| Summary: | Quantum communication and quantum computation form the two crucial facets of quantum information theory. While entanglement and its manifestation as Bell non-locality have been proved to be vital for communication tasks, contextuality (a generalisation of Bell non-locality) has shown to be the crucial resource behind various models of quantum computation. The practical and fundamental aspects of these non-classical resources are still poorly understood despite decades of research. We explore non-classical correlations exhibited by some of these quantum as well as super-quantum resources in the <i>n</i>-cycle setting. In particular, we focus on correlations manifested by Kochen⁻Specker⁻Klyachko box (KS box), scenarios involving <i>n</i>-cycle non-contextuality inequalities and Popescu⁻Rohlrich boxes (PR box). We provide the criteria for optimal classical simulation of a KS box of arbitrary <i>n</i> dimension. The non-contextuality inequalities are analysed for <i>n</i>-cycle setting, and the condition for the quantum violation for odd as well as even <i>n</i>-cycle is discussed. We offer a simple extension of even cycle non-contextuality inequalities to the phase space case. Furthermore, we simulate a generalised PR box using KS box and provide some interesting insights. Towards the end, we discuss a few possible interesting open problems for future research. Our work connects generalised PR boxes, arbitrary dimensional KS boxes, and <i>n</i>-cycle non-contextuality inequalities and thus provides the pathway for the study of these contextual and nonlocal resources at their junction.
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