An Efficient and Secure Semi-Quantum Secret Sharing Scheme Based on W State Sharing of Specific Bits

This paper presents a semi-quantum secret sharing (SQSS) protocol based on three-particle <i>W</i> states, designed for efficient and secure secret sharing in quantum-resource-constrained scenarios. In the protocol, a fully quantum-capable sender encodes binary secrets using <i>W</i>, while receivers with limited quantum capabilities reconstruct the secret through collaborative <i>Z</i> basis measurements and classical communication, ensuring no single participant can obtain the complete information independently. The protocol employs a four-state decoy photon technique ({|0⟩,|1⟩,|+⟩,|-⟩}) and position randomization, combined with photon number splitting (PNS) and wavelength filtering (WF) technologies, to resist intercept-resend, entanglement-measurement, and double controlled-NOT(CNOT) attacks. Theoretical analysis shows that the detection probability of intercept-resend attacks increases exponentially with the number of decoy photons (approaching 1). For entanglement-measurement attacks, any illegal operation by an attacker introduces detectable quantum state disturbances. Double CNOT attacks are rendered ineffective by the untraceability of particle positions and mixed-basis strategies. Leveraging the robust entanglement of <i>W</i> states, the protocol proves that the mutual information between secret bits and single-participant measurement results is strictly zero, ensuring lossless reconstruction only through authorized collaboration.