When are bosonic Gaussian states classical to learn?

Imagine you're developing a system that needs to understand and predict behaviors in both quantum and classical realms, like in advanced sensing technologies. Currently, learning from quantum systems, especially bosonic Gaussian states, is complex and often requires more data than learning from classical systems. This is problematic because it limits the efficiency and applicability of quantum technologies in real-world scenarios, particularly when trying to bridge the gap between quantum and classical information processing. The authors approach this challenge by examining the conditions under which these quantum states can be learned with fewer samples, akin to classical Gaussian distributions. They find that cold Gaussian states, which are close to the vacuum state, require significantly more data to learn than their classical counterparts, while warm Gaussian states, influenced by thermal fluctuations, can be learned with a sample complexity that matches classical learning. This insight not only provides a clearer understanding of the quantum-to-classical transition but also has practical implications for designing better quantum sensors and learning algorithms.

The work establishes a new understanding of the learnability of quantum states in relation to classical states.

The results are backed by rigorous mathematical proofs and clear conditions for learnability.