Fig. 4
From: Measuring, processing, and generating partially coherent light with self-configuring optics
Processing incoherent mixtures of delocalized single photons with PCLA. a An incoherent mixture of delocalized single photons (described by coherency matrix \({\rho }_{{\rm{in}}}\)) is sent through a PCLA. The result of projective measurements is used to sequentially optimize the power at each output mode. The result is a modal decomposition into mutually incoherent modes, where the number of pure quantum states in the mixture corresponds to the number of output modes with non-zero average power. b Experimental proposal, where single photons emitted at random times (therefore mutually incoherent) are mixed through a random unitary transformation and subsequently analyzed by the PCLA. c 10-mode example (with a total of 7 pure states in the mixture): the output clicks resulting from the sequential power optimization are ordered and map to the eigenvalues of \({\rho }_{{\rm{in}}}\). Inset: Matrix product showing that \({U}_{{\rm{PCLA}}}\) learns eigenvectors of \({\rho }_{{\rm{in}}}\) (up to a diagonal matrix of phases)
