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Assessing dimensions from evolution

Wolf, Michael and Pérez García, David (2009) Assessing dimensions from evolution. Physical Review Letters , 102 . ISSN 1079-7114

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Official URL: http://arxiv.org/abs/0901.2542

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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.

Item Type:Article
Uncontrolled Keywords:Teoría cuántica, Física matemática, Sistemas dinámicos, Quantum Physics, Mathematical Physics, Dynamical Systems
Subjects:Sciences > Physics > Mathematical physics
Sciences > Physics > Quantum theory
ID Code:12164
Deposited On:03 Feb 2011 10:11
Last Modified:06 Feb 2014 09:18

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