Device-independent randomness extraction for arbitrarily weak min-entropy source

Abstract

Expansion and amplification of weak randomness plays a crucial role in many security protocols. Using quantum devices, such procedure is possible even without trusting the devices used, by utilizing correlations between outcomes of parts of the devices. We show here how to extract random bits with an arbitrarily low bias from a single arbitrarily weak min-entropy source in a device independent setting. To do this we use Mermin devices that exhibit super-classical correlations. Number of devices used scales polynomially in the length of the random sequence $n$. Our protocol is robust, it can tolerate devices that malfunction with a probability dropping polynomially in $n$ at the cost of a minor increase of the number of devices used.

5 pages + 3 pages supplementary material

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• Rigidity of quantum steering and one-sided device-independent verifiable quantum computation
• Robust Device-Independent Randomness Amplification with Few Devices
• Maximal nonlocality from maximal entanglement and mutually unbiased bases, and self-testing of two-qutrit quantum systems
• Device-independent two-party cryptography secure against sequential attacks
• Robust self-testing of two-qubit states
• Measurement-dependent locality beyond i.i.d
• Semi-Device-Independent Random Number Generation with Flexible Assumptions
• A versatile construction of Bell inequalities for the multipartite scenario
• An explicit classical strategy for winning a ${\mathrm{CHSH}}_q$ game
• Tight bound on the classical value of generalized Clauser-Horne-Shimony-Holt games
• Trade-off relations between measurement dependence and hidden information for factorizable hidden variable models