Research On Theory Of Quantum Error Correction Codes In Quantum Secure Communications

By making use of its unique properties of quantum mechanical, quantum informationscience as a multidisciplinary field, can realize some works which the classical can not,such as secure communication, calculation and so on. However, because there always existsquantum errors and decoherence in quantum communication and calculation, it makes thecoherent superposition of quantum state in quantum information destroyed, and the operationresult further in?uenced. Therefore, how to exactly transmit information becomes one of thekey problems of theory and technology development in quantum information.Quantum error correction code is a main encoding scheme, which plays an importantrole of overcoming decoherence in quantum secure communication. Encoding quantum in-formation into longer quantum bits, can decrease even eliminate the in?uence to initial infor-mation brought by the independent appearance of few quantum bits errors. Quantum errorcorrection code hence is the assurance of completing quantum computation and communica-tion, as well as is also one of the optimal efficient ways that overcoming decoherence. SinceShor proposed the first quantum code which encoded a information bit into 9 quantum bits in1995, research on theory and technology of quantum error correction code develop rapidly.Despite researchers made great achievements in this field, it still needs the further improve-ment and development comparing with mature theoretical of classical error correction codes.This dissertation focuses on the theory and technology of quantum error correction in quan-tum secure communications. It mainly includes following contents:(1) We investigated error correction and construction theory of quasi-cyclic (QC) low-density parity-check (LDPC) codes. By applying circulant permutation and its block-cyclematrices, some new quantum codes with various lengths and rates, based on the proposedapproach, can be obtained. Then, we also amply the exponent chain corresponding to ablock-cycle, so that a family of quantum QC-LDPC codes with the longer classical self-dualcontaining codes are constructed. (2) How to get larger-length quantum error correction codes with simpler constructionmethod always is the research filed by researchers. Jacket matrix is a class matrices ofsimpler decoding procession and constructing for larger-length quantum codes with recursiverelation. We apply Jacket matrices to obtain good and larger-length nonbinary quantumstabilizer codes for the first time, and also investigate quaternary quantum Reed-Muller codeswith Gray relation, so that the theory of quantum codes construction over nonbinary field isextended more deeper.(3) With the intuition and other characters, we investigated construction method of em-ploying the entanglement of several indirected graphs to get a new graph state codes. Asso-ciating with the advantages of LDPC codes, we also employ recurrent permutation matricesto construct graphical quantum LDPC codes, so that the obtained codes have the advantagesof both graph codes and LDPC codes.(4) Associating with graph state codes, we design a quantum network anonymous vot-ing protocol, and further investigate quantum ballot protocol based on entanglement relation.This protocol employs the characters of quantum bit, so that the resulting ballot process isanonymous to every voters for protecting participants'privacy. At the same time, the pro-posed scheme realizes the voting about multi-objects researching among large data. There-fore, the scheme has its applications in practice. On the other hand, this scheme uses theentanglement properties to hold unconditional security, which improves the classical votingprotocol.(5) We first investigated quantum secret sharing protocol based on quantum stabilizercodes. Applying the basic idea of proposed protocol, we also design a quantum controlledsecure direct communication with entanglement relations. The character of scheme is thatthe information communication between participants can be realized with the admission ofa controller. Furthermore, in terms of the property of quantum bits, we present an efficientquantum communication protocol with one-time one-pad, so that the scheme can realizedusing present instruments.