Rui Soares Barbosa - Contextuality as a resource yielding quantum advantage

In contrast to classical physics, in quantum mechanics not all observables can be measured and be assigned values simultaneously. Contexts of compatible observables provide multiple partial, classical perspectives on a quantum system. Any two of these contexts fit nicely together, but they cannot all be pasted consistently into a global perspective. This gap between local consistency and global inconsistency is what constitutes contextuality, a concept that is elegantly expressed in the language of sheaf theory.
 
A fundamental phenomenon of quantum mechanics setting it apart from classical physical theories, recent results have also established its rôle as a source of advantage in informatic tasks, including the additional computational power in some specific schemes for quantum computation.
 
We’ll introduce the notion of contextuality and consider it from the point of view of resource theory, with an emphasis on operations that combine contextual systems and control their use as resources, and on quantum advantages in computational and information-processing tasks afforded by the presence of contextuality.