Device-independent quantum key distribution with arbitrarily small nonlocality

TL;DR

This paper demonstrates that device-independent quantum key distribution can be achieved with arbitrarily small nonlocality, challenging previous assumptions and opening new possibilities for cryptographic protocols.

Contribution

The authors show that no lower bound on nonlocality exists for DIQKD, providing schemes with correlations close to local and achieving maximum key rates with minimal nonlocality.

Findings

Key can be generated with correlations arbitrarily close to local

Maximum of 1 bit of key per entangled qubit pair achieved

Existence of quantum correlations with perfect key and randomness at low CHSH violation

Abstract

Device-independent quantum key distribution (DIQKD) allows two users to set up shared cryptographic key without the need to trust the quantum devices used. Doing so requires nonlocal correlations between the users. However, in [Phys. Rev. Lett. 127, 050503 (2021)] it was shown that for known protocols nonlocality is not always sufficient, leading to the question of whether there is a fundamental lower bound on the minimum amount of nonlocality needed for any DIQKD implementation. Here we show that no such bound exists, giving schemes that achieve key with correlations arbitrarily close to the local set. Furthermore, some of our constructions achieve the maximum of 1 bit of key per pair of entangled qubits. We achieve this by studying a family of Bell-inequalities that constitute all self-tests of the maximally entangled state with a single linear Bell expression. Within this family there exist non-local correlations with the property that one pair of inputs yield outputs arbitrarily close to perfect key. Such correlations exist for a range of Clauser-Horne-Shimony-Holt (CHSH) values, including those arbitrarily close to the classical bound. Finally, we show the existence of quantum correlations that can generate both perfect key and perfect randomness simultaneously, whilst also displaying arbitrarily small CHSH violation; this opens up the possibility of a new class of cryptographic protocol.