Self-testing in a constrained prepare-measure scenario sans assuming quantum dimension

Abstract: We present a device-independent (DI) self-testing protocol in a constrained prepare-measure scenario, based on the $n-$bit parity-oblivious multiplexing (POM) task. In this scenario, a parity-oblivious constraint is imposed on the preparations, allowing us to define a classical bound derived from a preparation noncontextual ontological model. We derive the optimal quantum success probability in the POM task devoid of assuming the dimension of the quantum system, an essential step towards DI self-testing, which has hitherto not been demonstrated in prepare-measure scenario. We demonstrate that the optimal quantum value exceeds preparation noncontextual bound and, as a result, this establishes DI self-testing of the preparations and the measurement devices. Furthermore, by explicitly constructing the required unitaries, we show that the optimal preparations and measurements in an unknown but finite dimensional Hilbert space, responsible for the observed input-output correlations, can be mapped, via an unitary, onto a known finite-dimensional quantum system. Our results thus pave the way for scalable, single system based DI certification protocols in the prepare-measure scenario.