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Device-independent quantum key distribution allows for proving the securityof a shared cryptographic key between two distant parties with potentiallyuntrusted devices. The security proof is based on the measurement outcomestatistics (correlation) of a Bell experiment, and security is guaranteed bythe laws of quantum theory. While it is known that the observed correlationmust be Bell non-local in order to prove security, recent results show thatBell non-locality is in general not sufficient for standard device-independentquantum key distribution. In this work, we show that conversely, there is nolower bound on the amount of non-locality that is sufficient fordevice-independent quantum key distribution. Even more so, we show that fromcertain correlations that exhibit arbitrarily small non-locality, one can stillextract unbounded device-independent key rates. Therefore, a quantitativerelation between device-independent key rates and Bell non-locality cannot bedrawn in general. Our main technique comprises a rigorous connection betweenself-testing and device-independent quantum key distribution, applied to arecently discovered family of Bell inequalities with arbitrarily manymeasurement outcomes.

Unbounded device-independent quantum key rates from arbitrarily small non-locality