Necessary and sufficient condition for a realistic theory of quantum systems

Details Necessary and sufficient condition for a realistic theory of quantum systems Necessary and sufficient condition for a realistic theory of quantum systems

2009-11-13

arxiv.org/abs/0911.2536v1

Physics

Quantum Physics

9 pages

Scientific paper

We study the possibility to describe pure quantum states and evens with classical probability distributions and conditional probabilities and show that the distributions and/or conditional probabilities have to assume negative values, except for a simple model whose realistic space dimension is not smaller than the Hilbert space dimension of the quantum system. This gives a negative answer to a question proposed by Montina [Phys.Rev.Lett.{\bf 97}, 180401 (2006)] whether or not does there exist a classical theory whose phase-space dimension is much smaller than the Hilbert space dimension for any quantum system. Thus, any realistic theory of quantum mechanics with nonnegative probability distributions and conditional probabilities requires a number of variables grows exponentially with the physical size.

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