Group representations in entanglement theory

Li-Xiang Cen, Xin-Qi Li, Yi Jing Yan

Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group SL (2, C ) ⊗ SL (2, C ), composed of local operators acting on the binary composite system, is realized in the four-dimensional complex space in terms of a set of novel bases that are pseudo-orthonormalized. The two-to-one homomorphism is then established for the group SL (2, C ) ⊗ SL (2, C ) onto the SO (4, C ). It is shown that the resulting representation theory leads to the complete characterization for the entanglement transformation of the binary composite system.

Mahdi Karamati, Mohammad Reza Rezapour

Abstract The intimate connection between the Banach space wavelet reconstruction method for each unitary representation of a given group and homogenous space, and the quantum entanglement description using group theory were both studied in our previous articles. Here, we present a universal description of quantum entanglement using group theory and non-commutative characteristic functions for homogenous space and projective representation of compact groups on Banach spaces for some well known examples, such as: Moyal representation for a spin; Dihedral and Permutation groups.

Shahabeddin Mostafanazhad aslmarand, Warner A. Miller, Doyeol Ahn +1 more

Anthony Chefles, Claire R Gilson, Stephen M Barnett