  Oscillations of superconducting current between clockwise and
counterclockwise directions in a flux qubit do not conserve the angular
momentum of the qubit. To compensate for this effect the solid containing the
qubit must oscillate in unison with the current. This requires entanglement of
quantum states of the qubit with quantum states of a macroscopic body. The
question then arises whether slow decoherence of quantum oscillations of the
current is consistent with fast decoherence of quantum states of a macroscopic
solid. This problem is analyzed within an exactly solvable quantum model of a
qubit embedded in an absolutely rigid solid and for the elastic model that
conserves the total angular momentum. We show that while the quantum state of a
flux qubit is, in general, a mixture of a large number of rotational states,
slow decoherence is permitted if the system is macroscopically large. Practical
implications of entanglement of qubit states with mechanical rotations are
discussed.
