Abstract
Quantum non-Gaussian (QNG) mechanical states from inherently nonlinear quantum processes are already required in quantum sensing, become essential in quantum thermodynamics, and also open directions in quantum computing with continuous variables. The discrete building blocks of such states are the energy eigenstates - Fock states. Despite the progress in their experimental preparation, the remaining energy uncertainty can still invisibly cause loss of the critical quantum non-Gaussian aspects of the phonon distribution relevant for the applications.
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