{"paper":{"title":"Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity","arxiv_id":"2610.02075","primary_cat":"quant-ph","submitted_at":"2026-10-01T17:15:11+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"Fermionic non-Gaussianity is a resource for universal quantum computation that can be generated by interactions in quantum many-body systems.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.06,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.03,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":0.88,"id":"s1","own":true,"role":"result","text":"Using the magic R\\'enyi 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.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.97,"main_claim_p":0.59,"quantitative":true,"quantitative_p":0.99,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.88,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.12,"interpretation":0.0}},{"i":2,"p":1.0,"id":"s2","own":true,"role":"result","text":"We also show that the MRE can differ extensively between states with identical covariance matrices.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.9,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.41,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":3,"p":0.95,"id":"s3","own":true,"role":"method","text":"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.","hedge":{"p":0.92,"label":"asserted"},"own_p":0.95,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.95,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.05,"interpretation":0.0}},{"i":4,"p":0.96,"id":"s4","own":true,"role":"result","text":"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.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.97,"main_claim_p":0.25,"quantitative":true,"quantitative_p":0.54,"role_probabilities":{"gap":0.0,"method":0.02,"result":0.96,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.0}},{"i":5,"p":0.98,"id":"s5","own":true,"role":"interpretation","text":"This transition represents a qualitative change in the non-Gaussianity of the state that is not 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