Device-independent quantum key distribution from generalized CHSH inequalities

Pavel Sekatski1, Jean-Daniel Bancal2, Xavier Valcarce3, Ernest Y.-Z. Tan4, Renato Renner4, and Nicolas Sangouard1,3

1Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
2Department of Applied Physics, University of Geneva, Chemin de Pinchat 22, 1211 Geneva, Switzerland
3Université Paris-Saclay, CEA, CNRS, Institut de physique théorique, 91191, Gif-sur-Yvette, France
4Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland

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Device-independent quantum key distribution aims at providing security guarantees even when using largely uncharacterised devices. In the simplest scenario, these guarantees are derived from the CHSH score, which is a simple linear combination of four correlation functions. We here derive a security proof from a generalisation of the CHSH score, which effectively takes into account the individual values of two correlation functions. We show that this additional information, which is anyway available in practice, allows one to get higher key rates than with the CHSH score. We discuss the potential advantage of this technique for realistic photonic implementations of device-independent quantum key distribution.

Device-independent quantum key distribution aims to distribute a secure key with devices that are largely uncharacterized and untrusted. Although it provides high security guarantees, the implementation of device-independent quantum key distribution is demanding in terms of experimental resources. For example, a source producing strongly entangled signals is needed to efficiently bound the eavesdropper information. The relevant measure of entanglement is the amount by which the measurement statistics violate a Bell inequality, such as the Clauser-Horne-Shimony-Holt (CHSH) inequality. Intuitively, a significant violation of this inequality guarantees that Alice and Bob’s state is close to a two-qubit maximally entangled state which cannot be shared with a third party. This, in turn, guarantees that information available to Eve –- the eavesdropper — about Alice and Bob’s measurement outcomes is bounded.
We here derive a security proof from generalisations of the CHSH inequality. While these generalisations exploit the same results than the standard CHSH test and are thus not more difficult to test in practice, we show that they allow one to get higher key rates than with the CHSH score while there are not more demanding in practice. We discuss the potential advantage of this technique for realistic photonic implementations of device-independent quantum key distribution.

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