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arXiv:quant-ph/0510039

Can a "Hidden Variable'' Quantum Theory Evade the "No-Cloning" Theorem?

Kirk T. McDonald

Published Oct 6, 2005• 0 citations
arXivHTMLPDF

Abstract

If YES, then we can look forward to physical realization of superluminal communication, as the original considerations of the ``no-cloning'' theorem were motivated in part as an explanation of why certain schemes for superluminal signaling cannot work. If NO, then it would seem that some aspects of the ``hidden'' variables must be ``intrinsically hidden'', i.e., ``unknowable'', such that ``hidden-variable'' theories belong more to the ``idealist'' than to the ``realist'' school of thought. I pose this question without proposing a definite answer. I am unaware of any commentary on this topic during these 23 years since the formulation of the ``no-cloning'' theorem, but I would be pleased to be enlightened by more knowledgeable readers.

DOI
10.48550/arxiv.quant-ph/0510039

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If YES, then we can look forward to physical realization of superluminal communication, as the original considerations of the no-cloning'' theorem were motivated in part as an explanation of why certain schemes for superluminal signaling cannot work. If NO, then it would seem that some aspects of the hidden'' variables must be intrinsically hidden'', i.e., unknowable'', such that hidden-variable'' theories belong more to the idealist'' than to the realist'' school of thought. I pose this question without proposing a definite answer. I am unaware of any commentary on this topic during these 23 years since the formulation of the no-cloning'' theorem, but I would be pleased to be enlightened by more knowledgeable readers.
In [Physical Review Letters 101, 050403 (2008)], we showed that quantum theory cannot be explained by a hidden variable model with a non-trivial local part. The purpose of this comment is to clarify our notion of local part, which seems to have caused some confusion in the recent literature. This notion is based on Bell's and demands that local hidden variables are physical, the idea being that, if discovered, they would not contradict basic physical principles. We explain why the recent supposed "counterexamples" that have appeared are not counterexamples to our theorem--in fact they are based on a definition of local hidden variables which would allow signalling and is therefore not physical.
An abstract definition of a general hidden-variables theory is given, and it is shown that such a theory is always possible in the present framework of quantum mechanics and is, in fact, unique in a certain sense. It is noted that the Bohm-Bub hidden-variables example is contained in this theory and an attempt is made to clarify the position of this theory with respect to hidden-variable impossibility proofs. The general definition is used in the consideration of quantum-mechanical ordering and the measurement process.
The question of the possible existence of hidden variables is re-examined. It is shown that hidden variables can exist only if every proposition (yes-no experiment) is compatible with every other one. It is further shown that this property is in contradiction with empirical facts. The theorem which leads to this conclusion is a strengthening of the theorem of von Neumann on the same subject. The question is raised whether there exist perhaps quantum mechanical systems which admit approximate dispersion-free states.
The aim of this article is to offer a rejoinder to an argument against scientific realism put forward by van Fraassen, based on theoretical considerations regarding microphysics. At a certain stage of his general attack to scientific realism, van Fraassen argues, in contrast to what realists typically hold, that empirical regularities should sometimes be regarded as “brute facts”, which do not ask for explanation in terms of deeper, unobservable mechanisms. The argument from microphysics formulated by van Fraassen is based on the claim that in microphysics the demand for explanation leads to a demand for the so-called hidden-variable theories, which “runs contrary to at least one major school of thought in twentieth-century physics”. It is shown here that this argument does not represent an insurmountable obstacle to scientific realism, not even when a series of important theoretical and experimental results against hidden-variable theories — and not merely a conflict with a certain school of thought—is taken into account.
This thesis consists of four parts. In the first part it is shown that optimal universal cloning of photons can be realized with the help of stimulated emission. Possible schemes based on three-level systems and on parametric down-conversion are analyzed in detail. The second part shows that the dynamical rules of quantum physics can be derived from its static properties and the condition that superluminal communication is forbidden. In the third part a very simple form of the Kochen-Specker theorem is presented, which leads to a proposal for a simple experimental test of non-contextual hidden variables. The fourth part shows how hidden-variable theorems can be derived in a completely operational way. In particular a Kochen-Specker theorem is derived that applies to experiments with finite precision.