Study On Properties Of Quantum Walks And Applications Of Non-orthogonal Quantum States Discrimination

Quantum mechanics was combined with information science and computer science,resulting in quantum computation and quantum information.Now more and more scientists are interested in this discipline.Quantum walks(QWs)are the counterpart of the classical random walks in the quantum world.Classic random walks are widely used in classical algorithms.Similarly,quantum walks are also a tool for developing efficient quantum algorithms.Because of the coherent superposition of quantum states,the characteristics of the quantum walks are different from the characteristics of the classical random walks.Compared with classical walks,the diffusion speed of quantum walks is quadratic.In this paper,the properties of standard one-dimensional quantum walks and two-dimensional quantum walks are introduced.Furthermore,the properties of two-dimensional quantum walks with phase defects and the discrimination of non-orthogonal quantum states based on quantum walks are investigated: 1.The effects of the discrete coin operations and joint operations on properties of quantum walks are discussed,and the effects of the initial state of the coin which is separable state or entangled state on the quantum walks properties are discussed.The local phenomena in two-dimensional quantum walks are explained by calculating the fidelity between the initial state and the local eigenstate of the evolution operator.2.Quantum walks can be used to construct positive operator valued measures(POVM).We can extend the coin system into a larger system by coupling the coin with the walker.The walker walks according to the coin state.After a few steps,he will appear in a different position.Then quantum state discrimination is implemented.On the basis of a quantum walk model,a special algorithm can be used to realize the discrimination of two-dimensional non-orthogonal quantum states.We can extend this algorithm,and apply it to the discrimination of three-dimensional quantum states.Finally,discrimination of any two three-dimensional non-orthogonal quantum states is achieved.The study on properties of quantum walks and the method of three-dimensional quantum state discrimination based on quantum walks can be extended to high-dimensional quantum states,and the discrimination of non-orthogonal high-dimensional quantum states will further promote the implementation of quantum computing and quantum communication in engineering.