Researches Of Device-independent Quantum Random Number Expansion Protocol And The Related Theory

Random numbers are widely used in cryptography,and critical to the security of cryptographic systems.The random number generated by the traditional device is generally apparent random,and its security is based on the credibility of the device.However,quantum devices can produce true random numbers,and also realize "device-independent",that is,we can still guarantee the security of generated random numbers without being able to determine whether the device is credible.In particular,the framework which promises trustworthy of a part of device is known as semi-device-independent.This thesis will focus on the(semi-)device-independent quantum random number extension protocol and the related theory.The obtained research results are as follows:To answer the open question whether the partially free random sources(partially free random sources are inferred as the ones who are mastered partially information by adversaries)can be used in the task of quantum random number expansion in the framework of semi-device-independent,the thesis proposes semi-device-independent quantum random number expansion protocol with partially free random sources,and gives a positive answer to the open question.In the meantime,the thesis points out which degree of partially free random source can be applied to realize the task of semi-device-independent quantum random number expansion,and gives the relationship between the random generation efficiency and the observed data.Aiming at the problem of how to improve the efficiency of random number generation,the thesis proposes a semi-device-independent quantum random number expansion protocol based on 3→1 quantum random access code with partially free random sources,then numerically proof that the protocol improves the random generation efficiency.Similarly,this thesis pointes out which degree of partially free random source can be applied to realize the protocol,and obtain the relationship between random generation efficiency and the observed data.It is generally believed that non-locality is the essential reason that the quantum world has some special abilities(such as the trustworth quantum information processing tasks like device-independent cryptography protocol).The existing research shows that the microscopic particles have the non-locality,while the infinite number of microscopic particles only have the locality.However,how to characterize the non-locality of microscopic particles has not been concluded yet.This paper studies how to quantify the nonlocality of microscopic particles,and presents two methods of numerical optimization and analytical calculation respectively to solve the problem of non-locality quantization.On this basis,the principle of "Many-box Locality" is proposed and the quantum theory is partially proved to meet many-box locality by means of slice sampling.This result is of great guiding significance for the feasibility of designing device-independent quantum random number expansion protocol using multi-micro particles.