When are bosonic Gaussian states classical to learn?
Cold bosonic Gaussian states need more samples to learn than classical Gaussians; warm states match.
The paper asks when an n-mode bosonic Gaussian state can be learned with the sample complexity of a classical 2n-variate Gaussian. States whose covariance is near the vacuum require Ω(n³) copies under single-copy measurements, above the classical Θ(n²) bound, and the gap persists with few-copy entangled measurements. Once thermal fluctuations exceed vacuum noise by a constant, non-adaptive unentangled heterodyne measurements achieve Θ(n²) copies.
- Cold near-vacuum states require Ω(n³) copies for single-copy tomography.
- Hardness remains when few-copy entangled measurements are allowed.
- Warm states with constant thermal noise match Θ(n²) classical complexity.
- Tight bound is achieved by non-adaptive heterodyne measurements.
From the original article
1 min read at arxiv.orgA fundamental question in physics is: When does classical behavior emerge from quantum systems? Bosonic Gaussian states provide a natural setting to explore this quantum-classical boundary, as they capture both the classical field behavior and the intrinsic quantum nature of light. Here, we address this problem from a learning-theoretic perspective by asking: When are bosonic Gaussian states classical to learn?
By Senrui Chen · arxiv.org
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