  We consider the creation of superpositions of macroscopically distinct states
by a completely-positive (CP) operation on a subsystem. We conclude that the
subsystem on which the CP operation acts must be macroscopically large if the
success probability of the CP operation does not vanish in the thermodynamic
limit. In order to obtain this conclusion, we show two inequalities each of
which represents a trade-off relation among the magnitude of an indicator for
superpositions of macroscopically distinct states, the success probability of a
CP operation, and the volume of the subsystem on which the CP operation acts.
