Research On Relaxing Measurement Based On Device-Independent Random Number Expansion Protocol

The Bell test is one of the most important tools in quantum information science.On the one hand,it enables fundamental tests of the basic physics laws of nature.On the other hand,it can also be applied in a variety of device-independent tasks such as quantum key distribution and random number generation.In practice,loopholes existing in experimental demonstrations of Bell tests may affect the validity of the conclusions.Most quantum information tasks based on Bell tests relie on the assumption of measurement independence.However,it is difficult to ensure that the assumption of measurement independence is always met in experimental operations,so it is crucial to explore the effects of relaxing this assumption on Bell tests.The contributions of this dissertation are mainly on analyzing the security of device-independent randomness expansion,and the effects of measurement dependence on Bell test was emphatically studied.Firstly,this paper discusses the effects of relaxing the assumption of measurement independence on 1-parameter family of Bell(1-PFB)tests.For both general and factorizable input distributions,we establish the relationship among measurement dependence,guessing probability,and the maximum value of 1-PFB correlation function that Eve can fake.The deterministic strategy when Eve fakes the maximum value is also given.Furthermore,the range of true random numbers that can be certified is given.Secondly,for both general and factorizable input distributions,we also establish the relationship among measurement dependence,guessing probability,and the maximum value of Chain correlation function that Eve can fake.We compare the unknown information rate of Chain inequality and 1-PFB inequality,and find the range of the parameter in which it is more difficult for Eve to fake the maximum quantum violation in 1-PFB inequality than in Chain inequality.