Optimal entanglement purification via entanglement swapping

Abstract

It is known that entanglement swapping can be used to realize entanglement purifying. By this way, two particles belong to different non-maximally entangled pairs can be projected probabilisticly to a maximally entangled state or to a less entangled state. In this report, we show, when the less entangled state is obtained, if a unitary transformation is introduced locally, then a maximally entangled state can be obtained probabilisticly from this less entangled state.The total successful probability of our scheme is equal to the entanglement of a single pair purification (if two original pairs are in the same non-maximally 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 non-maximally entangled states). The advantage of our scheme is no continuous indefinite iterative procedure is needed to achieve optimal purifying. 03.67.-a Typeset using REVT E X

Optimal multipartite entanglement concentration of electron-spin states based on charge detection and projection measurements

“…In the second group, they obtain some N-electron systems in another partially entangled state with less entanglement, which are the resource for entanglement concentration in the next round. By iterating the process several times, the present ECP has an optimal success probability, the theoretical limit as it is just the entanglement of the partially entangled state E, twice of those based entanglement swapping and a collective unitary evolution [39,40], far higher than other typical ECPs [41-43, 52, 53]. Moreover, it does not require a collective unitary evolution, which decreases the difficulty of its implementation.…”

“…In 1999, Bose et al [39] proposed another interesting ECP based on entanglement swapping of two photon pairs in a partially entangled pure state. Subsequently, Shi et al [40] presented a different ECP based on entanglement swapping and a collective unitary evolution. Both these ECPs [39,40] require that Alice and Bob know the information about the less-entangled pure state α|H A |H B + β|V A |V B .…”

“…Subsequently, Shi et al [40] presented a different ECP based on entanglement swapping and a collective unitary evolution. Both these ECPs [39,40] require that Alice and Bob know the information about the less-entangled pure state α|H A |H B + β|V A |V B . Here |H and |V represent the horizontal and the vertical polarizations of photons.…”

“…Compared with an EPP, an entanglement concentration protocol (ECP) is usually more efficient for the two parties in quantum communication, say Alice and Bob, to distill some maximally entangled systems from an ensemble in a less-entangled pure state. Up to now, there are some interesting ECPs [38][39][40][41][42][43][44][45]. For example, Bennett et al [38] proposed the first ECP for two-photon systems in 1996, called it the Schmidt projection method.…”

“…Certainly, they has a lower efficiency than those in Refs. [39,40]. In 2010, the first single-photon ECP [44] was discussed with cross-Kerr nonlinearity.…”