Some Researches On Key Problems In The Self-Testing Of Quantum Systems

Quantum information is special physical feature carried by quantum systems.The encoding and information transmission which are based on the characteristic of quantum mechanics as new information processing make it possible for the quantum communications achieve unconditioned security.Quantum devices are the necessary and important parties in the task of quantum information processing.The testing of the security and credibility of the the quantum devices is critical to guarantee the task proceeding smoothly.Hence,it is significant to certificate the devices before operating the information processing.The theory of self-testing for the quantum systems is an alternative technique which could positively address this problem.Self-testing is a concept of device independence whose conclusion verdict relies only on the observed correlation statistics of measurement inputs and outcomes under the sole assumptions.Currently,the self-testing techniques have become the research focus of the domestic and foreign scholars.Although the self-testing theory has been enriched,there has many problems need to be investigated.Such as the self-testing of the bipartite scenarios have had plentiful results,but the criteria of multipartite states are inadequate.The most of the results are based on the perfect observed statistics.However,the experimental noise and statistical error always exist.Thus,it is important to discuss the criteria perform in case of deviations from the ideal values.In view of the above problems,this paper focuses on bipartite and multipartite states,design different available self-testing schemes and approaches,and make deep analyses on the robustness.Firstly,for the case that full probability of the multiparty state are hard to measure,we proposed the self-testing using only marginal information by swap method and NPA hierarchy.The examples we presented all deal with the multipartite scenario and end up self-testing states of three-qubit W state,general W state and four-qubit W state.We proved that the maximal violation of an inequality built on one-and two-party statistics can self-test a three-qubit state.And all these criteria are robust.Our results provide the reference value for the self-testing of N-qubit states where N>3.Secondly,for a large family of symmetric three-qubit states wich is the superposition of W state and GHZ state,we proposed analytical and numerical two different self-testing schemes.The target states we mainly focused on is the superposition of W states and GHZ states due to the simple form and their wide applications in quantum information tasks.For the general case,only the simplest Pauli measurements are used in our work and the robustness of fidelity is in high precision.Further,we analysed the difference of the robustness for target state utilizing two different approaches which could offer the reference for the practical self-testing.Thirdly,for the numerical robust bounds for the whole set of self-testing criteria of singlet state are not tight enough,we constructed a general extraction map applying to all self-testing criteria of the singlet state with two binary measurements for each party.We derived analytic robustness bounds for the singlet in different regions of the boundary of the extremal quantum correlations set by operator inequality.The comparison shows that our robustness bounds are better than the known results and close to optimal for these self-testing criteria of a singlet state with two binary measurements.Further,we provided the general tilted-CHSH inquality are the self-testing criteria for partial entangled states wich enriched the self-testing criteria of bipartite states.