Characterizing Fermionic Non-Gaussianity in the Sachdev-Ye-Kitaev Model via Replica Twist Entropy

arXiv:2610.10123 · quant-ph, cond-mat.stat-mech, cond-mat.str-el · Submitted 2026-10-07 · Read on arXiv

quant-ph, cond-mat.stat-mech, cond-mat.str-el

Submitted: 2026-10-07

Updated: 2026-10-07

Terminology

• Non-Gaussianity — 23× in this paper · explained in 2 episodes
• SYK Model — 14× in this paper · explained in 2 episodes
• Entanglement — 9× in this paper · explained in 3 episodes
• Symmetry Breaking — 7× in this paper · explained in 3 episodes
• Quantum Circuits — 3× in this paper · explained in 2 episodes
• Deep Thermalization — 2× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Additivity — 1× in this paper · explained in 1 episode
• Benchmark — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Entanglement Entropy — 1× in this paper · explained in 2 episodes
• First-Order Transition — 1× in this paper · explained in 2 episodes
• Multipartite Entanglement — 1× in this paper · explained in 2 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Stabilizer States — 1× in this paper · explained in 2 episodes
• Unitary Dynamics — 1× in this paper · explained in 2 episodes

Sources

• All pure fermionic non-Gaussian states are magic states for matchgate computations
• Gaussian decomposition of magic states for matchgate computations
• The fermionic linear optical extent is multiplicative for 4 qubit parity eigenstates
• Quantifying fermionic nonlinearity of quantum circuits
• One-body entanglement as a quantum resource in fermionic systems
• Classical simulation of noninteracting-fermion quantum circuits
• Lagrangian representation for fermionic linear optics
• Stabilizer Codes and Quantum Error Correction
• The Heisenberg Representation of Quantum Computers
• New measure of electron correlation
• Properties of nonfreeness: an entropy measure of electron correlation
• Quantifying fermionic interactions from the violation of Wick's theorem
• Optimal trace-distance bounds for free-fermionic states: Testing and improved tomography
• Measurement-induced transitions beyond Gaussianity: a single particle description
• 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
• Local classical correlations between physical electrons in Hubbard systems
• Fermionic Magic Resources of Quantum Many-Body Systems
• Computable fermionic non-Gaussianity from the covariance matrix
• Fermionic entropy: an efficiently measurable strong monotone for non-Gaussianity

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