  Reaching agreement in the presence of arbitrary faults is a fundamental
problem in distributed computation, which has been shown to be unsolvable if
one-third of the processes can fail, unless signed messages are used. In this
paper, we propose a solution to a variation of the original BA problem, called
Detectable Byzantine Agreement (DBA), that does not need to use signed
messages. The proposed algorithm uses what we call $Q$-correlated lists, which
are generated by a quantum source device. Once each process has one of these
lists, they use them to reach the agreement in a classical manner. Although, in
general, the agreement is reached by using $m+1$ rounds (where $m$ is the
number of processes that can fail), if less than one-third of the processes
fail it only needs one round to reach the agreement.
