title: Assessing quantum dimensionality from observable dynamics.
abstract: Using 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.
authors.affiliation: Niels Bohr Institute, 2100 Copenhagen, Denmark, Universitad Complutense de Madrid, 28040 Madrid, Spain.
authors.forename: Michael M
authors.initials: MM
authors.lastname: Wolf
authors.forename: David
authors.initials: D
authors.lastname: Perez-Garcia