Measurement of polarization quantum states under chromatic aberration conditions

The wave plate is a basic device for transforming and measuring the polarization states of light. It is known that the transformation of light by means of two wave plates makes it possible to measure the state of polarization in an arbitrary basis. The finite spectral width of the light, however, leads to a chromatic aberration of the polarization quantum transformation caused by the parasitic dispersion of the birefringence of the plate material. This causes systematic errors in the tomography of quantum polarization states and significantly reduces its accuracy. This study is a development of our work1, in which an adequate model for quantum measurements of polarization qubits under chromatic aberration was first formulated. This work includes a generalization of the results obtained earlier for the cases of two-qubit states. Along with examples of random states those uniformly distributed over the Haar measure are considered. Using a matrix of complete information, it is quantitatively traced how the presence of chromatic aberrations under conditions of a finite spectral width of light leads to the loss of information in quantum measurements. It is shown that the use of the developed model of fuzzy measurements instead of the model of standard projection measurements makes it possible to suppress systematic errors of quantum tomography even when using high-order wave plates. It turns out that the fuzzy measurement model can give a significant increase in the reconstruction accuracy compared to the standard measurement model.