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

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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.

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Data availibility statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: There is no data because every calculation in this paper is analytical. No additional data is used and hence nothing to be deposited.]

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Acknowledgements

AKP acknowledges the support from the project DST/ICPS/QuEST/2018/Q-42.

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Correspondence to A. K. Pan.

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Pan, A.K. Semi-device-independent randomness certification using Mermin’s proof of Kochen–Specker contextuality. Eur. Phys. J. D 75, 98 (2021). https://doi.org/10.1140/epjd/s10053-021-00105-8

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