Wolf, MichaelPérez García, David2023-06-202023-06-2020091079-711410.1103/PhysRevLett.102.190504https://hdl.handle.net/20.500.14352/49544Using 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://arxiv.org/abs/0901.2542open access51-73530.145Teoría cuánticaFísica matemáticaSistemas dinámicosQuantum PhysicsMathematical PhysicsDynamical SystemsFísica matemáticaTeoría de los quanta2210.23 Teoría Cuántica