Publication: Assessing dimensions from evolution
Loading...
Official URL
Full text at PDC
Publication Date
2009
Authors
Wolf, Michael
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
The American Physical Society
Citations
Exportar
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.