When are bosonic Gaussian states classical to learn?

arXiv:2609.26705 · quant-ph, cs.IT, cs.LG, math-ph, math.IT, math.MP · Submitted 2026-09-22 · Read on arXiv

quant-ph, cs.IT, cs.LG, math-ph, math.IT, math.MP

Submitted: 2026-09-22

Updated: 2026-09-22

Comments: comments welcome

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Trace — 65× in this paper · explained in 2 episodes
• Trace Distance — 32× in this paper · explained in 3 episodes
• Sample Complexity — 24× in this paper · explained in 15 episodes
• Wigner function — 8× in this paper · explained in 2 episodes
• Entanglement — 6× in this paper · explained in 3 episodes
• Hilbert Space — 6× in this paper · explained in 2 episodes
• Anticoncentration — 5× in this paper · explained in 1 episode
• Fidelity — 4× in this paper · explained in 2 episodes
• Gibbs State — 3× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Adaptivity — 2× in this paper · explained in 1 episode
• Benchmarking — 2× in this paper · explained in 3 episodes
• Hamiltonian Learning — 2× in this paper · explained in 2 episodes
• Homogeneity — 2× in this paper · explained in 2 episodes
• Fisher Information — 1× in this paper · explained in 3 episodes
• Foundations of Computer Science — 1× in this paper
• Generalization — 1× in this paper · explained in 13 episodes
• No-Go Theorem — 1× in this paper · explained in 2 episodes
• Quantization — 1× in this paper · explained in 12 episodes
• Quantum Physics — 1× in this paper · explained in 10 episodes
• Spectral Gap — 1× in this paper · explained in 5 episodes

Sources

• Energy-independent tomography of Gaussian states
• Optimal tomography of bosonic and fermionic Gaussian states
• The log log jam in Gaussian state tomography
• Instance-optimal high-precision shadow tomography with few-copy measurements: A metrological approach
• An optimal tradeoff between entanglement and copy complexity for state tomography
• What resources are needed for optimal learning of bosonic Gaussian states?
• The total variation distance between high-dimensional Gaussians with the same mean
• On estimates of trace-norm distance between quantum Gaussian states
• Evaluating capacities of Bosonic Gaussian channels
• Tight Lower Bounds for State Tomography with Limited Entanglement
• Advances in quantum learning theory with bosonic systems
• Phase space formalism for quantum estimation of Gaussian states
• Optimal Low-Rank Quantum State Tomography with Bounded-Sample Joint Measurements
• Mixed state tomography reduces to pure state tomography
• When quantum thermal states look classical
• Entangled measurements are necessary for optimal tomography of mixed fermionic Gaussian states and of bosonic Gaussian states near the vacuum

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