing a two-stage strategy involving a unitary transformation and state estimation.

Contribution

It introduces a novel two-stage strategy for fidelity estimation between ensembles of unknown pure qubit states on the Bloch sphere's equator.

Findings

The optimal strategy involves a specific unitary transformation.

State estimation of transformed states improves fidelity accuracy.

The approach outperforms existing methods in fidelity estimation.

Abstract

Suppose, we are given two finite ensembles of pure qubit states, so that the qubits in each ensemble are prepared in identical (but unknown for us) states lying on the equator of the Bloch sphere. What is the best strategy to estimate fidelity between these two finite ensembles of qubit states? We discuss three possible strategies for the fidelity estimation. We show that the best strategy includes two stages: a specific unitary transformation on two ensembles and state estimation of the output states of this transformation.