Quantum Estimation of the Stokes Vector Rotation for a General Polarimetric Transformation

TL;DR

This paper investigates the fundamental limits of quantum polarimetric measurements of polarization rotation, analyzing different quantum states and noise effects, and proposes an experimental setup for NOON state-based quantum polarimetry.

Contribution

It introduces a quantum theoretical framework for polarimetry, evaluates the precision limits with various quantum states, and designs an experimental approach for NOON state measurements.

Findings

Quantum Fisher information varies with noise channels and state choice.

NOON states show high potential for precise polarization rotation estimation.

Analysis of noise effects guides optimal quantum probe state selection.

Abstract

Classical polarimetry is a well-established discipline with diverse applications across different branches of science. The burgeoning interest in leveraging quantum resources to achieve highly sensitive measurements has spurred researchers to elucidate the behavior of polarized light within a quantum mechanical framework, thereby fostering the development of a quantum theory of polarimetry. In this work, drawing inspiration from polarimetric investigations in biological tissues, we investigate the precision limits of polarization rotation angle estimation about a known rotation axis, in a quantum polarimetric process, comprising three distinct quantum channels. The rotation angle to be estimated is induced by the retarder channel on the Stokes vector of the probe state. The diattenuator and depolarizer channels, acting on the probe state, can be thought of as effective noise processes. We explore the precision constraints inherent in quantum polarimetry by evaluating the quantum Fisher information for probe states of significance in quantum metrology, namely NOON, Kings of Quantumness, and Coherent states. The effects of the noise channels as well as their ordering is analyzed on the estimation error of the rotation angle to characterize practical and optimal quantum probe states for quantum polarimetry. Furthermore, we propose an experimental framework tailored for NOON state quantum polarimetry, aiming to bridge theoretical insights with empirical validation.