Exponential complexity and ontological theories of quantum mechanics

Details Exponential complexity and ontological theories of quantum mechanics Exponential complexity and ontological theories of quantum mechanics

2007-11-29

arxiv.org/abs/0711.4770v2

Phys. Rev. A 77, 022104 (2008)

Physics

Quantum Physics

Scientific paper

10.1103/PhysRevA.77.022104

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.

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