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

Abstract

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.

A sufficient and necessary criterion for separability of bipartite quantum states

“…However, for the case of mixed bipartite states, no single practical procedure guaranteed to detect the entanglement of every entangled state has been found so far. There exists a considerable effect to analyze the separability and quantitative character of quantum entanglement [3][4][5][6][7][8][9][10][11][12][13][14][15][16] In Ref. [17], Peres discovered a very strong necessary condition of separability, namely, that the separable states remain positive if they are subjected to a partial transposition (PPT criterion).…”