Exponential complexity and ontological theories of quantum mechanics
Quantum Physics
2008-02-15 v2
Abstract
Ontological theories of quantum mechanics describe a single system by means of well-defined classical variables and attribute the quantum uncertainties to our ignorance about the underlying reality represented by these variables. We consider the general class of ontological theories describing a quantum system by a set of variables with Markovian (either deterministic or stochastic) evolution. We provide the first proof that the number of continuous variables can not be smaller than 2N-2, N being the Hilbert space dimension. Thus, any ontological Markovian theory of quantum mechanics requires a number of variables which grows exponentially with the physical size. This result is relevant also in the framework of quantum Monte Carlo methods.
Cite
@article{arxiv.0711.4770,
title = {Exponential complexity and ontological theories of quantum mechanics},
author = {Alberto Montina},
journal= {arXiv preprint arXiv:0711.4770},
year = {2008}
}