Theoretical Study Of The Problems On Quantum Secure Communication And Quantum Channel

Quantum secure communication and quantum channel capacities are some of the most fundamental theoretical problems in quantum information science. Quantum communication provides a new way for transmitting message securely. Many researches on quantum communi-cation have been done in both theory and experiment since the BB84quantum key distribution protocol in1984. Channel capacity, which characterizes the communication channel's capa-bility to faithfully transmit information against noises, is one of the central parts of quantum channel theory. Despite considerable progresses, tractable formulae for the classical, private and quantum capacities are still out of reach. The work of this thesis involves three areas in quantum information, i.e., quantum secure direct communication (QSDC), continuous variable quantum key distribution (CVQKD), and quantum channel capacities.For quantum secure direct communication, we propose two schemes combined ideas of user authentication and direct communication with dense coding. Each protocol is composed of two parts:one is for an authentication process and the other is for a direct communication with dense coding. First, Trent is the third party who is introduced to authenticate the two users par-ticipating in the communication. In communication procedure, the strategies of dense coding has been used to communicate the secret message directly. The privacy of authentication keys and the properties of the EPR pairs not only ensure the realization of identity authentication but also further improve the security of communication. Second, there are only two legitimate users, Alice and Bob, in this communication. Bell state as double carrier has been used to both authentication and direct communication with dense coding in the way of Ping-pong protocol. It is has been proven that this protocol is secure and is closer to practical condition.Different from classical case, the performance of quantum key distribution such as one-way continuous variable protocols, can be increased by adding some noise on the reference side of error correction in the error-correction phase. For this reason, we here study this possibility in the case of two-way continuous variable system, based on the the superadditive enhancement of the security thresholds in two-way protocols. The numerical results show that the using of additional noise gives two-way schemes better security performance in terms of secret key rates and resistance to channel excess noise. These results represent further steps to assess the advantages of two-way schemes in the context of continuous variable quantum cryptography.Reverse coherent information, as a symmetric counterpart of the coherent information, allows to define reverse coherent information capacity which is additive. We prove the convexity of such capacity for a general quantum channel, and investigate the effect of convex decomposition of quantum channel on its (reverse) coherent information. The result shows that for a general input state reverse coherent information is more sensitive to the convex decomposition of a channel than coherent information. Also, we calculate the reverse coherent information capacity of dephasing channel. Taking advantage of this result, we finally apply the convexity property to provide an upper bound on the reverse coherent information capacity for depolarizing channel and BB84channel, respectively.