{"paper":{"title":"Learning Local Fermionic Lindbladians under Parity Superselection","arxiv_id":"2610.00448","primary_cat":"quant-ph","submitted_at":"2026-09-30T17:57:21+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":"Parity superselection forbids direct measurement of odd Majorana observables.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.05,"main_claim_p":0.03,"quantitative":false,"quantitative_p":0.04,"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":0.94,"id":"s1","own":true,"role":"contribution","text":"We learn time-independent, parity-covariant, $k$-mode-local Lindbladians on $m$ modes using even preparations and measurements with uninterrupted short-time evolution.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.34,"quantitative":false,"quantitative_p":0.2,"role_probabilities":{"gap":0.0,"method":0.06,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.94,"interpretation":0.0}},{"i":2,"p":1.0,"id":"s2","own":true,"role":"method","text":"Internal markers turn odd probes into even observables, and pair measurements among three separated markers calibrate their dynamical contributions.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.86,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.27,"role_probabilities":{"gap":0.0,"method":1.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":3,"p":0.99,"id":"s3","own":true,"role":"method","text":"Signed Fierz inversion recovers canonical coefficients, while semidefinite fitting yields a valid generator.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.86,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.99,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.0}},{"i":4,"p":0.96,"id":"s4","own":true,"role":"result","text":"For finite-range models on known bounded-degree graphs with suitable marker access and a supplied weighted-strength bound $\\bar\\alpha$, entrywise error $\\varepsilon$ is achieved using $\\widetilde{\\mathcal{O}}(\\bar\\alpha^2\\varepsilon^{-2}\\log(m/\\delta))$ samples, without external modes or known nonzero coefficient locations.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.91,"main_claim_p":0.32,"quantitative":true,"quantitative_p":0.98,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.96,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.04,"interpretation":0.0}},{"i":5,"p":0.96,"id":"s5","own":true,"role":"result","text":"Recovery to diamond-norm error $\\varepsilon$ costs an additional factor $m^2$, matching lower bounds for short-time experiments on fresh systems up to logarithmic and fixed geometric factors.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.84,"main_claim_p":0.15,"quantitative":true,"quantitative_p":0.98,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.96,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.04}},{"i":6,"p":0.92,"id":"s6","own":true,"role":"result","text":"Without a supplied graph, one idle ancillary mode per system mode and potentially nonlocal pair operations give total absolute coefficient error at most $\\varepsilon$ per mode using $\\widetilde{\\mathcal{O}}_k(\\bar\\alpha^2\\mathsf d^2m^{\\lfloor k/2\\rfloor}\\varepsilon^{-2}\\log(m/\\delta))$ samples, under a supplied approximate coefficient-degree bound $\\mathsf d$ and controlled weak-coefficient tails.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.91,"main_claim_p":0.12,"quantitative":true,"quantitative_p":0.97,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.92,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.08,"interpretation":0.0}},{"i":7,"p":0.91,"id":"s7","own":true,"role":"result","text":"All guarantees hold with probability at least $1-\\delta$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.79,"main_claim_p":0.05,"quantitative":true,"quantitative_p":0.81,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.91,"background":0.0,"limitation":0.03,"future_work":0.0,"contribution":0.01,"interpretation":0.05}},{"i":8,"p":0.96,"id":"s8","own":true,"role":"result","text":"For geometric models, fixed-support even observables can be predicted with logarithmic system-size sample complexity at fixed time and accuracy.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.86,"main_claim_p":0.12,"quantitative":true,"quantitative_p":0.72,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.96,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.03,"interpretation":0.01}},{"i":9,"p":0.85,"id":"s9","own":true,"role":"contribution","text":"We also give finite-volume and exponential-tail extensions.","hedge":{"p":0.97,"label":"asserted"},"own_p":0.89,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.13,"background":0.0,"limitation":0.0,"future_work":0.02,"contribution":0.85,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":0.86,"text":"We learn time-independent, parity-covariant, $k$-mode-local Lindbladians on $m$ modes using even preparations and measurements with uninterrupted 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