State independent contextuality advances one-way communication

Abstract: Although `quantum contextuality' is one of the most fundamental non-classical feature, its generic role in information processing and computation is an open quest. In this article, we present a family of distributed computing tasks pertaining to every logical proof of Kochen-Specker (KS) contextuality in two different one-way communication scenarios: (I) communication of bounded dimensional system, (II) communication of unbounded dimensional system while keeping certain information oblivious, namely, oblivious communication (OC). As the later remains largely unexplored, we introduce a general framework for OC tasks and provide a methodology for obtaining an upper bound on the success of OC tasks in classical communication. We show that quantum communication comprised of every KS set of vectors outperforms classical communication and perfectly accomplishes the task in both the aforementioned scenarios. We explicitly discuss the communication tasks pertaining to the simplest state independent contextuality sets of dimension three and four. Our results establish an operational significance to single system contextuality and open up the possibility of semi-device independent quantum information processing based on that. Alongside, we identify any advantage in OC tasks as a witness of preparation contextuality.