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

TL;DR

This paper demonstrates that creating superpositions of macroscopically distinct states requires operations on a macroscopically large subsystem, especially when success probabilities remain finite in large systems.

Contribution

It establishes a fundamental trade-off relation showing the necessity of macroscopic operations for generating such superpositions.

Findings

Superpositions require large subsystems for non-vanishing success probability.

Two inequalities relate superposition indicators, success probability, and subsystem volume.

Macroscopic operations are essential for creating macroscopically distinct superpositions.

Abstract

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.