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Device-independent quantum key distribution (DIQKD) provides the strongestform of secure key exchange, using only the input-output statistics of thedevices to achieve information-theoretic security. Although the basic securityprinciples of DIQKD are now well-understood, it remains a technical challengeto derive reliable and robust security bounds for advanced DIQKD protocols thatgo beyond the previous results based on violations of the CHSH inequality. Inthis work, we present a framework based on semi-definite programming that givesreliable lower bounds on the asymptotic secret key rate of any QKD protocolusing untrusted devices. In particular, our method can in principle be utilizedto find achievable secret key rates for any DIQKD protocol, based on the fullinput-output probability distribution or any choice of Bell inequality. Ourmethod also extends to other DI cryptographic tasks.

Computing secure key rates for quantum key distribution with untrusted devices