Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals (1803.06219v1)

Abstract: From dice to modern complex circuits, there have been many attempts to build increasingly better devices to generate random numbers. Today, randomness is fundamental to security and cryptographic systems, as well as safeguarding privacy. A key challenge with random number generators is that it is hard to ensure that their outputs are unpredictable. For a random number generator based on a physical process, such as a noisy classical system or an elementary quantum measurement, a detailed model describing the underlying physics is required to assert unpredictability. Such a model must make a number of assumptions that may not be valid, thereby compromising the integrity of the device. However, it is possible to exploit the phenomenon of quantum nonlocality with a loophole-free Bell test to build a random number generator that can produce output that is unpredictable to any adversary limited only by general physical principles. With recent technological developments, it is now possible to carry out such a loophole-free Bell test. Here we present certified randomness obtained from a photonic Bell experiment and extract 1024 random bits uniform to within $10^{-12}$. These random bits could not have been predicted within any physical theory that prohibits superluminal signaling and allows one to make independent measurement choices. To certify and quantify the randomness, we describe a new protocol that is optimized for apparatuses characterized by a low per-trial violation of Bell inequalities. We thus enlisted an experimental result that fundamentally challenges the notion of determinism to build a system that can increase trust in random sources. In the future, random number generators based on loophole-free Bell tests may play a role in increasing the security and trust of our cryptographic systems and infrastructure.

Overview of "Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals"

This paper investigates the creation of certifiable random numbers harnessed from quantum processes, specifically through a loophole-free Bell test. The researchers focus on producing random bits that are unpredictable by any adversary, grounded on the principles of quantum physics that prohibit superluminal signals. Such randomness is pivotal for cryptography and secure communications, where assurances of unpredictability are crucial.

The team presents a practical methodology for generating randomness using photonic systems tested under well-controlled conditions. They report extracting 1024 random bits with a uniformity within $10^{-12}$, effectively demonstrating their approach's capability to maintain unpredictability against any local realism or faster-than-light communication scenarios.

Methodology and Results

The core of the paper is based on a loophole-free Bell test, which achieves high detection efficiency and spatial separation of measurement stations. This configuration is critical to ensuring that observed quantum correlations cannot be explained by classical physics with hidden variables.

• Protocol Design: The authors detail the development of a new protocol, which is particularly optimized for apparatuses with low per-trial violation of Bell inequalities. This optimization allows effective randomness certification, even when the Bell inequality violation is marginal in individual trials.
• Experiment Execution: The experimental setup involves pairs of entangled photons distributed to two distant measurement stations named Alice and Bob. Measurement choices are made randomly, and outcomes are space-like separated, sustaining the conditions for a valid Bell test.
• Randomness Certification: The randomness obtained is evaluated under assumptions of independence and non-signaling between measurement settings and outcomes. Any violation of these assumptions would imply possible communication faster than the speed of light.
• Numerical Results: Five datasets were collected with a significant amount of data yielding 1024 random bits verified to be uniform to within $10^{-12}$. Additionally, more randomness was harvested from earlier experiments with different error thresholds.

Implications and Future Work

The implications of this research extend to strengthening quantum cryptographic processes by generating randomness independently of device-based assumptions. The method's device-independent nature is particularly appealing for applications demanding high trust levels in random number generation, such as secure communications and cryptographic systems.

The authors speculate on leverages possible adaptive protocols to respond to experimental drifts dynamically. They also point out the necessity for future studies to consider quantum side information, which may warrant more conservative randomness estimates. Enhancements in experimental setups are anticipated to amplify the violation margins of Bell inequalities and increase trial rates, paving the way for higher-volume high-certainty randomness extraction.

Theoretical Considerations

From a theoretical perspective, this paper rigorously tackles explanations for ensuring unpredictability of randomness and offers a comprehensive criterion for evaluating randomness under varying settings distributions. The protocol soundness theorem and entropy production theorem underline the safe extraction of randomness, accommodating imperfections in settings randomness.

Conclusion

The paper is a significant addition to quantum measurement standards, advocating that with current technologies, loophole-free Bell tests can harness randomness with minimal assumptions. Their method demonstrates promise for robust, device-independent generation of random numbers, marking a crucial step towards enhancing the reliability of cryptographic applications.