  The quantum measurement procedure based on the Lorentz transformation
formalism and weak perturbation of the system is considered. In the simple case
of a single-qubit it turns out that one can perform 4-dimension pseudo-rotation
along with ordinary 3-dimension rotations on the Bloch sphere. These
pseudo-rotations are similar to the Lorentz transformation in special
relativity theory. The extension of the Lorentz transformation for many-qubit
systems is also considered. The quantum measurement protocols based on the
Lorentz transformation are proposed. It has been shown that these protocols
cease to form the decomposition of unity and could be superefficient providing
the fidelity higher than any POVM-measurement protocol. However, one can
perform the complement of the Lorentz protocol to POVM-protocol by an
additional measurement operator. If the initial mixed state is close to the
pure one this operator corresponds to weak perturbation of the state while the
original Lorentz protocol sets the strong perturbations. As the result, the
feedback provides an effective control of a quantum system introducing weak
perturbations to the quantum state. The results of this research are essential
for the development of methods for the control of quantum information
technologies.
