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Foundations of Physics

Graded tensor products of quantum logics

R. L. Hudson, Sylvia Pulmannová

Published Jan 1, 1994• 4 citations
Publisher
DOI
10.1007/bf02053910

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We consider the grading structure on the tensor product corresponding to the tensor rank; the relation to the notion of entanglement is discussed. We also study a complex problem of finding the minimal (with respect to the aforementioned grading structure) representation of elements of the tensor product. The general construction is presented over an arbitrary number field. Hence, it can be applied not only to the conventional notion of entanglement over the field of complex numbers, but even for models of non-Archimedean (in particular, p-adic) quantum physics. The problem of tensor reduction is also studied for an arbitrary number field, but only in the two dimensional case.