Two-map distillation protocols guarantee to reobtain a desired maximally entangled pure state

An idea of hybrid maps is proposed to establish purification protocols in which the demerits of the IBM and Oxford protocols are overcome. Examples of two-map protocol have been shown that they can be performed in distilling a desired maximally entangled pure state with certainty with equal efficiency as if the Oxford protocol is implemented. PACS: 03.67.-a Quantum information processings such as quantum teleportation[1], quantum data compression[2,3], and quantum cryptography[4] rely on the transmission of maximally entangled qubit pairs over quantum channels between a sender(Alice) and a receiver(Bob). The quantum channel, however, is always noisy due to the interation with the environment and even possibly the measurement controlled by an eavesdropper. Therefore, the pairs shared by Alice and Bod are no longer of the desired pure ones to begin with. The resource in the noisy channel then can be viewed as a mixed state, or equivalently, an ensemble of pure states with definite random probabilities. Accordingly, Alice and Bob need to take an action of entanglement purification to regain, at least asymptotically, the desired maximally entangled state. This aim can be achieved by Alice and Bob, step by step, using local operations and classical communication (LOCC). The first entanglement purification protocol (the IBM protocol) was developed by Bennett et al.[5,6] in achieving a faithful quantum teleportation. Soon later, an improved protocol entitled ”Quantum Privacy Amplification” (QPA, or the Oxford protocol) was addressed by Deutsch et al.[7] in consideration of the security of a quantum cryptography over noisy channels. The analytical convergence in the recurrence scheme of the Oxford protocol has been proved by Macchiavello[8]. These typical protocols have revealed that a small number of maximally entangled qubit pairs can be distilled from a larger number of partly entangled pairs. Other algorithms as modifications in improving the efficiencies of the mentioned ones can be found