Separable states can be used to realize the fair quantum communication

Abstract

When Alice and Bob are never entangled with each other, can they share equal amount of information via noiseless channels? When the transfered subsystem B is classical, this basic question concerning communication capacity has a very satisfying answer: the amount of accessible information, as quantified by the classical correlation on B, is always equal. If the subsystem B is in a nonclassical state, the amount of accessible information, like their classical counterparts, is also well quantified by classical correlation, but the similarity ends here: the amount of accessible information from shared states may not be equal, because the subsystem B cannot be accessed perfectly by classical means. In this work, we show how to establish fair quantum communications. Our results give sufficient conditions for fair quantum communications and show that symmetric discord is the essential resource for this task. We further demonstrate that the fair quantum communication is fundamentally the same as the Shannon noisy channel coding theorem.