Security analysis of qutrit quantum secret sharing with linear optical correlation measurement.

In this paper, we investigate a possibility of three-dimensional extension of correlation measurement based quantum secret sharing (QSS) with a three-dimensional cyclic-entangled state, called qutrit cyclic-entangled state. The qutrit cyclic-entangled state can be post-selected by a correlation measurement setup with linear optical elements. Thus, this protocol can provide a measurement-device-independent security against a potential eavesdropper, since the measurement results reveals only a correlation among qutrits sent from the three parties, not the exact quantum states. We show that our protocol can be implemented with current state-of-the-art technologies. The security of QSS with a qutrit cyclic-entangled state is analyzed for the cases, when all players are trusted as well as there are malicious players. Possibility of higher-dimensional, qudit extension and conditions for an advantage with qudit are investigated as well.