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Kochen-Specker (KS) theorem lies at the heart of the foundations of quantummechanics. It establishes impossibility of explaining predictions of quantumtheory by any noncontextual ontological model. Spekkens generalized the notionof KS contextuality in [Phys. Rev. A 71, 052108 (2005)] for arbitraryexperimental procedures (preparation, measurement, and transformationprocedure). Interestingly, later on it was shown that preparation contextualitypowers parity-oblivious multiplexing [Phys. Rev. Lett. 102, 010401 (2009)], atwo party information theoretic game. Thus, using resources of a givenoperational theory, the maximum success probability achievable in such a gamesuffices as a \emph{bona-fide} measure of preparation contextuality for theunderlying theory. In this work we show that preparation contextuality inquantum theory is more restricted compared to a general operational theoryknown as \emph{box world}. Moreover, we find that this limitation of quantumtheory implies the quantitative bound on quantum nonlocality as depicted by theCirel'son bound.

Limited preparation contextuality in quantum theory and its relation to the Cirel'son bound