The State of the Art in Quantum Communications

This chapter shows a remarkable equivalence between the appearance of contextuality and the possibility of universal quantum calculation via the magic state that is call distillation, which is the main model for creating a quantum computer with tolerance to breakdown. Quantum contextuality is one of the fundamental notions in quantum mechanics. It has been shown that some tests of the Kochen‐Specker theorem, such as those based on rays, can be converted into a non‐state independent contextuality inequality. A constructive proof provides a general approach for determining an inequality independent of state non‐contextuality from a demonstration of the Kochen‐Specker theorem. Non‐local correlations between spatially separated systems have been discussed broadly in the context of the Einstein, Podolsky and Rosen paradox (EPR) and Bell inequalities. An inequality equivalent to Bell is introduced to clarify the correlations that can supervene between observables of independent degrees of freedom.