Cryptanalysis of quantum secret sharing with $d$-level single particles

In a recent paper [V. Karimipour and M. Asoudeh, Phys. Rev. A 92, 030301(R) (2015)], a multiparty quantum secret-sharing protocol based on $d$-level single particles was proposed. We discussed the security of this protocol and found that it is not secure for any one dishonest participant who can recover the secret without the aid of other participants.

Figure 1

An empty circle represents the signal particle $q_1$ received by ${\mathrm{R}}_j$, and a solid circle represents that this particle has been encoded by ${\mathrm{R}}_j$ and transmitted to ${\mathrm{R}}_{j+1}$.

Figure 2

A solid circle represents the particle $q_{2j}$ that was intercepted by ${\mathrm{R}}_N^{*}$, two empty circles connected by a solid line represent a entangled pair in the state $\left|\psi \right(0,0)\rangle$.

Figure 3

A circle trip of signal particles in the T protocol.