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.

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.

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.

Quantum resources such as superposition and entanglement have been used to provide unconditional key distribution, secret sharing and communication complexity reduction. In this letter we present a novel quantum information protocol for dining cryptographers problem and anonymous vote casting by a group of voters. We successfully demonstrate the experimental realization of the protocol using single photon transmission. Our implementation employs a flying particle scheme where a photon passes by the voters who perform a sequence of actions (unitary transformations) on the photonic state at their local stations.

We theoretically introduce and experimentally demonstrate the realization of a nonclassicality test that allows for arbitrarily low detection efficiency without invoking any extra assumptions as independence of the devices. Our test and its implementation is set in a prepare-and-measure scenario with an upper limit on the communication capacity of the channel through which the systems are communicated. The essence for our novel test is the use of two preparation and two measurement devices, which are randomly paired in each round. Our work opens up the possibility of experimental realizations of device independent protocols with current off-the-shelf technology.