Device-independent (DI) protocols have experienced significant progress in
recent years, with a series of demonstrations of DI randomness generation or
expansion, as well as DI quantum key distribution. However, existing security
proofs for those demonstrations rely on a typical assumption in DI
cryptography, that the devices do not leak any unwanted information to each
other or to an adversary. This assumption may be difficult to perfectly enforce
in practice. While there exist other DI security proofs that account for a
constrained amount of such leakage, the techniques used are somewhat unsuited
for analyzing the recent DI protocol demonstrations. In this work, we address
this issue by studying a constrained leakage model suited for this purpose,
which should also be relevant for future similar experiments. Our proof
structure is compatible with recent proof techniques for flexibly analyzing a
wide range of DI protocol implementations. With our approach, we compute some
estimates of the effects of leakage on the keyrates of those protocols, hence
providing a clearer understanding of the amount of leakage that can be allowed
while still obtaining positive keyrates.Comment: Changelog: more detailed analysis of conditioning on acceptance
events, implemented tighter version of fidelity constraints and replaced SDP
formulation with more stable approach, updated figures accordingl