Quantum technologies provide solutions for information processing tasks that are not achievable with classical methods. Basic resources like the creation of private and unexpected random numbers or a secure key that is shared between two parties are examples of these capabilities. However, estimating the amount of generated randomness or generated key is not easy. This work presents a thorough analysis of quantum randomness generation (QRNG) and quantum key distribution (QKD) protocols using various Bell inequalities. We specifically focus on the so-called modified Clauser-Horne-Shimony-Holt and three-setting Braunstein-Caves expressions, demonstrating their efficiency in both use cases due to their robustness against noise and high asymptotic generation rates. Our findings highlight that these two inequalities not only perform best in terms of certified randomness and secure key rates, but also enable the use of the same experimental setup for both QRNG and QKD. This dual functionality offers significant design advantages for large-scale implementation. We also include an analysis of finite-data effects using the entropy accumulation theorem, providing a realistic assessment of the protocols. The insights of the investigation contribute to the development of more efficient and versatile quantum cryptography systems based on entangled photons.

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• Quantum communication
• Quantum protocols