  In order to perform Quantum Cryptography procedures it is often essencial to
ensure that the parties of the communication are authentic. Such task is
accomplished by quantum authentication protocols which are distributed
algorithms based on the intrinsic properties of Quantum Mechanics. The choice
of an authentication protocol must consider that quantum states are very
delicate and that the channel is subject to eavesdropping. However, even in
face of the various existing definitions of quantum authentication protocols in
the literature, little is known about them in this perspective, and this lack
of knowledge may unfavor comparisons and wise choices. In the attempt to
overcome this limitation, in the present work we aim at showing an approach to
evaluate quantum authentication protocols based on the determination of their
quantum communication complexity. Based on our investigation, no similar
methods to analyze quantum authentication protocols were found in the
literature. Pursuing this further, our approach has advantages that need to be
highlighted: it characterizes a systematic procedure to evaluate quantum
authentication protocols; its evaluation is intuitive, based only on the
protocol execution; the resulting measure is a concise notation of what
resources a quantum authentication protocol demands and how many communications
are performed; it allows comparisons between protocols; it makes possible to
analyze the communication effort when an eavesdropping occurs; and, lastly, it
is likely to be applied in almost any quantum authentication protocol. To
illustrate the proposed approach, we also bring results about its application
in ten existing quantum authentication protocols (data origin authentication
and identity authentication). Such evaluations increase the knowledge about the
existing protocols, presenting its advantages, limitations and contrasts.
