Random Numbers Certified by Bell's Theorem (0911.3427v3)

Abstract: Randomness is a fundamental feature in nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize mathematically, and their generation must rely on an unpredictable physical process. Inaccuracies in the theoretical modelling of such processes or failures of the devices, possibly due to adversarial attacks, limit the reliability of random number generators in ways that are difficult to control and detect. Here, inspired by earlier work on nonlocality based and device independent quantum information processing, we show that the nonlocal correlations of entangled quantum particles can be used to certify the presence of genuine randomness. It is thereby possible to design of a new type of cryptographically secure random number generator which does not require any assumption on the internal working of the devices. This strong form of randomness generation is impossible classically and possible in quantum systems only if certified by a Bell inequality violation. We carry out a proof-of-concept demonstration of this proposal in a system of two entangled atoms separated by approximately 1 meter. The observed Bell inequality violation, featuring near-perfect detection efficiency, guarantees that 42 new random numbers are generated with 99% confidence. Our results lay the groundwork for future device-independent quantum information experiments and for addressing fundamental issues raised by the intrinsic randomness of quantum theory.

• The paper demonstrates a device-independent method for generating cryptographically secure random numbers using entanglement and Bell violation.
• Using entangled atoms, the experiment achieved high detection efficiency and generated 42 new random bits certified by a Bell inequality violation.
• This method offers a secure, device-independent source of randomness with significant implications for cryptography and understanding quantum randomness.

Random Numbers Certified by Bell's Theorem: An Essay

The paper "Random Numbers Certified by Bell's Theorem" proposes a significant advancement in the field of quantum information processing by conceptualizing a novel approach to random number generation. The authors, spanning multiple esteemed institutions, present an innovative method to generate cryptographically secure random numbers by leveraging the intrinsic randomness within quantum systems, as certified by Bell's theorem.

Overview of Core Concepts

The fundamental premise of the paper is to exploit the nonlocal correlations present in entangled quantum particles. The authors propose that these correlations can provide an unequivocal certification of genuine randomness. Traditional random number generators (RNGs) often rely on unpredictable physical processes, but they can be vulnerable due to discrepancies in theoretical modeling or external adversarial manipulation. This vulnerability undermines the randomness, making it potentially predictable.

The authors introduce a device-independent framework where randomness is certified by the violation of a Bell inequality, specifically through the CHSH (Clauser-Horn-Shimony-Holt) form. The cornerstone of this approach is that the randomness is bound to the quantum mechanical principle that guarantees no local hidden variables can pre-determine the outcomes, as evidenced by the Bell violation.

Methodology and Experimental Demonstration

Central to the methodology is an experiment involving entangled states of two atoms separated by approximately one meter. The experiment achieves near-perfect detection efficiency, enabling the authors to demonstrate the generation of 42 new random bits with 99% confidence. This demonstration is not merely a theoretical exercise but an experimental proof-of-concept that adheres to the tenets of quantum theory.

The paper meticulously outlines the conditions required for non-interacting systems and unbiased input to maintain device-independence. The assumptions critical to this include: compliance with quantum mechanics, independence of input settings from quantum systems, and non-interaction between spatially separated systems during measurement.

Implications and Future Directions

From a cryptographic standpoint, the implications are profound. The authors lay the groundwork for RNGs that do not require assumptions about the internal workings of devices, hence achieving device independence. This model offers robust security against adversaries with unrestricted access to the internal state of the RNG devices.

Theoretically, the work underscores the inherent randomness of quantum mechanics and offers a tangible approach to explore the boundary between classical determinism and quantum indeterminacy. It also opens avenues for exploring randomness in strongly adversarial scenarios, providing a significant stepping stone for developing more intricate randomness expansion protocols.

In practical terms, the observable Bell violation and the derived min-entropy bounds establish an entropy source independent of classical randomness, potentially revolutionizing digital security frameworks.

Conclusion

The authors' work elegantly bridges a gap between theoretical quantum mechanics and applied cryptography, offering a new paradigm in random number generation. The paper not only affirms the intrinsic randomness inherent in quantum systems but also provides a blueprint for harnessing this randomness securely and efficiently in real-world applications. Looking forward, these findings are anticipated to catalyze advances in both theoretical quantum physics and practical cryptography, potentially leading to universally-composable secure randomness expansion protocols and more efficient quantum information processing systems.