Testing quantum Gaussianity with constant sample complexity

arXiv:2609.40270 · quant-ph · Submitted 2026-09-30 · Read on arXiv

quant-ph

Submitted: 2026-09-30

Updated: 2026-09-30

Comments: 7 + 77 pages, 2 + 1 figures

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

Terminology

• Trace — 22× in this paper · explained in 2 episodes
• Robustness — 16× in this paper · explained in 5 episodes
• Sample Complexity — 16× in this paper · explained in 15 episodes
• Gradient Flow — 15× in this paper · explained in 2 episodes
• Non-Gaussianity — 13× in this paper · explained in 2 episodes
• Hilbert Space — 9× in this paper · explained in 2 episodes
• Trace Distance — 9× in this paper · explained in 3 episodes
• Accuracy — 4× in this paper · explained in 1 episode
• Spectral Gap — 4× in this paper · explained in 5 episodes
• Entanglement — 2× in this paper · explained in 4 episodes
• Fidelity — 2× in this paper · explained in 2 episodes
• Stabilizer States — 2× in this paper · explained in 2 episodes
• Adaptation — 1× in this paper · explained in 1 episode
• Commentary — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Quantization — 1× in this paper · explained in 12 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes
• Wigner function — 1× in this paper · explained in 2 episodes

Sources

• Fermionic non-Gaussianity via Bell sampling: monotones and efficient quantum algorithms
• Discrete Quantum Gaussians and Central Limit Theorem
• Quantum Higher Order Fourier Analysis and the Clifford Hierarchy
• Quantum Computation, Complexity, and Many-Body Physics
• Quadratic tensors as a unification of Clifford, Gaussian, and free-fermion physics
• Optimal trace-distance bounds for free-fermionic states: Testing and improved tomography
• Optimal tomography of bosonic and fermionic Gaussian states
• Practical Tests and Witnesses of Fermionic non-Gaussianity
• Is it Gaussian? Testing bosonic quantum states
• Fermionic Gaussian Testing and Non-Gaussian Measures via Convolution
• Measuring Non-Gaussian Magic in Fermions: Convolution, Entropy, and the Violation of Wick's Theorem and the Matchgate Identity
• A random purification channel for arbitrary symmetries with applications to fermions and bosons
• Fermionic entropy: an efficiently measurable strong monotone for non-Gaussianity
• Efficient Measurement of Bosonic Non-Gaussianity
• Measuring non-Gaussianity with Correlation
• Uncovering Non-Gaussianity through Multi-Copy Symmetries
• Testing matrix product states
• An Optimal Analysis of the Product Test
• Fermionic tomography and learning
• Learning the closest Slater determinant

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• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity