Security of Key Distribution and Complementarity in Quantum Mechanics

Abstract

Complementarity is one of the fundamental properties of quantum mechanics, which prohibits the control of both of a pair of physical quantities even if either one alone is accessible. This property is useful in understanding the relation between quantum communication and secret communication: It gives a simple explanation why basic quantum key distribution protocols are secure against any eavesdropping attack. The imperfection in the final secret key is determined through the failure probabilities of a pair of complementary tasks, which have a clear operational meaning. It also serves as a powerful tool for proving the security under the use of practical imperfect devices. Finally, it gives a comprehensive understanding of how quantum correlations provide the ability of secret communication, since one can prove that for every case in which a secret key is obtained though quantum communication, there exists an explanation in terms of complementarity.