Central-moment description of polarization for quantum states of light

TL;DR

This paper introduces a moment expansion approach for analyzing quantum light polarization, enabling polarization tomography without full state reconstruction and revealing the significance of higher-order moments in certain quantum states.

Contribution

It develops a systematic method linking polarization moments to Stokes measurements, providing a new way to characterize quantum polarization states.

Findings

Experimental polarization characterization of two-photon states

Identification of states dominated by higher-order polarization moments

Method enables polarization tomography without full state tomography

Abstract

We present a moment expansion method for the systematic characterization of the polarization properties of quantum states of light. Specifically, we link the method to the measurements of the Stokes operator in different directions on the Poincar\'{e} sphere, and provide a method of polarization tomography without resorting to full state tomography. We apply these ideas to the experimental first- and second-order polarization characterization of some two-photon quantum states. In addition, we show that there are classes of states whose polarization characteristics are dominated not by their first-order moments (i.e., the Stokes vector) but by higher-order polarization moments.