Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity

Abstract:Fermionic non-Gaussianity is a resource for universal quantum computation that can be generated by interactions in quantum many-body systems. Using the magic Rényi entropy (MRE) as a measure of non-Gaussianity, we derive its universal upper bound and Haar mean, proving that typical Haar-random states attain the maximal MRE density of $\ln(4/3)$ per Majorana in the large-system limit. We also show that the MRE can differ extensively between states with identical covariance matrices. To investigate how non-Gaussianity grows toward this maximal density, we evolve a Gaussian state in imaginary and real time under the Sachdev-Ye-Kitaev Hamiltonian. By varying the imaginary- and real-time durations, we identify a first-order transition marked by a kink in the MRE density and spontaneous breaking of the permutation symmetry among the four copies used to evaluate the MRE. This transition represents a qualitative change in the non-Gaussianity of the state that is not reflected in the thermal free energy.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el)

arXiv:2610.02075 [quant-ph]

(or arXiv:2610.02075v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.02075 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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