Wolf, Michael M.Pérez García, David2023-06-202023-06-202009-05-150031-900710.1103/PhysRevLett.102.190504https://hdl.handle.net/20.500.14352/42494Using tools from classical signal processing, we show how to determine the dimensionality of a quantum system as well as the effective size of the environment's memory from observable dynamics in a model-independent way. We discuss the dependence on the number of conserved quantities, the relation to ergodicity and prove a converse showing that a Hilbert space of dimension D+2 is sufficient to describe every bounded sequence of measurements originating from any D-dimensional linear equations of motion. This is in sharp contrast to classical stochastic processes which are subject to more severe restrictions: a simple spectral analysis shows that the gap between the required dimensionality of a quantum and a classical description of an observed evolution can be arbitrary large.engjournal articlehttp://link.aps.org/doi/10.1103/PhysRevLett.102.190504http://www.aps.org/open access530.1Física matemática