Study On Parallel Quantum Key Distribution Using Multiple Bell Bases

Quantum key is a cross research discipline of communication, cryptography, quantum mechanics, and it has the natural advantage of absolute security as one of the core national competitive strategies in the secure communication fields. In view of the problem of low bit rates of quantum key distribution, the transmission steps of parallel quantum key distribution with quantum entangled states are focused on in theory. The main work is summarized as follows.1. To solve the problem that the traditional Bell basis is too single in four-dimensional Hilbert space, the structure of the quantum circuit of Bell Basis are analyzed. The Hadamard gate is transformed unitarily with three Pauli gates in this circuit, and multiple Bell bases(i. e. increasing three new Bell bases) are derived from the traditional Bell basis. It is shown that four Bell bases have identical general formula, and their quantum circuits are similar. The relations of unitary transformations among four Bell bases are equivalent, and there are two groups of equivalent Bell bases. All of four Bell bases can be applied in the quantum communications including quantum teleportation and quantum entanglement swapping. The analyses results show that there are objective multiple Bell bases in four-dimensional Hilbert space, which is of great important significance in the theoretical developments of Bell bases and the applications of quantum cryptography, quantum communication and quantum computation.2. To make up for the shortage of low bit rate for the quantum key distribution using the traditional Bell basis, the parallel quantum key distribution schemes with multiple Bell bases are proposed to transmit the unknown quantum state information of multi-path quantum key according to the principle of superposing states in quantum mechanics. To further improve the performance of the quantum channels, the method of Tianji horseracing is adopted to put forward a scheme of parallel quantum key distribution of multiple Bell bases. The strategies of attack and defense can be analyzed quantitatively by both the communication sides and eavesdropper in this scheme. The analyses results illustrate that the securities of the quantum channels have been enhanced by this scheme, while the numbers of quantum channels with successful eavesdropping by eavesdropper have been reduced. The average probabilities of successful transmission of quantum keyshave been increased, and the bit rates of quantum key distribution have been further raised.3. For the potentially insecurity problem that "smart" eavesdropper may recognize the measure bases in the quantum key distribution system of multiple Bell bases, a scheme of parallel quantum key distribution is proposed with the approaches of Tian Ji horseracing method with Bell bases cycle groups. By proving and applying the one-order, two-order, three-order and four-order Bell bases cycle groups in the algebraic systems of Bell bases, the different-performance channels can be formed, and the parallel quantum keys are transmitted with the Tian Ji horseracing strategy. Performance analysis results show that the difficulty for the eavesdroppers to acquire the information of the Bell bases which are used by the sender and receiver is increased, and the security of quantum channel is also enhanced. The average probabilities for eavesdroppers to steal the quantum keys in parallel quantum channels are reduced, and the bit rate of quantum key distribution are also increased.4. For the problem that the quantum key distribution systems of multiple Bell bases using Bell bases cycle groups need the operations of Hadamard gates, a scheme of parallel quantum key distribution with multiple Bell bases is presented using the Tianji horseracing method of Hadamard gate groups. In this scheme, the one-order, two-order, three-order and four-order Hadamard gate groups are introduced and used, and the parallel quantum key distribution systems of different-performance channels are constructed. Utilizing the strategies of Tianji horseracing, the unknown quantum bit information of quantum keys is transmitted in parallel quantum channels. Performance analysis shows that eavesdroppers have to steal and gain the quantum keys more difficultly than before. The number of quantum channels that are not eavesdropped on successfully rises, and the goal to further increase the bit rates of quantum key distribution has been achieved.5. In view of the problem that the algebraic operations of the Hadamard gates that exist in the quantum key distribution system with the Hadamard gate groups depend on the choices of Pauli gates, the schemes of parallel quantum key distribution of multiple Bell bases are constructed with the ways of Tianji horseracing of Pauli gates groups. Through determining and proving whether all algebraic systems of the existing eight-order Pauli gate group are their subgroups or not, the tree and forest of Pauli gate groups and subgroups are constructed to form the channels of different performance. The parallelquantum key distributions are implemented with the method of Tianji horseracing. The performance analysis results show that the successful eavesdropping for eavesdroppers becomes more and more difficult using the tree and forest of Pauli gate groups. The numbers of quantum channels that are eavesdropped on by eavesdropper are cut down, and the performance of bit rates of quantum key distribution is improved.Using the Bell bases cyclic groups, Hadamard gates groups, Pauli gates group and its subgroups, three kinds of methods of parallel quantum key distribution of multiple Bell bases have been obtained in turn by combining with the models of Tianji horseracing. The former depends on the latter. The algebraic operation results of the latter are used in the former, and the successful eavesdropping for the systems of parallel quantum key distribution is more difficult than before. The bit rates of quantum key distribution are also increased further.