Juan Xu - Nanjing University of Aeronautics and Astronautics
Quantum secret sharing (QSS) mainly deals with the splitting and distributing of an arbitrary secret among n sharers using quantum resources. While quantum secret sharing schemes often use shared entangled states, it is also possible to define a notion of quantum secret sharing without the use of entangled states. QSS protocols without entanglement may use local unitary operations, which are used to encode the information in quantum states and scramble the quantum states so that the eavesdropper cannot reliably distinguish the quantum states using measurements. Can any unitary operations guarantee the security of the protocols? We propose an attack strategy for such protocols (which we call Bell state attack), using Bell states, as well as a definition of the minimum failure probability of such an attack. A quantitative analysis of security corresponding to different unitary operations is also provided, when the protocols are subject to the Bell state attack. As a result, the relation between the selection of unitary operations and the effect of Bell state attack is shown, which can serve as an important guidance for the selection of unitary operations in designing and implementing quantum secret sharing schemes without entanglement.