Quantum scalar product via quantum walks

In this paper, in order to calculate the scalar product of two private vectors from two communicants without leaking them, we propose a novel secure two-party quantum scalar product (TPQSP) protocol based on two-direction quantum walks on a circle (TDQWC) which needs the assistance of a semi-honest third party (TP). Here, TP is allowed to misbehave on her own wills but cannot conspire with others. The proposed protocol adopts the quantum walk (QW) states as the initial quantum resource, which are two-particle product states rather than quantum entangled states. The proposed protocol only needs $d$-dimensional and two-dimensional single particle measurements rather than quantum entangled state measurements. We prove in detail that the proposed protocol not only has information-theoretically security but also is secure against both the outside attacks and the participant attacks. Moreover, we not only deduce out the correctness of the proposed protocol theoretically, but also validate it through quantum circuits simulated on IBM Qiskit platform.