Device independent dimension witnesses (DW) are a remarkable way to test the dimension of a quantum system in a prepare-and-measure scenario imposing minimal assumptions on the internal features of the devices. However, as the dimension increases, the major obstacle in the realization of DW arises due to the requirement of many outcome quantum measurements. In this article, we propose a new variant of a widely studied communication task (random access code) and take its average payoff as the DW. The presented DW applies to arbitrarily large quantum systems employing only binary outcome measurements.
I. INTRODUCTIONRealizing higher-dimensional quantum systems with full control is one of the crucial barriers towards implementing many quantum information processing protocols and testing the foundations of physics. While the process of quantum tomography allows us to reconstruct a quantum system, however, it requires the assumption of fully characterized measurement devices. The device independent framework [1,2] in a prepare-and-measure experiment provides a methodology to obtain a lower bound on the dimension without assuming the internal features of the devices. Moreover, quantum advantages in information processing, for example, quantum communication complexity [3,4] are linked to this approach. Despite its merits, implementing device independent dimension witnesses (DWs) for higher dimensional quantum systems [5-9] faces several complications.