Some Researches On Key Problems In Quantum Randomness Certification

Random number is one of the most important components of cryptography area, which plays an important role in the information security domain. If the randomness of the generated random numbers is not strong enough, attackers may be able to handle partial or entire information, which is a serious threat to the information security. The randomness certification of generated random numbers is extremely crucial to avoid this type of insecure threat. However the true randomness does not exists in the classical cryptography scenario, hence it is impossible to certify these true random numbers.With the development of quantum theories and quantum technologies, it becomes possible to utilize the quantum devices to generate random numbers and certify their randomness according to the related quantum theories. Currently researchers have made great progress in the certification of quantum random numbers, and proposed several device independent and semi-device independent random number expansion models. However,the existing models are mostly based on known quantum non-locality experiments, which are not suitable for other unknown experiments. In addition, the safety analysis and certification methods of semi-device independent random number expansion models are incomplete. Focusing on the mentioned limitations, this paper includes the following details:Firstly, for the self-testing task of single state and two binary measurement systems, previous works only propose one solution:Bell-CHSH criteria test. This paper proposes a necessary and sufficient condition for this system self-testing task. Based on the proposed condition, we can locate all the Bell-type criteria and utilize these criteria to certify the random numbers, which increases the flexibility of choose of the real random number certification straiegies. Therefore, our work is not only enriches the singlet self-testing theory, but also contributes to the practical applications.Secondly, this paper focuses on two problems in the semi-device independent random number expansion model. First, when the dimension hypothesis and 'free will' input hypothesis are relaxed, we respectively introduce a user-tested classical model to simulate the 2-dimensional quantum witness violation. In this scenario, the generated random numbers are no longer true. Our experiments prove the importance of dimension and 'free will' assumptions. Second, considering with or without the local reference system, we propose approaches to ensure the occurrence of 2-dimensional quantum witness violation when the calibration system changes.Thirdly, different from the previous T2-inequality based random number certification method, in the semi-device independent protocol we propose to certify the random numbers directly based on the full probabilities. Meanwhile, we theoretically prove the proposed method is the best when certifying the maximum random number. Based on the full probability model and the classical side channel, our method considers different types of average maximum guessing probabilities and utilizes the Navascues-Pironio-Acin (NPA) method to solve the optimization problem.