Controller independent controlled bidirectional quantum secure direct communication

Abstract Controlled bidirectional quantum secure direct communication (CBQSDC) is an important research direction in quantum secure direct communication. It can enable two legitimate users to confidentially exchange secret messages only with the permission of the controller. In many practical scenarios, CBQSDC needs to avoid the controller from obtaining useful information on the secret messages. Therefore, in this paper, we introduce the concept of controller independent controlled bidirectional quantum secure direct communication (CICBQSDC) that has a controller to control the communication but restricts the controller to obtain useful information on the secret messages. In other words, we only require the controller of CICBQSDC to cooperate, not to be trusted. In addition, a novel CICBQSDC protocol is constructed. To make CICBQSDC protocols have broad application scenarios, we point out that they need to avoid four security problems: the information leakage problem, the problem of violating simultaneity, the problem of communication not being controlled, and the problem of controllers stealing secret information. Furthermore, we show that the constructed CICBQSDC protocol can avoid the four security problems. Moreover, the unconditional security of the constructed CICBQSDC protocol is demonstrated in the asymptotic scenario.