Computing secure key rates for quantum cryptography with untrusted devices

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