Can a polarization scrambler really depolarize light?

TL;DR

This paper explores the quantum nature of polarized light, questioning whether polarization scramblers truly depolarize light by analyzing quantum states and proposing a new measure of polarization independent of classical ignorance.

Contribution

It introduces a quantum-based perspective on polarization, clarifies the distinction between classical and quantum ignorance, and proposes a novel definition of single-photon polarization degree.

Findings

Quantum ensembles with the same density operator are indistinguishable in measurement.

Classical and quantum ignorance have different implications for polarization.

A new polarization measure for single photons is proposed.

Abstract

According to quantum theory, two ensembles of quantum systems that are described by the same density operator are indistinguishable. For example, unpolarized light can be obtained either by an incoherent mixture of two orthogonal pure states or by tracing out a photon from a maximally polarization-entangled photon pair. In both cases, one is unable to guess with probability greater than 50% the outcome of any polarization measurement, but the reasons are conceptually different: whereas the first case is a matter of classical ignorance (the photons were prepared in a definite but unknown way), the second one is of the quantum ignorance kind - if one cannot access the other degrees of freedom of the quantum state, there is no information that could be used to predict a measurement result. We use these concepts to discuss the quantum-physical interpretation of partially polarized light from the point of view of quantum communication and whether a polarization scrambler can really depolarize light. A novel definition of the degree of polarization of a single photon which does not depend on classical ignorance is also provided.