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

Quantum Physics