Entanglement Concentration And Entanglement Purification Of Three-qubit W-like States

Quantum entanglement plays an important role in quantum information field and hasbeen widely applied to quantum communication as an important quantum resource. Dur-ing quantum communication, quantum entanglement is unavoidably afected by noise.The noise will lead to the degradation of the entangled states that are used as the quan-tum channel and the degradation will further afect quantum communication. In order toachieve reliable and secure quantum communication, it is necessary to deal with the de-graded entangled states which can provide high-quality entanglement resources. Entan-glement concentration and entanglement purification are efective and feasible methodsto solve the problem by using local operations and classical communication. They aresignificant and meaningful to quantum communication.At present, there is a lot of research on bipartite entanglement concentration andbipartite entanglement purification. Multipartite entanglement concentration and entan-glement purification schemes are relatively less. As for tripartite entangled states, thereare two kinds of states——GHZ state and W state. Entanglement concentration and entan-glement purification mainly focus on GHZ states, and the concentration and purificationon W states have not been researched extensively and thoroughly. We mainly study onconcentrating the partially entangled three-atom W state with known and unknown coef-ficients, concentrating the partially entangled three-photon W state with unknown coef-cients, and purifying the three-qubit W-like state afected by amplitude damping.In cavity QED system, based on the far of-resonant interaction between three-levelatoms and fields, we propose two kinds of entanglement concentration schemes of par-tially entangled three-atom W states, in which the coefcients of the partially entangledthree-atom W states are known and unknown, respectively. Firstly, we propose two entan-glement concentration schemes of partially entangled three-atom state with known coef-ficients. The entanglement concentration schemes can be probabilistically completed byintroducing one auxiliary atom, choosing appropriate interaction time, and choosing sim-ple single-qubit operations. Secondly, we propose an entanglement concentration schemeof partially entangled W state with unknown coefcients. The entanglement concentra-tion scheme can be probabilistically completed via one of the participants choosing ap-propriate interaction time and single-qubit operations. It is found that the nonlocal and maximally entangled pair and the three-atom entangled state which can be reconcentratedare probabilistically obtained during the entanglement concentration. The entanglementconcentration schemes we proposed reduce the requirement of cavity quality factor andare insensitive to cavity decay.We propose two entanglement concentration schemes of partially entangled three-photon W state with unknown coefcients via cross-Kerr nonlinearity. Cross-Kerr non-linearity is a powerful tool to construct a quantum non-demolition detector. The firstentanglement concentration scheme is based on one quantum non-demolition measure-ment and the second one mainly takes advantage of two two-qubit polarization parityquantum non-demolition detectors. In the two concentration schemes, one of the partici-pants performs local operations via less linear optical elements and cross-Kerr nonlinearmedia, then communicates with the other two participants via classical communication.The success probability is greatly improved and both schemes do not need to use so-phisticated single-photon detectors. Moreover, valuable local and nonlocal maximallyentangled pairs can be probabilistically obtained in the first concentration scheme. Thesecond concentration scheme is an iterative one with higher yield because of the reusablethree-photon entangled state that is probabilistically obtained.Based on local controlled-NOT gate we propose a2â†'1recurrence entanglementpurification scheme for three-qubit W-like state in amplitude damping. We give the an-alytic expression of the entanglement purification range, analyze the importance of thesingle-qubit operation in the entanglement purification, and then discuss the entangle-ment purification for the asymmetric W state in general form. We point out that nonlocaland maximally entangled pairs can be obtained during the entanglement purification. TheW-like state is the W state in general form, and the entanglement purification scheme isnot only applied to symmetric W state, but also applied to asymmetric W state. Therefore,the entanglement purification scheme we proposed is more general.