Study On The Capacity Of Quantum Broadcast Channel And Uantum LDPC Codes

With the development of the quantum information technology, quantum communication would be widrly used for communications in the future. Hence, it is valuable to research the capacity of quantum channel as well as the quantum error-correcting coding methods.In this thesis, quantum broadcast channel with only one sender and two receivers is firstly be studied. According to the quantum entanglement generation theorem, I prove the capacity theorems of noisy quantum broadcast channels, including the classical-quantum and the quantum-quantum capacity region theorems, by which the retackle region of the quantum broadcast channel beneath the environment of quantum depolarizing channel could be obtained. According to this retackle region, it is possible to transmit both entanglement copies as well as quantum error correcting codes in quantum communication.Secondly, by using the Entanglement-Assisted Quantum Error-Correcting (EAQEC) Theory, the classical Low-Density Parity-Check (LDPC) codes constructed from Balanced Incomplete Block Design (BIBD) and Finite Geometries are quantized into quantum LDPC codes, which could be named as Entanglement-Assisted Quantum LDPC (EAQLDPC) codes. Compared to the Quantum LPDC codes constructed by the traditional CSS or Stabilizer codes, we could see that these EAQLDPC codes have better performance in simulation with only one pair of entanglement.