Research On Self-testing Of Quantum Systems And Nonlocality Sharing

Quantum information technology has great application value and has become the strategic commanding heights of scientific and technological competition in various countries in the world.All quantum information processing tasks are inseparable from quantum devices,so whether quantum devices are trustworthy is crucial to the successful completion of quantum information processing tasks.Self-testing of quantum systems is a key technology to realize the creditability certification of quantum devices,and is an important research content in the field of quantum information.In addition,nonlocality,as an important quantum resource,is the theoretical basis for the realization of self-testing of device independent quantum systems.Whether nonlocality can be shared by multiple observers can be seen as a generalization of self-testing in quantum systems with multiple observers.In essence,it is a kind of certification of entanglement in quantum systems through sequential measurements.Although selftesting of quantum systems and nonlocality sharing have achieved rapid development,there are still many problems that need to be solved urgently.For example,self-testing cannot tolerate noise or error under the prepareand-measure model based on 3→1 quantum random access code(QRAC).Only 4 quantum states and 2 measurements can be self-tested under the prepare-transform-measure model,and the number of quantum states and measurements that can be self-tested is relatively small.In addition,the nonlocality sharing of multiple observers for multipartite entangled states is not yet perfect and requires further study.In view of the above problems,this dissertation focuses on the self-testing of semi-device independent quantum systems and the nonlocality sharing of three-qubit state among multiple observers.The main work is as follows:Firstly,in view of the problem that self-testing under the semi-device independent prepare-and-measure model is susceptible to statistical errors in practical experiments and applications,we constructed an extraction maps operator inequality that can traversal the entire Bloch sphere.Based on this operator inequality,we gave the self-testing robustness of quantum state and quantum measurement respectively,which is conducive to the application of self-testing in practice.Secondly,in view of how to self-test more quantum states and how to improve random number generation efficiency in the prepare-transformmeasure model under semi-device independent framework,we proposed the prepare-transform-measure model based on the 3 →1 sequential QRACs.Specifically,first of all,we gave the optimal trade-off between two correlation witnesses based on 3 →1 sequential QRACs and proved that the two correlation witnesses cannot be achieved the double classical correlation witness violation simultaneously.Then we analyzed the selftesting and robustness of the quantum systems.Finally,based on the 2→1,3→1 sequential QRACs and determinant values,the random number generation efficiency under different sharpness parameters is analyzed and compared,and we found that within a certain range,the 3→1 sequential QRACs can generate more random numbers.The result can promote the application of quantum random numbers in the network.Thirdly,aiming at the problem of how many observers can share the nonlocality of the general three-qubit entangled states,we studied the sharing of tripartite nonlocality with multiple observers on one side and came to the following conclusions:1.For the general GHZ state and the W state under different parameter values,there are at most m(m ∈{0,1,2,…,6})and n(n ∈{0,1,2,3})Charlies at one side,which can simultaneously demonstrate standard tripartite nonlocality with the single Alice and single Bob.2.For the general GHZ state under different parameter values,there are at most 0,1 and 2 Charlies on one side respectively,which can simultaneously demonstrate genuine tripartite nonlocality with the single Alice and single Bob.3.For the standard GHZ state,we designed an optimal protocol of genuine nonlocality sharing among multiple observers.After Charlie1 using unsharp measurements with near-maximum strength,Charlie2 can also demonstrate genuine tripartite nonlocality with the single Alice and single Bob.Our protocol has expanded the region of double Svetlichny inequality violation.Our results not only shed light on the interplay between nonlocality and quantum measurements,but also can be applied to many quantum information processing tasks,such as unbounded randomness certification,quantum steering and quantum communication network.