  Semi-quantum key distribution (SQKD) allows sharing random keys between a
quantum user and a classical user. However, implementing classical user
operations is challenging, posing a hurdle to achieving the Single-state
protocol. By using the "selective modulation" method, the feasibility of SQKD
is verified in principle. The proposal of the selective modulation method
enables the realization of other protocols for SQKD. To advance experimental
progress in SQKD, we propose and implement a phase-encoded semi-quantum key
distribution system based on the Single-state protocol and the "selective
modulation" method. The system operates at a frequency of 100MHz and an average
photon number of 0.1. The interference contrast achieved 96.52%, the average
quantum bit error rate was 1.19%, and the raw key rate reached 88Kbps. Our
experimental results demonstrate the feasibility and stability of the proposed
phase-encoded semi-quantum key distribution system. Furthermore, by leveraging
the "selective modulation" scheme proposed in this paper, we develop a
comprehensive theoretical description of selective modulation. Through an
analysis of quantum state evolution, we assess the security of our system,
ultimately demonstrating its resilience against attacks targeting quantum
states. The classical user of our system requires only two optical devices,
significantly reducing the equipment requirements and enhancing its application
potential. This work validates the feasibility of semi-quantum key distribution
experiments and provides ideas for future research on semi-quantum key
distribution experiments and security studies.
