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Dynamics-based certification of quantumness is an approach to witnessing thenonclassical character of some continuous-variable states, under the assumptionthat their dynamics is known. Contrary to other tests of nonclassicality forsingle systems, it does not require sequential measurements. This family ofprotocols was introduced for harmonic dynamics. In this work we discussdynamics-based certification for one degree of freedom evolving under a generictime-independent Hamiltonian. We characterize the conditions under which such acertification is possible. Several examples are explicitly studied, some thatare approximately harmonic in the limits of low energy (Kerr nonlinearities,the pendulum, and the Morse potential) and one that is not (the particle in aninfinite well).

Dynamics-based quantumness certification of continuous variables using time-independent Hamiltonians with one degree of freedom