The Calculation Of Quantum Capacity And The Performance Of Cascade Code In Generic Pauli Channels Based On Diagram State

The uniqueness of quantum information determine that the quantum communication has the incomparable superiority compare with classic communication. For the classical theories of information, shannon’s second theorem has gaven a expounded about its capacity in the field of classical. For the quantum channel, some related research shows that it can transfer not only the common classical information like classical channel, but also the confidential classical information, besides, it can transmit the mysterious quantum information. The Channel Capacity is one of the most basic and important theoretical question in communication field, it character the ability of reliable transmission of information in a noisy environment, that is the maximum reliable transmission of information. During quantum communication and quantum information processing, the channel coherence information is a very important parameter, because the quantum channel capacity and noise tolerance are closely related with it. The quantum coding theorem for nosiy channels states that for the channels absence of secondary resources, its quantum capacity is equal to the maximum of regularized coherent information respect to the input quantum states. The Generic Pauli channel is the most commonly used channel model, which has the very good representative, but its quantum capacity is unable to accurately calculate, we can only approach it by using the multi-channel coherent information.In this paper, we apply quantum diagram state cascade coding, by making good use of the orthogonal of state diagram, which can make big matrix be diagonal ization or block diagonalization, we can get the analytical formulas of coherent information in multi-channel coding, then we can fast calculate the approximation value of quantum channel capacity in generic Pauli general. Due to the influence of the external environment and channel itself, quantum information inevitably occur missing during transmission. And when the noise intensity reaches a certain extent, some quantum codes cannot be used to transmit quantum information. Different quantum codes can bear different noise intensity, that is different noise tolerance. With the aid of computer matlab programming, using the iterative algorithm, we can calculate the noise tolerance of all kinds of Quantum cascade code, that is, the relationship among Px,Py,pz when respect to ICN=0. And analyze the performance among different concatenated codes and random coding in different channel, and sums up factors of judgment to choose the optimal coding way for different channel.The main content of this paper are as follow:1. the introduction of background and the latest progress about Quantum information.2. the introduction of basic knowledge of quantum information theory.3. the method to structure cascade code, and the transition of cascade code to diagram state.4. the model of transmission in quantum channel, for the generic Pauli channels, find out the analytical formulas of channel correlation information to tree graph and forest graph respectively, get the limit capacity of quantum.5. calculate the noise tolerance of different concatenated codes in different channels, analyze the performance of different concatenated codes in different channels, and sum up the factors of judgment to choose the optimal coding way for different channels, and put forward a propose to structure the Pauli channel adaptive code.