Experimental Investigation Of Quantum Self-Testing And Optimal Verification Of Entangled States With Local Measurements

As a cutting-edge science,quantum mechanics has been developed for more than 100 years from its birth.Many of its conclusions have been widely questioned for its counter-intuition,and it has often been endorsed by experiments.Today,quantum me-chanics has revolutionized and supplemented traditional physics in almost every aspect,and has profoundly affected human life.Quantum information is an interdisciplinary subject of quantum mechanics and informatics.It helps people to interpret quantum me-chanics from the perspective of information theory,and also provides a broader meaning for informatics research.Current research shows that classical physics is a special case of quantum mechanics in some specific situations,so researches on quantum mechanics can guide real-world phenomena at a higher level.Recently,due to the rapid progress of experiments and theories,quantum information has produced many influential re-sults,and it has also attracted more and more people to participate in its research.In addition,the study of light as a universal natural phenomenon has played an important role in many scientific breakthroughs,such as Young's double slit interference,black body radiation,constant light speed,and so on.In this paper,photon is used as the carrier of qubits,and the experimental research on quantum system verification is realized through linear optical systems with advan-tages such as easy operation,long coherence time,and many degrees of freedom.The main research results obtained in this paper are as follows:1.Experimentally Robust Self-testing for Bipartite and Tripartite Entangled States.We experimentally investigate these two bounds with high-quality two-qubit and three-qubit entanglement sources.The results show that these bounds are valid for var-ious entangled states that we prepared.Thereby,a proof-of-concept demonstration of robust self-testing is achieved,which improves on the previous results significantly.2.Experimental demonstration of robust self-testing for bipartite entangled states.In our work,by constructing a versatile entanglement source,we experimentally demonstrate a generalized self-testing proposal for various bipartite entangled states up to four dimensions.We show that the high-quality generated states can approach the maximum violations of the utilized Bell inequalities,and thus,their Schmidt coefficients can be precisely inferred by self-testing them into respective target states with near-unity fidelities.Our results indicate the superior completeness and robustness of this method and promote self-testing as a practical tool for developing quantum techniques.3.Experimental Realization of Robust Self-Testing of Bell State Measure-ments.We implement a full Bell state measurement and achieve a high degree of Bell violation on the remaining two qubits,which are required for nontrivial self-testing of a Bell state measurement.Furthermore,our results combine the correlations before and after the swapping;thus,the quality of the performed Bell state measurement can be precisely inferred.4.Experimental Optimal Verification of Entangled States using Local Mea-surements.We modify the original proposal to be robust to practical imperfections,and exper-imentally implement a scalable quantum state verification on two-qubit and four-qubit entangled states with non-adaptive local measurements.For all the tested states,the es-timated infidelity is inversely proportional to the number of measurements,which illus-trates optimal scaling defined in original theoretic proposal.Compared to the globally optimal strategy which requires nonlocal measurements,the efficiency in our experi-ment is only worse by a small constant factor.Furthermore,the measurement settings are also largely simplified.5.Classical Communication Enhanced Quantum State Verification.By introducing classical communication,we experimentally implement an adap-tive quantum state verification.The constant-factor is minimized from about 0.4 to 1.5 in this experiment,which means that 40%less measurements are required to achieve a certain value of ? compared to optimal non-adaptive local strategy.Our results indi-cate that classical communication significantly enhances the performance of quantum state verification,and leads to an efficiency that further approaches the globally optimal bound.