Contextuality of quantum theory, discovered by Kochen and Specker, is known to manifest itself as violation of contextual inequalities. This violation has the same mathematical root as the violation of Bell inequalities.
Bell inequalities are known to exhibit the property of monogamy, which has been useful in secure quantum key distribution, interactive proof systems, and in the emergence of a local realistic description for correlations in the macroscopic domain.
We first show that this Bell monogamy can be derived from the principle of no-signalling, which generalizes to Gleanson's principle of no-disturbance.
We use this no disturbance-principle to prove that monogamy also exists for contextual inequalities.
This work was done in collaboration with Ravishankar Ramanathan, Pawel Kurzynski, and Dagomir Kaszlikowski.