Device-independent self-testing of unsharp measurements

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