Graded Tensor Products and the Problem of Tensor Grade Computation and Reduction

Andrei Khrennikov (1) , Elemer Elad Rosinger (2) , Augustin van Zyl (2)

1 International Centre for Mathematical Modelling in Physics and Cognitive Sceinces
2 Department of Mathematics and Applied Mathematics [Pretoria]

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.

Mots clés: tensor products; entanglement; reduction of entanglement

Domaines: Physique Quantique [quant-ph]

Andrei Khrennikov, Elemer Elad Rosinger, Augustin van Zyl. Graded Tensor Products and the Problem of Tensor Grade Computation and Reduction. 2012. ⟨hal-00717662⟩