Randomness is a fundamental feature of nature and essential for applications like cryptography and simulations. However, generating truly random numbers is challenging, as they must rely on unpredictable physical processes. This study demonstrates that quantum entangled particles can be used to certify the presence of genuine randomness, enabling a new type of cryptographically secure random number generator that does not require assumptions about device behavior. This randomness is guaranteed by a violation of Bell inequalities, which is impossible classically but achievable in quantum systems. The researchers conducted a proof-of-concept experiment using two entangled ytterbium ions separated by about 1 meter. They observed a Bell inequality violation of 2.414 with 99% confidence, generating 42 new random numbers. This result shows that randomness can be certified without detailed device models, laying the groundwork for future device-independent quantum information experiments. The study addresses the challenge of verifying true randomness, as no finite set of statistical tests can fully characterize it. Quantum theory is fundamentally random, but experimental randomness is often mixed with noise. The study shows that Bell inequality violations can certify the unpredictability of quantum measurement outcomes, providing a method to generate certified private randomness. The researchers developed a method to quantify the randomness of output strings using min-entropy, showing that the entropy of the outputs is bounded by a function of the Bell violation. This method is robust against adversarial attacks and does not require assumptions about device behavior. The results demonstrate that randomness can be expanded from a small seed to a longer string, with the efficiency improving as the number of trials increases. The study also discusses the implications of these results for quantum cryptography and randomness expansion. The results show that randomness can be generated from a small seed using quantum devices, with the security of the protocol depending on the violation of Bell inequalities. The study highlights the importance of device independence in ensuring the security of quantum protocols. The experimental results demonstrate the feasibility of generating certified randomness using quantum entangled particles, with the potential for future applications in secure communication and quantum computing. The study provides a foundation for further research into device-independent quantum information processing and the fundamental nature of randomness in quantum theory.Randomness is a fundamental feature of nature and essential for applications like cryptography and simulations. However, generating truly random numbers is challenging, as they must rely on unpredictable physical processes. This study demonstrates that quantum entangled particles can be used to certify the presence of genuine randomness, enabling a new type of cryptographically secure random number generator that does not require assumptions about device behavior. This randomness is guaranteed by a violation of Bell inequalities, which is impossible classically but achievable in quantum systems. The researchers conducted a proof-of-concept experiment using two entangled ytterbium ions separated by about 1 meter. They observed a Bell inequality violation of 2.414 with 99% confidence, generating 42 new random numbers. This result shows that randomness can be certified without detailed device models, laying the groundwork for future device-independent quantum information experiments. The study addresses the challenge of verifying true randomness, as no finite set of statistical tests can fully characterize it. Quantum theory is fundamentally random, but experimental randomness is often mixed with noise. The study shows that Bell inequality violations can certify the unpredictability of quantum measurement outcomes, providing a method to generate certified private randomness. The researchers developed a method to quantify the randomness of output strings using min-entropy, showing that the entropy of the outputs is bounded by a function of the Bell violation. This method is robust against adversarial attacks and does not require assumptions about device behavior. The results demonstrate that randomness can be expanded from a small seed to a longer string, with the efficiency improving as the number of trials increases. The study also discusses the implications of these results for quantum cryptography and randomness expansion. The results show that randomness can be generated from a small seed using quantum devices, with the security of the protocol depending on the violation of Bell inequalities. The study highlights the importance of device independence in ensuring the security of quantum protocols. The experimental results demonstrate the feasibility of generating certified randomness using quantum entangled particles, with the potential for future applications in secure communication and quantum computing. The study provides a foundation for further research into device-independent quantum information processing and the fundamental nature of randomness in quantum theory.