Quantum-optical input-output relations and entanglement distillation by anisotropic planar multilayers

By using the Green-function approach to the problem of quantization of the electromagnetic field, the propagation of quantized radiation through dispersive and absorptive anisotropic multilayer structures is studied. Input-output relations are derived. Based on these relations, an efficient method to perform procrustean distillation and concentration for quantum entanglement has been proposed. The Clauser-Horne-Shimony-Holt parameter for an entangled pure state, the quantum relative entropy and linear entropy for a mixed state have been calculated theoretically. It is shown that the efficiency of such a method is not only much higher for the distillation of non-maximally entangled pure states than those using partial polarizers, but it is also good for the concentration for the mixed states. Both the purity and the degree of entanglement of the mixed states can be improved simultaneously several times by using such a method. Another advantage of the scheme is that it can be widely adjusted by a proper choice of the structural parameters and the external field.