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arXiv:1109.1016

Can a polarization scrambler really depolarize light?

Guilherme P. Temporão, Jean Pierre von der Weid

Published Sep 5, 2011• 0 citations
arXivHTMLPDF

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.

DOI
10.48550/arxiv.1109.1016

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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.
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Quantum polarization is an important property that has been extensively used for quantum communication purposes. In this work, the mixture of an unpolarized two-mode state and a two-mode pure state is analysed. This mixture is controlled by a single parameter, namely the degree of purity. The quantum polarization of the two-mode mixed state is discussed using the quantum Stokes parameters and the quantum degree of polarization. A relation between the degree of purity and the quantum degree of polarization is established. The mixture is used to model coherent light amplified by an erbium-doped fibre amplifier, which focuses the loss of polarization due to the unpolarized light resulting from spontaneous emission. Finally, the use of such a mixed state in the quantum key distribution using multiphoton pulses is analysed.
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It takes some convincing to realize that light has a polarization degree of freedom, as our eyes are usually ignorant of light's polarization. Since overcoming this hurdle of intuition, polarization has become a fantastic resource that can be easily manipulated both physically and mathematically, opening the door to a wide variety of applications. We have only recently begun to appreciate how many more doors are opened by the quantum mechanical degrees of freedom inherent to optical polarization. One use of optical polarization is for polarimetry: measuring the changes in light's polarization after it interacts with a material is an excellent procedure for nondestructively probing the characteristics and composition of the intervening material. More sensitive measurements require brighter probe light; however, sufficiently intense light will begin to destroy the sample being probed. In this thesis, we seek to provide more sensitive polarimetry without resorting to bright beams of light. Tailoring the quantum properties of various states of light has been shown to increase their usefulness for other estimation protocols and we show how to extend this paradigm to quantum enhancements in polarimetry. We begin by finding the quantum states underlying classical polarization. Each particular set of classical polarization properties corresponds to a large variety of quantum states. Next, we establish quantum descriptions of classical polarization transformations corresponding to arbitrary Jones and Mueller matrices, including quantum mechanical insights into the distinction between processes that can and cannot be described by Jones matrices. We propose candidates for the most likely quantum states underlying classical decompositions into polarized and unpolarized fractions, carefully inspecting how these quantum states behave under polarization transformations. This language allows us to inspect quantum-enhanced sensing in the multiparameter context of polarimetry. We show the dramatic possibilities for quantum enhancements in any metrological scenario that is mathematically equivalent to a rotation, of which polarization rotations are a primary example; in contrast, we also show most attenuating and depolarizing polarization transformations to forbid such dramatic enhancements. Finally, we discuss polarization and its generalizations in the context of generating quantum entanglement via linear optics. These applications serve as mere examples of the usefulness promised by light’s quantum polarization degrees of freedom.
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We establish that a connection exists between wave-particle duality of photons and partial polarization of a light beam. We perform a two-path lowest-order (single photon) interference experiment and demonstrate both theoretically and experimentally that the degree of polarization of the light beam emerging from an output of the interferometer depends on path distinguishability. In our experiment, we are able to change the quantum state of the emerging photon from a pure state to a fully mixed state without any direct interaction with the photon. Although most lowest-order interference experiments can be explained by classical theory, our experiment has no genuine classical analog. Our results show that a case exists where the cause of partial polarization is beyond the scope of classical theory.