%0 Journal Article
%A Wolf, Michael M.
%A Pérez García, David
%T Assessing Quantum Dimensionality from Observable Dynamics
%D 2009
%@ 0031-9007
%U https://hdl.handle.net/20.500.14352/42494
%X 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.
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