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We introduce a protocol for a quantum switch in the gravitational field of aspherical mass and determine the time interval required for its realization inthe gravity of Earth. One of the agents that perform operations with indefiniteorder is a quantum system in a path superposition state. Entanglement betweenits proper time and position is explored as a resource for the implementationof the quantum switch. The realization of the proposed protocol would probe thephysical regime described by quantum mechanics on curved spacetimes, which hasnot yet been explored experimentally.

Quantum switch in the gravity of Earth