Optimization of a quantum tomography protocol for polarization qubits

An operational method has been proposed for estimating the efficiency of quantum cryptography protocols for quantum states with discrete variables. The method is based on the estimate of the quality of the protocol by means of a universal asymptotic distribution of the characteristic of the accuracy of the reconstruction of the quantum state, which is called fidelity. For a specially designed measurement matrix, the condition number, which is minimal for the optimal protocol, is introduced. The method has been tested in a numerical simulation and real experiments with polarization qubits. It has been shown that the optimal choice of a polarization transformer makes it possible to strongly improve the quality of the reconstruction of states.