Optimal entanglement purification via entanglement swapping

It is known that entanglement swapping can be used to realize entanglement purification. In this way, two particles belonging to different nonmaximally entangled pairs can be projected probabilistically to a maximally entangled state or to a less entangled state. In this paper, we show, when the less entangled state is obtained, then a maximally entangled state can be obtained probabilistically from this less entangled state if a unitary transformation is introduced locally. The probability of success of our scheme is equal to the entanglement of a single pair purification (if two original pairs are in the same nonmaximally entangled states) or to the smaller entanglement of a single pair purification of these two pairs (if two original pairs are not in the same nonmaximally entangled states). The advantage of our scheme is that no continuous indefinite iterative procedure is needed to achieve optimal purification.