Study On The Lower Bound Of The Quantum State Fidelity

The problem on fidelity between an arbitrary quantum state in quantum information theory belongs to the field of quantum information and quantum computation science. In the field of quantum information, the study of quantum state fidelity not only has its scientific research values in the theoretical research, but also be crucial to many technology applications. Its physical meaning is the level of maintaining the initial state during the process of information transmission and processing. It affects not only the calculation accuracy, but also affects the reliability of information transmission, and the correctness of the copy. Therefore, the study on the fidelity of quantum information theory not only has theoretical significance, but also has profound practical significance. In this thesis, we mainly study the lower bound of the quantum state fidelity, and give the lower bound of the fidelity under different conditions.first, it focuses on the source of the subject, background and theoretical and practical significance connected with the fidelity, the domestic and foreign research status in the field of research related to the subject and the achieved research results.second, the related background knowledge and basic concepts of quantum state fidelity are mainly described. these provide great convenience for the reference of the main content of this paper.again, first of all, it finds out a sufficient condition under which the fidelity lower bound can be got in the Fuchs- van de Graaf fidelity inequality in the finite dimensional space, and then get a stronger lower bound of fidelity between the pure states and mixed states, moreover, an example shows that the lower bound at the general situation is not established, but in the two dimensional space one kind of quantum state is established.In the last chapter, firstly, we establish the relationship of the fidelity and the trace norm between the pure state and the affine mixed path, then obtain the lower bound of the fidelity than that in the Fuchs- van de Graaf fidelity inequality. Secondly, in the infinite dimensional space, the lower bound of the arbitrary quantum state and the fidelity is constructed through using the maximum relative entropy.