Self-testing of different entanglement resources via fixed measurement settings

Self-testing, which refers to device-independent characterization of the state and the measurement, enables the security of a quantum information processing task certified independently of the operation performed inside the devices. Quantum states lie at the core of self-testing as key resources. However, for different entangled states, usually, different measurement settings should be taken in self-testing recipes. This may lead to the redundancy of measurement resources. In this work, we use fixed two-binary measurements and answer the question of which states can be self-tested with the same settings. By investigating the structure of generalized tilted-Clauser-Horne-Shimony-Holt Bell operators with the sum-of-squares decomposition method, we show that a family of two-qubit entangled states can be self-tested with the same measurement settings. The robustness analysis indicates that our scheme is feasible for practical experiment instruments. Moreover, our results can be applied to various quantum information processing tasks.

Automated summary

In this study, we investigate which states can be self-tested with the same measurement settings by using fixed two-binary measurements. By analyzing the structure of generalized tilted-Clauser-Horne-Shimony-Holt Bell operators with the sum-of-squares decomposition method, we demonstrate that a specific class of two-qubit entangled states can be self-tested with the same measurement settings. The robustness analysis confirms the feasibility of our scheme for practical experiment instruments, and the results have potential applications in various quantum information processing tasks.