Secure Three-Party Quantum Summation based on W-class States

Secure multi-party quantum summation, which allows n participants to jointly compute the summation of their private inputs, is one of the fundamental problems in secure multi-party quantum computation. We propose a three-party semi-quantum summation protocol based on W-class states in which a third party (TP) helps three participants compute the bitwise modulo 2 summation of their private bit strings. TP is assumed to be semi-honest, i.e., TP honestly executes the protocol, but he/she may try to obtain the participants’ private bit strings by using all the intermediate results. All three participants are classical, and for a qubit they receive, they can perform only three operations on it: (1) measure the qubit in the Z-basis ( \(\{|0\rangle , |1\rangle \}\) $\{|0⟩,|1⟩\}$ ), (2) generate a qubit in the Z-basis and send it, and (3) reflect the qubit without interference. To obtain the summation of the participants’ private bit string, each participant measures particles of the W-class states sent by TP in the Z-basis and generates random quantum bits \( |0\rangle \) $|0⟩$ or \( |1\rangle \) $|1⟩$ that are then sent to TP. They then employ the measurement results to generate private keys that are used to encrypt their private bit strings. Finally, they send their encrypted bit strings to TP and TP computes and publishes the summation. We also show that the proposed protocol is secure against internal and external attack and analyze the effect of collective noise on it. In addition, the protocol has a higher qubit efficiency compared with current similar protocols.