Mechanism design is a reverse problem of game theory. Nash implementation and Bayesian implementation are two important parts of mechanism design theory. The former one corresponds to a setting with complete information, whereas the latter one corresponds to a setting with incomplete information. A recent work Wu (Int J Quantum Inf 9:615–623, 2011) shows that when an additional condition is satisfied, the traditional sufficient conditions for Nash implementation will fail in a quantum domain. Inspired by this work, in this paper we will propose that the traditional sufficient conditions for Bayesian implementation will also fail if agents use quantum strategies to send messages to the designer through channels (e.g., Internet, cable etc) and two additional conditions are satisfied.