Improved device-independent randomness expansion rates using two sided randomness

Abstract

A device-independent randomness expansion protocol aims to take an initial random string and generate a longer one, where the security of the protocol does not rely on knowing the inner workings of the devices used to run it. In order to do so, the protocol tests that the devices violate a Bell inequality and one then needs to bound the amount of extractable randomness in terms of the observed violation. The entropy accumulation theorem lower bounds the extractable randomness of a protocol with many rounds in terms of the single-round von Neumann entropy of any strategy achieving the observed score. Tight bounds on the von Neumann entropy are known for the one-sided randomness (i.e., where the randomness from only one party is used) when using the Clauser-Horne-Shimony-Holt (CHSH) game. Here we investigate the possible improvement that could be gained using the two-sided randomness. We generate upper bounds on this randomness by attempting to find the optimal eavesdropping strategy, providing analytic formulae in two cases. We additionally compute lower bounds that outperform previous ones and can be made arbitrarily tight (at the expense of more computation time). These bounds get close to our upper bounds, and hence we conjecture that our upper bounds are tight. We also consider a modified protocol in which the input randomness is recycled. This modified protocol shows the possibility of rate gains of several orders of magnitude based on recent experimental parameters, making device-independent randomness expansion significantly more practical. It also enables the locality loophole to be closed while expanding randomness in a way that typical spot-checking protocols do not.

12+35 pages, 6 figures, v3: new title and new lower bounds added, v4: correction to the x-axis of figure 3

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Cited by in corpus (8)

• Device-independent lower bounds on the conditional von Neumann entropy
• Device-independent quantum key distribution with arbitrarily small nonlocality
• The future of secure communications: device independence in quantum key distribution
• Expanding bipartite Bell inequalities for maximum multi-partite randomness
• Seedless extractors for device-independent quantum cryptography
• Composable framework for device-independent state certification
• Genuine multipartite entanglement is not necessary for standard device-independent conference key agreement
• Sequential Semi-Device-Independent Quantum Randomness Certification