Unconditionally secure multi-party quantum commitment scheme

Abstract

A new unconditionally secure multi-party quantum commitment is proposed in this paper by encoding the committed message to the phase of a quantum state. Multi-party means that there are more than one recipient in our scheme. We show that our quantum commitment scheme is unconditional hiding and binding, and hiding is perfect. Our technique is based on the interference of phase-encoded coherent states of light. Its security proof relies on the no-cloning theorem of quantum theory and the properties of quantum information.

Appendix A: experimental data of interfering phase

In the cost matrix $\mathbf C$, the diagonal elements represent the cases when recipient uses the same phase as sender, the off-diagonal elements represent the cases when recipient uses the phase different from sender. In 2012, Clarke et al. [14] presented us a practical experimental data, the cost matrix $\mathbf C$ realized by experimental setup using 8 different phase states and with average photon number of $|\alpha ^2|=0.16$ per pulse is given by

$$\begin{aligned} \mathbf C=\begin{pmatrix}3.89&{} \quad 4.40&{} \quad 5.24&{} \quad 5.95&{} \quad 6.35&{} \quad 6.00&{} \quad 5.29&{} \quad 4.39\\ 4.56&{} \quad 3.88&{} \quad 4.43&{} \quad 5.29&{} \quad 6.04&{} \quad 6.39&{} \quad 6.02&{} \quad 5.20\\ 5.28&{} \quad 4.60&{} \quad 3.89&{} \quad 4.42&{} \quad 5.29&{} \quad 6.02&{} \quad 6.37&{} \quad 5.95\\ 5.68&{} \quad 5.22&{} \quad 4.58&{} \quad 3.90&{} \quad 4.40&{} \quad 5.24&{} \quad 5.91&{} \quad 6.30\\ 6.36&{} \quad 5.68&{} \quad 5.27&{} \quad 4.59&{} \quad 3.89&{} \quad 4.43&{} \quad 5.24&{} \quad 6.01\\ 5.62&{} \quad 6.36&{} \quad 5.66&{} \quad 5.23&{} \quad 4.57&{} \quad 3.89&{} \quad 4.41&{} \quad 5.30\\ 5.26&{} \quad 5.68&{} \quad 6.40&{} \quad 5.70&{} \quad 5.22&{} \quad 4.60&{} \quad 3.88&{} \quad 4.40\\ 4.61&{} \quad 5.24&{} \quad 5.65&{} \quad 6.36&{} \quad 5.68&{} \quad 5.22&{} \quad 4.56&{} \quad 3.88\end{pmatrix}\\\times 10^{-3}. \end{aligned}$$