Hierarchical simultaneous entanglement swapping for multi-hop quantum communication based on multi-particle entangled states

Entanglement swapping is a key technology for multi-hop communication based on entanglement in quantum networks. However, the end-to-end delay of the traditional sequential entanglement swapping (SEQES) grows rapidly withthe increase of network scale. To solve this problem, we first propose a low-delay multi-particle simultaneous entanglementswapping (SES) scheme to establish the remote four-particle Greenberger–Horne–Zeilinger (GHZ) channel states for thebidirectional 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 simultaneously. Bob (or Alice) only needs to carry out a proper unitary operation according to the information he (or she) hasreceived. Further, we put forward a hierarchical simultaneous entanglement swapping (HSES) scheme to reduce the classical information transmission cost, which is composed of level-1 SES and level-2 SES (schemes). The former is an innersegment SES, and the latter is an inter segments SES. Theoretical analysis and simulation results show the HSES can obtainthe optimal performance tradeoff between end-to-end delay and classical cost.

Hierarchical simultaneous entanglement swapping for multi-hop quantum communication based on multi-particle entangled states