Patterns of maximally entangled states within the algebra of biquaternions

Abstract

This paper proposes a description of maximally entangled bipartite states within the algebra of biquaternions–. We assume that a bipartite entanglement is created in a process of splitting one particle into a pair of two indiscernible, yet not identical particles. As a result, we describe an entangled correlation by the use of a division relation and obtain twelve forms of biquaternions, representing pure maximally entangled states. Additionally, we obtain other patterns, describing mixed entangled states. Finally, we show that there are no other maximally entangled states in than those presented in this work.