Optimal entanglement purification via entanglement swapping with least classical communication

Scott Parker, Sougato Bose, Martin Bodo Plenio

Run-Ze Cong, Shuang Xu

We study the entanglement purification via entanglement swapping in terms of optimal output state concurrence. A strict formula that governs the process is first given analytically for the case where both input entangled pairs are in arbitrary pure states. Then, it is generalized, with strong numerical evidence, to the case with one of the entangled pairs being in an arbitrary mixed state. The formula subsequently gives a formal upper bound of entanglement purification via entanglement swapping, as well as how the maximum entanglement purification can be attained by engineering the pure state entangled pair. Moreover, the formalism of the upper bound in turn suggests that entanglement swapping is most suited for reducing the influence of pure dissipative noise, which can be applied to extend the lifespan of stationary qubits in quantum communications.

Wolfgang Dür, Hans J. Briegel, J. I. Cirac +1 more

We study the use of entanglement purification for quantum communication over long distances. For distances much longer than the coherence length of a corresponding noisy quantum channel, the fidelity of transmission is usually so low that standard purification methods are not applicable. It is possible, however, to divide the channel into shorter segments that are purified separately and then connected by the method of entanglement swapping. This method can be much more efficient than schemes based on quantum error correction, as it makes explicit use of two-way classical communication. An important question is how the noise, introduced by imperfect local operations (that constitute the protocols of purification and the entanglement swapping), accumulates in such a compound channel, and how it can be kept below a certain noise level. To treat this problem, we first study the applicability and the efficiency of entanglement purification protocols in the situation of imperfect local operations. We then present a scheme that allows entanglement purification over arbitrary long channels and tolerates errors on the percent level. It requires a polynomial overhead in time, and an overhead in local resources that grows only logarithmically with the length of the channel.

Jian-Wei Pan, Christoph Simon, Časlav Brukner +1 more

Gong Ren-shan

Purification of non-maximally entangled two-atom states and three-atom states is investigated by means of entanglement swapping,which is generalized to non-maximally entangled multi-atom states' purification.It is found that the purification probabilities in all kinds of entangled atom states are the same, 2|b|~2,which is equal to twice modulus of the least coefficient of four coefficients in entangled atom states.

Meng-Zheng Zhu, Liu Ye