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In this paper, we propose an efficient semiquantum key distribution (SQKD)protocol which is based on single photons in both polarization and spatial-modedegrees of freedom. This protocol is feasible for a quantum communicantdistributing a random private key to a classical communicant. This protocolneedn't require the classical communicant to use any quantum memory or unitaryoperation equipment. We validate the complete robustness of the transmissionsof single photons between two communicants. It turns out that during thesetransmissions, if Eve wants not to be detected by two communicants, she willobtain nothing useful about the final shared key bits. Compared with Boyer etal.'s famous pioneering SQKD protocol (Phys Rev Lett, 2007, 99:140501), thisprotocol has double quantum communication capacity, as one single photon withtwo degrees of freedom for generating the key bits can carry two private bits;and this protocol has higher quantum communication efficiency, as it consumesless qubits for establishing a private key of the same length. Compared withthe only existing SQKD protocol with single photons in two degrees of freedom(Int J Theor Phys, 2020, 59: 2807), this protocol has higher quantumcommunication efficiency.

Efficient semiquantum key distribution based on single photons in both polarization and spatial-mode degrees of freedom