Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Logical inconsistency in combining counterfactual results from
  non-commutative operations: Deconstructing the GHZ-Bell theorems   The Greenberger, Horne, Zeilinger (GHZ) theorem is critically important to
consideration of the possibility of hidden variables in quantum mechanics.
Since it depends on predictions of single sets of measurements on three
particles, it eliminates the sampling loophole encountered by the Bell theorem
which requires a large number of observations to obtain a small number of
useful joint measurements. In evading this problem, the GHZ theorem is believed
to have confirmed Bell's historic conclusion that local hidden variables are
inconsistent with the results of quantum mechanics. The GHZ theorem depends on
predicting the results of sets of measurements of which only one may be
performed, i.e., counterfactuals. In the present paper, the non-commutative
aspects of these unperformed measurement sequences are critically examined.
Three classical examples and two variations on the GHZ construction are
analyzed to demonstrate that combined counter factual results of non-commuting
operations are in general logically inconsistent with performable measurement
sequences that take non-commutation into account. As a consequence, negative
conclusions regarding local hidden variables do not follow from the GHZ and
Bell theorems as historically reasoned.

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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: math
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol