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Communication games are one of the widely used tools that are designed todemonstrate quantum supremacy over classical resources. In that, two or moreparties collaborate to perform an information processing task to achieve thehighest success probability of winning the game. We propose a specifictwo-party communication game in the prepare-measure scenario that relies on anencoding-decoding task of specific information. We first demonstrate thatquantum theory outperforms the classical preparation non-contextual theory, andthe optimal quantum success probability of such a communication game enablesthe semi-device-independent certification of qubit states and measurements.Further, we consider the sequential sharing of quantum preparationcontextuality and show that, at most, two sequential observers can share thequantum advantage. The sub-optimal quantum advantages for two sequentialobservers form an optimal pair that certifies a unique value of the unsharpnessparameter of the first observer. Since the practical implementation inevitablyintroduces noise, we devised a scheme to demonstrate the robust certificationof the states and unsharp measurement instruments of both the sequentialobservers.

Robust certification of unsharp instruments through sequential quantum advantages in a prepare-measure communication game