  Multiple and single measurements of quantum states of mesoscopic
superconducting loops are carried out in order to investigate a possibility of
macroscopic quantum superposition and of creation of a superconductor quantum
register. Asymmetric superconducting rings are used in order to be convinced
that single measurement gives result corresponding to one of permitted states
and multiple one gives an average value on these states. We have measured
magnetic dependencies of resistance, rectified voltage and critical current on
these rings. The observed quantum oscillations of the resistance and the
rectified voltage, corresponding to multiple measurement of quantum states,
give evidence of two permitted states at the magnetic flux inside the ring
divisible by half of the flux quantum. But the observed quantum oscillations of
the critical current, corresponding to single measurement, not only does not
confirm these two quantum states, but are in a direct contradiction with the
observed oscillations of the resistance. It is assumed that the observed
contradiction between the results of measurements made on the same ring can
testify to violation of the principle of realism on the mesoscopic level that
is a necessary condition for an opportunity of creation of a quantum computer.
