  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.
