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.

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.

Collaborative communication tasks such as random access codes (RACs) employing quantum resources have manifested great potential in enhancing information processing capabilities beyond the classical limitations. The two quantum variants of RACs, namely, quantum random access code (QRAC) and the entanglement-assisted random access code (EARAC), have demonstrated equal prowess for a number of tasks. However, there do exist specific cases where one outperforms the other. In this article, we study a family of 3 → 1 distributed RACs [19] and present its general construction of both the QRAC and the EARAC. We demonstrate that, depending on the function of inputs that is sought, if QRAC achieves the maximal success probability then EARAC fails to do so and vice versa.Moreover, a tripartite Bell-type inequality associated with the EARAC variants reveals the genuine multipartite nonlocality exhibited by our protocol. We conclude with an experimental realization of the 3 → 1 distributed QRAC that achieves higher success probabilities than the maximum possible with EARACs for a number of tasks.

Quantum communication with systems of dimension larger than two provides advantages in information processing tasks. Examples include higher rates of key distribution and random number generation. The main disadvantage of using such multi-dimensional quantum systems is the increased complexity of the experimental setup. Here, we analyze a not-so-obvious problem: the relation between randomness certification and computational requirements of the post-processing of experimental data. In particular, we consider semi-device independent randomness certification from an experiment using a four dimensional quantum system to violate the classical bound of a random access code. Using state-of-the-art techniques, a smaller quantum violation requires more computational power to demonstrate randomness, which at some point becomes impossible with today's computers although the randomness is (probably) still there. We show that by dedicating more input settings of the experiment to randomness certification, then by more computational postprocessing of the experimental data which corresponds to a quantum violation, one may increase the amount of certified randomness. Furthermore, we introduce a method that significantly lowers the computational complexity of randomness certification. Our results show how more randomness can be generated without altering the hardware and indicate a path for future semi-device independent protocols to follow.

The quantum Zeno effect (QZE) is the phenomenon where the unitary evolution of a quantum state is suppressed e.g. due to frequent measurements. Here, we investigate the use of the QZE in a class of communication complexity problems (CCPs). Quantum entanglement is known to solve certain CCPs beyond classical constraints. However, recent developments have yielded CCPs where super-classical results can be obtained using only communication of a single d-level quantum state (qudit) as a resource. In the class of CCPs considered here, we show quantum reduction of complexity in three ways: using i) entanglement and the QZE, ii) single qudit and the QZE, iii) single qudit. The final protocol is motivated by experimental feasibility, and we have performed a proof of concept experimental demonstration.