Research On Entanglement Correlation Based On Quantum Walk

Quantum information technology is the product of organic combination of quantum mechanics and information science.Quantum walk have secondary acceleration and diffusion properties that classical random walk do not have,and can be used to realize quantum communication and build quantum algorithms with higher efficiency and better performance.Therefore,quantum walk have received widespread attention,and the related theoretical and experimental studies are gaining more and more importance.We focus on the preparation of coin-walker entangled states,or coin-position entangled states,based on quantum walk.In practical implementations,coin-position entanglement is usually an association between two different degrees of freedom of a single microscopic particle.Compared with the entanglement between two bits,this entanglement can be used in a simpler setup to test quantum fundamentals,improve information encoding capabilities,enable fault-tolerant quantum computing,and can also be used to improve the efficiency and performance of quantum algorithms.The specific work has two aspects as follows:(1)Theoretically calculated the entanglement relationship between coins and walkers in quantum walk.The main work is to discuss the effect of adding phase factors at different locations in space on the properties of quantum walk in an ordered quantum walk model that is invariant with time.In this project,we calculated the changes of the entanglement degree with the evolution of quantum walk operation coefficient,initial state coefficient and evolution time.When all the position evolution operations are the same,changing the initial state of the system cannot obtain the maximum entangled state.In contrast,for adding a suitable bit-phase operation at the origin and then choosing a suitable system initial state,the high-dimensional quantum entangled state can be obtained after a smaller number of evolutionary steps.This thesis proposes a scheme to achieve the maximum coinwalker entangled state after fewer steps except step 2,which provides a more easily implemented method for the experimental preparation of high-dimensional entangled state modulation.(2)Inhomogeneous quantum walk are realized in optical systems to obtain maximum entanglement of coin-positions while maintaining secondary acceleration diffusion of the walker.Two coin states are represented by horizontal and vertical polarization states of light,and the position states are encoded in discrete time formed by different path lengths to achieve quantum walk in two different lengths of the ring.The maximum entanglement between the coin and the walker is obtained by a spatially nonuniform quantum walk achieved by a coin operation that changes with position.After processing and analyzing the experimental data obtained from the measurements,the maximum entanglement can be generated in any odd number of steps or in an even number of steps larger than10,and the experiment agrees with the theoretical calculation.In our experimental optical path diagram,we are able to extend to high-dimensional quantum walk and also promote the study of coinwalker interactions based on quantum walk.