Quantum Cryptographic Security from Contextuality

Quantum mechanics is contextual, that is, the outcome of a measurement does depend on how that value is measured. This somewhat bizarre, non-classical feature is a consequence of the Kochen-Specker theorem, which asserts that there is no non-contextual hidden variable theory that reproduces quantum theory. Contextuality is a property of quantum systems with Hilbert spaces of d > 2, as it can be shown that a consistent non-contextual assignment of values is possible for qubits. Contextuality via the Kochen-Specker theorem also serves as a precondition for secure quantum key distribution in EPR-type protocols such as E91 and BBM92. In these cryptographic schemes, security is proven by violations of inequalities that also contradict assumptions in local realistic theories of the Kochen-Specker type. Device-independent security from contextuality is also demonstrated by considering a distributed box of Peres-Mermin observables for the Kochen Specker theorem. The security of the corresponding key distribution protocol is certified by checking for not-too-strong violations of Bell inequalities.