Universal Optimal Estimation of the Polarization of Light with Arbitrary Photon Statistics

TL;DR

This paper introduces a universal, optimal measurement method for estimating the polarization of light with any photon statistics, achieving the collective bound and outperforming adaptive measurements, with implications for quantum communication security.

Contribution

It develops a continuous ML-POVM approach for pure polarization states, attaining the collective bound and demonstrating advantages over adaptive measurements.

Findings

Achieves the collective bound of polarization estimation with mean fidelity.

Estimation performance is similar for Fock and Poisson states, worse for thermal light.

Thermal light offers potential security benefits in quantum communication.

Abstract

A universal and optimal method for the polarimetry of light with arbitrary photon statistics is presented. The method is based on the continuous maximum-likelihood positive operator-valued measure (ML-POVM) for pure polarization states over the surface of the Bloch sphere. The success probability and the mean fidelity are used as the figures of merit to show its performance. The POVM is found to attain the collective bound of polarization estimation with respect to the mean fidelity. As demonstrations, explicit results for the N photon Fock state, the phase-randomized coherent state (Poisson distribution), and the thermal light are obtained. It is found that the estimation performances for the Fock state and the Poisson distribution are almost identical, while that for the thermal light is much worse. This suggests that thermal light leaks less information to an eavesdropper and hence could potentially provide more security in polarization-encoded quantum communication protocols than a single-mode laser beam as customarily considered. Finally, comparisons against an optimal adaptive measurement with classical communications are made to show the better and more stable performance of the continuous ML-POVM.