Quantum algebras associated with Bell states

The Bell matrix has become an interesting interdisciplinary topic involving quantum information theory and the Yang-Baxter equation. It is an antisymmetric unitary solution of the braided Yang-Baxter equation and yields all the Bell states by acting on the product basis. In this paper, using the Faddeev-Reshetikhin-Takhtadjian (FRT) construction, we obtain a quantum algebra associated with the Bell matrix. We explore two characteristic algebraic structures in its four-dimensional representation. One is a representation with a composition series, namely, it has irreducible subrepresentations but is not completely reducible. The other is a direct sum of two-dimensional cyclic representations, and can be spanned by four maximally entangled states as local unitary transformations of the Bell states. Both of them are expected to be realized in physical systems and exploited in quantum information theory. Besides, we present the other quantum algebra associated with the unitary evolution of the Bell states (or the Yang-Baxterization of the Bell matrix).