Photo-detection correlation degrees of a two-photon source.

It is shown that the canonical correlation method used with the intrinsic degrees of coherence (IDOCs) to describe coherence properties of partially polarized light is effective to identify relevant properties of the photo-detection correlations of a two-photon source described with its density operator. The results are compared with other global correlation measures.

Polarization coherence frustration.

From the joint analysis of polarization and coherence properties of light, a remarkable concept referred to as polarization coherence frustration is introduced and analyzed. It is shown that two kinds of partially polarized and partially coherent light, with different levels of complexity, can be distinguished and that they mathematically correspond to different equivalence classes. On the one hand, light has polarization coherence properties that are not frustrated in a spatial domain when there exists a configuration of local polarization devices at each location of the light field that allows the maximization of the modulus of the scalar degree of coherence between any couple of points in .

Compressed Raman classification method with upper-bounded error probability.

Classification of different species with Raman measurements is analyzed when a total of exactly $ N $N photons are detected with binary filtered Raman spectra instead of fixing the measuring time. The optimal classification method for this problem leads to classification error probabilities upper-bounded by the Bhattacharyya bound and that are invariant to the multiplication of the spectrum intensities by an unknown factor. Furthermore, it is shown that this approach can be implemented with a number of binary filters smaller than the number of species to discriminate.

Bhattacharyya bound for Raman spectrum classification with a couple of binary filters.

Bhattacharyya bounds of classification error probability between two species with Raman and binary compressed Raman measurements limited by Poisson photon noise are analyzed. They exhibit the relevant physical parameters and lead to a simple expression of a minimal number of photons necessary to upper bound the optimal classification error probability.

Precision of proportion estimation with binary compressed Raman spectrum.

The precision of proportion estimation with binary filtering of a Raman spectrum mixture is analyzed when the number of binary filters is equal to the number of present species and when the measurements are corrupted with Poisson photon noise. It is shown that the Cramer-Rao bound provides a useful methodology to analyze the performance of such an approach, in particular when the binary filters are orthogonal. It is demonstrated that a simple linear mean square error estimation method is efficient (i.