Semi-device-independent certification of multiple unsharpness parameters through sequential measurements

Based on a sequential communication game, semi-device-independent certification of an unsharp instrument has recently been demonstrated [K. Mohan, A. Tavakoli, and N. Brunner, New J. Phys. 21, 083034 (2019)]. In this paper, we provide self-testing protocols in the prepare-measure scenario to certify multiple unsharpness parameters along with states measurement settings. This is achieved through quantum advantage shared by independent observers suitable game known as parity-oblivious random-access code. We demonstrate that three-bit code at most three can sequentially share advantage. The optimal pair (triple) advantages enables us uniquely qubit states, settings, parameter(s). practical implementation given protocol involves inevitable losses. suboptimal scenario, derive certified interval within which specific parameter be confined. extend our treatment four-bit case show two for system. Further, outline argue four two-qubit system, thereby enabling parameters.