Hierarchical simultaneous entanglement swapping for multi-hop quantum communication based on multi-p

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Entanglement swapping is a key technology for multi-hop communication based on entanglement in quantum net-works.However,the end-to-end delay of the traditional sequential entanglement swapping(SEQES)grows rapidly with the increase of network scale.To solve this problem,we first propose a low-delay multi-particle simultaneous entanglement swapping(SES)scheme to establish the remote four-particle Greenberger-Horne-Zeilinger(GHZ)channel states for the bidirectional teleportation of three-particle GHZ states,in which the intermediate nodes perform Bell state measurements,send the measurement results and the Bell state type to the user node Bob(or Alice)through classical channel simulta-neously.Bob(or Alice)only needs to carry out a proper unitary operation according to the information he(or she)has received.Further,we put forward a hierarchical simultaneous entanglement swapping(HSES)scheme to reduce the clas-sical information transmission cost,which is composed of level-1 SES and level-2 SES(schemes).The former is an inner segment SES,and the latter is an inter segments SES.Theoretical analysis and simulation results show the HSES can obtain the optimal performance tradeoff between end-to-end delay and classical cost.
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