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Trapped Ion Quantum Computing

Assessing dimensions from evolution

arXiv
Authors: Michael M. Wolf, David Perez-Garcia

Year

2009

Paper ID

9252

Status

Preprint

Abstract Read

~2 min

Abstract Words

120

Citations

N/A

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.

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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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:0901.2542 [2] arXiv https://arxiv.org/abs/0901.2542 [3] Publisher https://arxiv.org/abs/0901.2542

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