Wolf, Michael and Pérez García, David (2009) Assessing dimensions from evolution. Physical Review Letters , 102 . ISSN 10797114

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