We comprehensively review the quantum theory of the polarization properties of light. In classical optics, these traits are characterized by the Stokes parameters, which can be geometrically interpreted using the Poincare sphere. Remarkably, these Stokes parameters can also be applied to the quantum world, but then important differences emerge: now, because fluctuations in the number of photons are unavoidable, one is forced to work in the three-dimensional Poincare space that can be regarded as a set of nested spheres. Additionally, higher-order moments of the Stokes variables might play a substantial role for quantum states, which is not the case for most classical Gaussian states. This brings about important differences between these two worlds that we review in detail. In particular, the classical degree of polarization produces unsatisfactory results in the quantum domain. We compare alternative quantum degrees and put forth that they order various states differently. Finally, intrinsically nonclassical states are explored and their potential applications in quantum technologies are discussed.

中文翻译：

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光偏振中的量子概念

我们全面回顾了光偏振特性的量子理论。在经典光学中，这些特性由斯托克斯参数表征，可以使用庞加莱球进行几何解释。值得注意的是，这些斯托克斯参数也可以应用于量子世界，但随后出现了重要的差异：现在，由于光子数量的波动是不可避免的，人们被迫在可以被视为一个三维庞加莱空间的三维庞加莱空间中工作。一组嵌套的球体。此外，斯托克斯变量的高阶矩可能对量子态起重要作用，而大多数经典高斯态并非如此。这带来了我们详细审查的这两个世界之间的重要差异。特别是，经典的偏振度在量子域中产生了不令人满意的结果。我们比较了不同的量子度，并提出它们对各种状态的排序不同。最后，探讨了本质上的非经典状态，并讨论了它们在量子技术中的潜在应用。