Quantum Algebras Associated With Bell States

Details Quantum Algebras Associated With Bell States Quantum Algebras Associated With Bell States

2006-10-17

arxiv.org/abs/math-ph/0610036v2

J. Phys. A: Math. Theor. 41 (2008) 055310

Physics

Mathematical Physics

v1: 15 pages, 2 figures, latex; v2: 18 pages, 2 figures, latex, references and notes added

Scientific paper

The antisymmetric solution of the braided Yang--Baxter equation called the Bell matrix becomes interesting in quantum information theory because it can generate all Bell states from product states. In this paper, we study the quantum algebra through the FRT construction of the Bell matrix. In its four dimensional representations via the coproduct of its two dimensional representations, we find algebraic structures including a composition series and a direct sum of its two dimensional representations to characterize this quantum algebra. We also present the quantum algebra using the FRT construction of Yang--Baxterization of the Bell matrix.

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