As optical systems are one of the candidates for implementation of a scalable quantum computer, it is important to develop an adequate method of description of both quantum states of light and operations performed by optical elements. Using the concept of chi-matrix representation of quantum operations and Choi-Jamiolkowski isomorphism we expand Jones calculus to allow description of evolution of mixed polarization states in linear optical systems. The developed method is then used to give a full description of polarization echo effect, which was described in 1 based on an analogy between the effects of polarization optics and spin dynamics. Theoretical predictions are confirmed by reconstructing operations performed by a series of quartz waveplates using quantum process tomography protocols.
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