Random access codes (RACs) are used by a party to, with limited communication, access an arbitrary subset of information held by another party. Quantum resources are known to enable RACs that break classical limitations. Here, we study quantum and classical RACs with high-level communication. We derive average performances of classical RACs and present families of high-level quantum RACs. Our results show that high-level quantum systems can significantly increase the advantage of quantum RACs over their classical counterparts. We demonstrate our findings in an experimental realization of a quantum RAC with four-level communication.

Random access codes are important for a wide range of applications in quantum information. However, their implementation with quantum theory can be made in two very different ways: (i) by distributing data with strong spatial correlations violating a Bell inequality, or (ii) using quantum communication channels to create stronger-than-classical sequential correlations between state preparation and measurement outcome. Here, we study this duality of the quantum realization. We present a family of Bell inequalities tailored to the task at hand and study their quantum violations. Remarkably, we show that the use of spatial and sequential quantum correlations imposes different limitations on the performance of quantum random access codes: sequential correlations can outperform spatial correlations. We discuss the physics behind the observed discrepancy between spatial and sequential quantum correlations.

Contextuality is a fundamental property of quantum theory and a critical resource for quantum computation. Here, we experimentally observe the arguably cleanest form of contextuality in quantum theory [A. Cabello et al., Phys. Rev. Lett. 111, 180404 (2013)] by implementing a novel method for performing two sequential measurements on heralded photons. This method opens the door to a variety of fundamental experiments and applications.

A communication game consists of distributed parties attempting to jointly complete a task with restricted communication. Such games are useful tools for studying limitations of physical theories. A theory exhibits preparation contextuality whenever its predictions cannot be explained by a preparation noncontextual model. Here, we show that communication games performed in operational theories reveal the preparation contextuality of that theory. For statistics obtained in a particular family of communication games, we show a direct correspondence with correlations in spacelike separated events obeying the no-signaling principle. Using this, we prove that all mixed quantum states of any finite dimension are preparation contextual. We report on an experimental realization of a communication game involving three-level quantum systems from which we observe a strong violation of the constraints of preparation noncontextuality.