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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

## 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 |
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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: | 03 Dec 2014 08:57 |

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