Assessing Quantum Dimensionality from Observable Dynamics



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Wolf, Michael M. and Pérez García, David (2009) Assessing Quantum Dimensionality from Observable Dynamics. Physical Review Letters, 102 . pp. 190504-1. ISSN 0031-9007

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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.

Item Type:Article
Subjects:Sciences > Physics > Mathematical physics
ID Code:17748
Deposited On:17 Jan 2013 09:51
Last Modified:09 Dec 2014 08:41

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