Quantum Communication Complexity of Quantum Authentication Protocols

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 bring results about its application in ten existing quantum authentication protocols ( data origin and identity authentication). Such evaluations increase the knowledge about the existing protocols, presenting their advantages, limitations and contrasts.