Improvements on “multiparty quantum key agreement with single particles”

Recently, Liu et al. (Quantum Inf Process 12: 1797–1805, 2013) proposed a secure multiparty quantum key agreement (MQKA) protocol with single particles. Their protocol allows N parties to negotiate a secret session key in such away that (1) outside eavesdroppers cannot gain the session key without introducing any errors; (2) the session key cannot be determined by any non-trivial subset of the participants. However, the particle efficiency of their protocol is only \(\frac{1}{(k+1)N(N-1)}\). In this paper, we show that the efficiency of the MQKA protocol can be improved to \(\frac{1}{N(k+1)}\) by introducing two additional unitary operations. Since, in some scenarios, the secret keys are confidential, neither party is willing to divulge any of the contents to the other. Therefore, in our protocol, no participant can learn anything more than its prescribed output, i.e., the secret keys of the participants can be kept secret during the protocol instead of being exposed to others, thus, the privacy of the protocol is also improved. Furthermore, we explicitly show the scheme is secure.