Semiquantum key distribution network protocol with single photons in both polarization and spatial-mode degrees of freedom

In order to make the communicants at different nodes of network use the semiquantum key distribution technology to constitute a secure semiquantum key distribution network as a whole, a novel semiquantum key distribution network protocol was proposed by using single photons with polarization and spatial-mode degrees of freedom. Only single photons rather than quantum entangled states were adopted as quantum resource, only single-photon measurements were required, and none of quantum entanglement swapping operations, quantum delay lines and Hadamard operations were needed. Within the proposed protocol, a participant with full quantum capabilities establishesd a private key with each semiquantum participant, and simultaneously helped two adjacent semiquantum participants to establish a private key between them. The proposed protocol could be applied into semiquantum summation, semiquantum private comparison and semiquantum secret sharing, which meaned that it had extensive application potential. As the preparation, the measurement and the implementation with unitary operations on single photons with polarization and spatial-mode degrees of freedom are all easy to realize under the present technologies, this protocol possesses the good practical feasibility.