Quantum secret sharing with classical Bobs

Boyer, Kenigsberg, and Mor [Phys.Rev.Lett.99, 140501(2007)] proposed a novel idea of semi-quantum key distribution where a key can be securely distributed between Alice who can perform any quantum operation and Bob who is classical. Extending the idea of “semiquantum” to other tasks of quantum information processing is of interest and worth considering. In this article, we consider the issue of semi-quantum secret sharing where a quantum participant Alice can share a secret key with two classical participants Bobs. After analyzing the existing protocol, we propose a new protocol of semi-quantum secret sharing. Our protocol is more realistic, since it utilizes product states instead of entangled states. We prove that any attempt of an adversary to obtain information necessarily induces some errors that the legitimate users could notice.