Semi-device independent randomness certification using Mermin's proof of Kochen-Specker contextuality

Abstract: Randomness is a potential resource for cryptography, simulations and algorithms. Non-local correlations violating Bell's inequality certify the generation of bit strings whose randomness is guaranteed in a device-independent manner. We provide interesting semi-device independent randomness certification protocols by Kochen-Specker (KS) contextuality. For this, we first cast the Mermin's magic-square proof of KS contextuality for two-qubit system as a semi-device independent communication game in prepare-measure scenario. This provides a semi-device independent certification of two-bit of randomness. Further, by using Mermin's magic-star proof of KS theorem involving three-qubit system, we certify three-bit of randomness. We conjecture that our proposals can be extended to certify any arbitrary bit of randomness through a suitable KS proof of contextuality valid for higher dimensional system.