Random Number Certification Based On Entangled Werner States

Random number certification is critical in quantum information processing tasks.Quantum entanglement is an important resource for quantum non-locality,which can be used to certify random number.Therefore,it's important to judge quantum entanglement for random number certification.The thesis studies random number certification and entanglement witness from two aspects:device-independence scenario and measurement-device-independent scenario.And entanglement witness form in the measurement-device-independent scenario.Firstly,for given entangled Werner states,we propose a new random number certification protocol based on the device-independent scenario.The paper combines the self-testing techniques in the device-independent scenario and entanglement witness form in the measurement-device-independent scenario.In this case,classic bit input under the device-independent condition can be transferred into trusted quantum state input.In semi-quantum non-local scenario(trusted quantum inputs),all entangled states are non-local.The new protocol shows that all entangled states can certify random number.Therefore,compared with the previous device-independent protocol,the new protocol can greatly improve the utilization range of entanglement of quantum states for random number certification,which is of great significance for the actual entangled resources in the future.Secondly,in the measurement-device-independent protocol,for entangled Wermer states,we propose a new random number certification protocol with different quantum inputs.According to the Euler's theorem,we conclude that different quantum state inputs have great differences for random number certification.However,there is no necessary connection between the number of quantum states inputs and random number certification.And random number certification protocol with six quantum state inputs can be simulated to obtain the highest randomness.Thirdly,in the measurement-device-independent scenario,we have achieved different entanglement witness form for three-particle quantum states.For the quantum state of the three-particle form,according to the LPP mapping principle,the detailed proof process is designed for the measurement device-independent entanglement witness form in the case of three particles.And for the three-particle quantum state-W state,the specific coefficient expression value for entangled witness is given.