We describe an entanglement purification protocol (EPP) for atomic entangled pair using photonic Faraday rotation. It is shown that after the two single photons input-output process in cavity QED, the high quality entangled atomic state can be obtained from the low quality mixed entangled atomic states. Different from other EPPs, the two pairs of mixed states do not need to intact directly. As the photonic Faraday rotation works on the low-Q cavities, this EPP is useful in both quantum communication and computation.PACS numbers: 03.67. Bg, 42.50.Dv
I. INTRODUCTIONEntanglement is the important resource in current quantum information processing [1]. For example, quantum teleportaton [2,3], quantum dense coding [4], quantum key distribution [5], quantum state sharing [6][7][8], and quantum direct secure communication [9][10][11], they all require the maximally entangled state to set up the quantum channel. However, the entanglement will inevitably interact with the environment and it will degrade during the process of distribution and storage in the solid system. Entanglement purification is a powerful way for distilling the high quality mixed entangled states in a small ensemble from the low quality mixed states in a large ensembles. In the early works of entanglement purification, they usually used the CNOT gates or similar logic gates, such as the entanglement purification protocol (EPP) proposed by Bennett et. al. [12], the improved EPP proposed by Deustch et. al. [13], the EPP for multipartite entangled systems [14], and so on [15]. In long-distance quantum communication, the photons as the flying qubits are the good candidate for carrying quantum information. So there are many EPPs based on the photons. For example, In 2001, Pan et al. proposed the EPP with the linear optics [16]. In 2003, they realized their protocol in experiment [17]. In 2002, Simon and Pan proposed an EPP using spatial entanglement [18]. In 2008, EPP based on the cross-Kerr nonlinearity was proposed [19]. There are also other EPPs for photonic systems [20-24]. Actually, the flying qubits distribute the entangled states between distance locations, and they should be stored into the solid memory systems for the further application. So there are other EPPs for such solid systems [25-31]. In 2005, Cao et al. proposed an EPP for arbitrary unknown ionic states via linear optics [25]. In the same year, Feng et. al. proposed an EPP with charge detection [26]. In 2006, Reichle et. al. reported their experimental report for purification of two-atom entanglement [27]. In 2011, Wang et al. proposed an EPP for hybrid entangled state using quantum-dot and microcavity coupled system [28].On the other hand, over the pase decades, cavity quantum electrodynamics (QED) has become an important platform for understanding the basic principle of quantum mechanics and quantum information processing [32]. Some excellent experiments, such as the coupling of the trapped atoms with cavity [33], generation of single photons [34], conditional logic gate [35] have b...