Graded tensor products and the problem of tensor grade computation and reduction
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Date
Authors
Khrennikov, Andrei Yu.
Rosinger, Elemer E.
Van Zyl, A.J. (Gusti)
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Abstract
We consider a non-negative integer valued grading function on tensor products which aims to measure the extent of entanglement. This grading, unlike most of the other measures of entanglement, is defined exclusively in terms of the tensor product. It gives a possibility to approach the notion of entanglement in a more refined manner, as the non-entangled elements are those of grade zero or one, while the rest of elements with grade at least two are entangled, and the higher its grade, the more entangled an element of the tensor product is. The problem of computing and reducing the grade is studied in products of arbitrary vector spaces over arbitrary fields.
Description
Keywords
Graded tensor product, Entanglement
Sustainable Development Goals
Citation
Khrennikov, AY, Rosinger, EE & Van Zyl, AJ 2012, 'Graded tensor products and the problem of tensor grade computation and reduction', p-Adic Numbers, Ultrametric Analysis and Applications, vol. 4, no. 1, pp. 20-26, doi: 10.1134/S2070046612010037.