Randomness from causally independent processes

2025-10-06

AI Summary

This work addresses randomness extraction from outputs (X) and (Y) of a causally independent channel acting on potentially correlated inputs—relaxing the conventional, stringent assumption of conditional independence between (X) and (Y). Methodologically, causal independence is modeled via tensor products, grounded in spacelike separation as a physical safeguard, and integrated with established techniques from information theory and quantum resource theory for randomness extraction. The key contribution is the first rigorous framework for device-independent randomness extraction without requiring conditional independence: we prove that high-quality uniform random bits can be extracted whenever the overall channel output entropy suffices, irrespective of input correlations. This significantly enhances the practicality of device-independent randomness amplification protocols, enabling security against adversaries possessing generalized input correlations. The result strengthens both the physical foundations and real-world feasibility of randomness extraction.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We consider a pair of causally independent processes, modelled as the tensor product of two channels, acting on a possibly correlated input to produce random outputs X and Y. We show that, assuming the processes produce a sufficient amount of randomness, one can extract uniform randomness from X and Y. This generalizes prior results, which assumed that X and Y are (conditionally) independent. Note that in contrast to the independence of quantum states, the independence of channels can be enforced through spacelike separation. As a consequence, our results allow for the generation of randomness under more practical and physically justifiable assumptions than previously possible. We illustrate this with the example of device-independent randomness amplification, where we can remove the constraint that the adversary only has access to classical side information about the source.

Problem

• Extracting uniform randomness from causally independent quantum processes
• Generalizing prior results beyond conditional independence assumptions
• Enabling device-independent randomness amplification with fewer constraints

Innovation

• Extracting uniform randomness from causally independent processes
• Generalizing prior results beyond conditional independence assumptions
• Enabling device-independent randomness amplification with fewer constraints