Research On Quantum Randomness Certification,Random Number Generation And Post-processing Based On A Positive Operator-valued Measurement

Random numbers are important basic resources and are widely used in science,industry and business.In modern cryptography,the preparation of truly random numbers is the basic task of all information security protocols.In quantum information science,truly random numbers are the security foundation of quantum key distribution protocols.However,the random number generated by computer deterministic algorithm cannot theoretically prove their randomness,and cannot guarantee that the output sequence is safe.There are certain hidden dangers.In recent years,with the development of quantum information technology,the inherent randomness of quantum mechanics makes the quantum system a perfect source of truly random numbers.Among them,the device-independent quantum random number generator is considered to be the highest security random number generation method.This paper mainly studies the device-independent quantum randomness certification and random number generation scheme based on a positive operator-valued measurement?POVM?,mainly including the following contents:?1?Experimental verification of quantum randomness certification based on a symmetric informationally complete POVM?SIC-POVM?.Compared with the traditional random certification scheme based on projection measurement,this scheme can certify 2-bit randomness from a two-photon maximum entangled state.Under the condition of the relaxed hypothesis,we report a proof-of-principle implementation of this scheme through a linear optical system.According to the observed quantum nonlocal correlation under device-independent conditions in the experiment,follow-up research can prove the advantages of POVM in the randomness certification scheme through the method of semi-positive definite programming in the future.This work provides a valuable reference for the future research of the limit of randomness certification.?2?Experimental implementation of quantum random number generation scheme based on SIC-POVM.This scheme uses the properties of SIC-POVM,the marginal condition probabilities are equal,and encodes four random events into two classical bits.In the experiment,we collected a total of about 9 Mbit of raw random numbers.Through two different randomness extractors for post-processing,we can obtain random bit strings with autocorrelation coefficient less than 10^-3,which can pass all randomness tests of the standard NIST-STS.In the future,the obtained true random numbers can be used in quantum key distribution,quantum digital signature and other encryption systems with high-security level requirements.