Entanglement recycled quantum key distribution scheme without sifting over arbitrary long distance

Abstract: Quantum key distribution(QKD) is an important area in quantum information theory. Nowadays, there are many protocols such as BB84 protocol, Lo-Chau's protocol and GR10 protocol. They usually require legitimated parties have the ability to create particles, using a sifting procedures (BB84, GR10), or must destroy entangled states (Lo-Chau). In this paper, we give a QKD scheme which can recycle entangled states and need not to run sifting procedures. The protocol use teleportation and mutual unbiased bases of qudits. Moreover, The scheme can be modified to add a third party who assumes all the states creating procedures and so the communicated parties need not to create states. This is in fact an entanglement distribution protocol. Also, the protocol can be modified for distributing key over arbitrary long distance. We compare our protocol with the previous protocols and discuss the security of it by corresponding to BB84 protocol.