Construction of the Einstein-Podolsky-Rosen Entangled States

As simultaneous eigenstates of a complete set of commuting observables, construction of the Einstein-Podolsky-Rosen entangled states for a two-particle system is investigated and a sufficient condition to ensure the entanglement between a pair of commuting observables is given. It is found that for a two-particle system, four types of entangled states concerning the usually interested observables may be constructed.