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

Necessity of macroscopic operation for the creation of superpositions of macroscopically distinct states