The Entanglement-assisted Entropic Uncertainty Principle And Its Application In Quantum Information

Based on the basic principles of quantum mechanics, quantum communication hasthe characteristics of high efficiency and absolute safety, and thus becomes aninternational research focus in quantum physics and information science. Entropy is animportant research tool in information science and quantum entropy is one of the keyconcepts of quantum information theory，it is used to measure the uncertainty of thestate in physical system. Quantum entanglement involves fundamental problems ofquantum mechanics such as factuality, locality, hidden variables and measurementtheory, and plays an important role in the research of quantum computation andquantum communication. Two-particle entangled state is a simple and important part ofthe entangled state, it is of great significance to the study their teleportation. Theuncertainty principle is an important rule in quantum physics, it is a very basic theorywhich reflects the nature of the particles. It points out the limits of using classic concept,the limit to Planck’s constant. The entanglement-assisted entropy uncertainty principleintroduces entropy with entanglement to uncertainty principle, thus expandinguncertainty principle in the study of information communication. However, due tovarious inevitable environmental noises, the quality of the quantum entangled state willget worse under the influence of environment. Bell state is the maximum entangled stateof two particles, in the process of transmission, bell state is no longer the maximumentangled state under the influence of noise, the degree of entanglement and uncertaintywould change with it.This paper mainly studies the bell state affected by noise. According to the conceptof entanglement degree and the principle of entropic uncertainty, analyze from twoaspects how bell state changes after affected by the noise.The content is divided intothree parts, In the first part, three kinds of typical quantum entangled states (four-particle GHZ state, four-particle cluster state and EPR state) are used as quantumchannel to propose solutions of teleporting three different kinds of two-particle partiallyentangled states. In the second part, Partial entropy of entanglement is used to calculatethe four bell states in the case of ideal situation. Entanglement of formation is used tocalculate the relationship between entanglement degree and noise effects of four bellstates under the influence of white noise and color noise, the result shows entanglementdegree varies with the purity p. In the third part, entropic uncertainty principle is used tocalculate the condition entropy of four bell states in ideal situation, under the influenceof white noise and color noise, the result shows the uncertainty is zero in ideal situationand decreases with the increasing the purity of p under the effect of noise. On the basisof studying the teleportation of two-particle partially entangled state the change ofbell-state in ideal situation and under the influence of the white noise and colored noiseis analyzed from two different angles, the result of the two aspects coordinates mutuallyand provides a theoretical basis for the effect of noise to the entangled state and is alsoinstructive to the experiment.