Device-independent self-testing of unsharp measurements

Abstract

Semi-device-independent certification of an unsharp instrument has recently been demonstrated [New J. Phys. 21, 083034 (2019)] based on the sequential sharing of quantum advantages in a prepare-measure communication game by assuming the system to be qubit. In this work, we provide device-independent (DI) self-testing of the unsharp instrument through the quantum violation of two Bell inequalities where the devices are uncharacterized and the dimension of the system remains unspecified. We introduce an elegant sum-of-squares approach to derive the dimension-independent optimal quantum violation of Bell inequalities which plays a crucial role. Note that the standard Bell test cannot self-test the post-measurement states and consequently cannot self-test unsharp instrument. The sequential Bell test possess the potential to self-test an unsharp instrument. We demonstrate that there exists a trade-off between the maximum sequential quantum violations of the Clauser-Horne-Shimony-Holt inequality, and they form an optimal pair that enables the DI self-testing of the entangled state, the observables, and the unsharpness parameter. Further, we extend our study to the case of elegant Bell inequality and we argue that it has two classical bounds - the local bound and the non-trivial preparation non-contextual bound, lower than the local bound. Based on the sharing of preparation contextuality by three independent sequential observers, we demonstrate the DI self-testing of two unsharpness parameters. Since an actual experimental scenario involves losses and imperfection, we demonstrate robustness of our certification to noise.

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Cited by in corpus (9)

• Quantum Correlation Sharing: A Review On Recent Progress From Nonlocality To Other Non-Classical Correlations
• Unbounded Sharing of Nonlocality Using Projective Measurements
• Self-testing of multiple unsharpness parameters through sequential violations of non-contextual inequality
• Towards Necessary and sufficient state condition for violation of a multi-settings Bell inequality
• Security of Device-independent Quantum Key Distribution under Sequential Attack
• Semi-device-independent self-testing of unitary operations
• Robust self-testing and certified randomness based on chained Bell inequality
• Designing generalized elegant Bell inequalities in higher dimensions from a Tsirelson bound
• Robust device-independent characterization of sharpness and incompatibility of unsharp instruments