We consider realistic measurement systems, where measurements are accompanied by decoherence processes. The aim of this work is the construction of methods and algorithms for precise quantum measurements with fidelity close to the fundamental limit. In the present work the notions of ideal and non-ideal quantum measurements are strictly formalized. It is shown that non-ideal quantum measurements could be represented as a mixture of ideal measurements. Based on root approach the quantum state reconstruction method is developed. Informational accuracy theory of non-ideal quantum measurements is proposed. The monitoring of the amount of information about the quantum state parameters is examined, including the analysis of the information degradation under the noise influence. The study of achievable fidelity in non-ideal quantum measurements is performed. The results of simulation of fidelity characteristics of a wide class of quantum protocols based on polyhedrons geometry with high level of symmetry are presented. The impact of different decoherence mechanisms, including qubit amplitude and phase relaxation, bit-flip and phase-flip, is considered.
Three different levels of noisy quantum schemes modeling are considered: vectors, density matrices and Choi- Jamiolkowski related states. The implementations for personal computers and supercomputers are described, and the corresponding results are shown. For the level of density matrices, we present the technique of the fixed rank approximation and show some analytical estimates of the fidelity level.
The influence of amplitude and phase relaxation on evolution of quantum states within the formalism of quantum operations is considered. The model of polarizing qubits where noises are determined by the existence of spectral degree of freedom that shows up during the light propagation inside anisotropic mediums with dispersion is studied. Approximate analytic model for calculation of phase plate impact on polarizing state with dispersion influence taken into consideration is suggested.