Randomly Generating Four Mixed Bell-Diagonal States with a Concurrences Sum to Unity

A two-qubit system in quantum information theory is the simplest bipartite quantum system and its concurrence for pure and mixed states is well known. As a subset of two-qubit systems, Bell-diagonal states can be depicted by a very simple geometrical representation of a tetrahedron with sides of length 2 √2. Based on this geometric representation, we propose a simple approach to randomly generate four mixed Bell decomposable states in which the sum of their concurrence is equal to one.