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Although polarization is historically defined as a local property, one can also regard it as a nonlocal feature of correlated fields for which the correlation between the field components at any locations and fluctuating along any orthogonal directions does not factorize. For such fields, the local states of polarization are randomly distributed on the surface of the Poincare sphere while their average lie somewhere inside of it, but not necessarily at its center. An average degree of polarization can then be defined as distance between this point and the origin of the sphere. Of course, because of nonlocality, there will be different types of randomly polarized fields which, on average, will have the same average degree of polarization. Because these fields could have different physical origins or can be the result of different field transformations, finding a proper way to discriminate among them is an important issue. We introduce the scalar average similarity of an ensemble of randomly polarized states. This global measure is based on the complex degree of mutual polarization between any pair of vector fields in the ensemble. We show that, in the case of fully-correlated and globally unpolarized fields, the variation of this parameter is bounded and its value can effectively discriminate between different configurations of pure states.
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