Optimal estimation of entanglement in optical qubit systems

TL;DR

This paper develops and experimentally implements optimal quantum estimators for precisely measuring entanglement in two-qubit optical systems, surpassing traditional tomography methods and enabling better noise modeling.

Contribution

It introduces a method using quantum estimation theory to achieve the ultimate precision in entanglement measurement, validated through experiments on various two-qubit states.

Findings

Optimal estimators reach the quantum limit of measurement precision.

Tomography provides less precise entanglement estimates than optimal estimators.

The approach allows for better assessment of decoherence noise models.

Abstract

We address the experimental determination of entanglement for systems made of a pair of polarization qubits. We exploit quantum estimation theory to derive optimal estimators, which are then implemented to achieve ultimate bound to precision. In particular, we present a set of experiments aimed at measuring the amount of entanglement for states belonging to different families of pure and mixed two-qubit two-photon states. Our scheme is based on visibility measurements of quantum correlations and achieves the ultimate precision allowed by quantum mechanics in the limit of Poissonian distribution of coincidence counts. Although optimal estimation of entanglement does not require the full tomography of the states we have also performed state reconstruction using two different sets of tomographic projectors and explicitly shown that they provide a less precise determination of entanglement. The use of optimal estimators also allows us to compare and statistically assess the different noise models used to describe decoherence effects occuring in the generation of entanglement.