Researchers from the University of Science and Technology of China (USTC) of the Chinese Academy of Sciences revealed that not all forms of quantum nonlocality guarantee intrinsic randomness. They demonstrated that violating two-input Bell inequalities is both necessary and sufficient for certifying randomness, but this equivalence breaks down in scenarios involving multiple inputs. The study was published in Physical Review Letters.

Quantum mechanics is inherently probabilistic, and this intrinsic randomness has been leveraged for applications like random number generation. However, ensuring the security of these random numbers in real-world scenarios is challenging due to potential vulnerabilities in the devices used. 

Bell nonlocality, where particles exhibit correlations that cannot be explained by classical physics, offers a way to certify randomness without trusting the devices. Previous studies have shown that violating Bell inequalities can certify randomness in simple two-input, two-output systems. However, the applicability of this principle to more complex, multiple-input, multiple-output (MIMO) systems has been unclear.

Researchers conducted a comprehensive study to explore the relationship between Bell nonlocality and randomness in MIMO scenarios. They began by examining the theoretical foundations of Bell inequalities and their role in randomness certification. They discovered that while violating Bell inequalities was both necessary and sufficient for randomness certification in two-input systems, this relationship did not hold for more complex MIMO systems. 

Specifically, researchers found that certain Bell inequalities, such as the facet inequalities, could exhibit nonlocality without guaranteeing randomness. In contrast, another class of Bell inequalities, known as the Salavrakos-Augusiak-Tura-Wittek-Acín-Pironio (SATWAP) inequalities, consistently demonstrated a strong connection between nonlocality and randomness, even in MIMO scenarios.

To validate their theoretical findings, researchers designed and conducted experiments using high-dimensional photonic systems. They generated entangled photon pairs and performed measurements that violated various Bell inequalities. The experimental setup involved a continuous-wave laser and a type-II spontaneous parametric down-conversion process to create high-dimensional entangled states. They then used a series of wave plates and beam displacers to perform high-dimensional projection measurements. 

Researchers found that the SATWAP inequality was particularly effective in certifying randomness, achieving a private randomness generation rate of 1.867 bits per photon pair in a four-dimensional system. This result highlights the importance of selecting appropriate Bell inequalities for randomness certification in high-dimensional systems.

Moreover, researchers explored the practical implications of their findings. They demonstrated that the SATWAP inequalities were more sensitive to randomness certification compared to other inequalities like the facet inequalities. This sensitivity makes SATWAP inequalities a powerful tool for randomness certification, even in scenarios with imperfect detection efficiency. 

The findings of this study suggest that by using SATWAP inequalities, researchers can certify randomness within a broader range of detection efficiency, making it more feasible for practical applications.