Computing secure key rates for quantum key distribution with untrusted devices

Device-independent quantum key distribution (DIQKD) provides the strongest form of secure key exchange, using only the input-output statistics of the devices to achieve information-theoretic security. Although the security principles of DIQKD are now well-understood, it remains a technical challenge to derive reliable security bounds for generic DIQKD protocols beyond the standard ones. In this Letter, we present a numerical framework based on semi-definite programming that gives reliable lower bounds on the asymptotic secret key rate of any QKD protocol using untrusted devices. In particular, our method can in principle be utilized to find achievable secret key rates for any DIQKD protocol, based on the full input-output probability distribution instead of specialized Bell inequalities.