Quantum speed limit and stability of coherent states in quantum gravity

Abstract

Utilizing the program of expectation values in coherent states and its recently developed algorithmic tools, this letter investigates the dynamical properties of cosmological coherent states for Loop Quantum Gravity. To this end, the Quantum Speed Limit is adapted to Quantum Gravity, yielding necessary consistency checks for any proposal of stable families of states. To showcase the strength of the developed tools, they are applied to a prominent model: the Euclidean part of the quantum scalar constraint. We report the variance of this constraint evaluated on a family of coherent states showing that, for short times, this family passes the Quantum Speed Limit test, allowing the transition from one coherent state to another one.

Quantum lower and upper speed limits using reference evolutions

“…The idea of treating the distance between the time-evolved state and a reference state has been discussed in several works [16][17][18][19]. For example, when the system Hamiltonian is changed slowly in time, the state is approximately given by the adiabatic state.…”