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

Quantum Physics