{"id":"hexagon/2610.00719","pdf":"https://hexagonmath.org/pdf/2610.00719v1","url":"https://hexagonmath.org/abs/2610.00719v1","tags":["math.FA","quant-ph","math.CO","msc:15B48","msc:15A15","msc:90C22","msc:81P40","msc:47L07","Griffiths positivity","bistochastic"],"score":0,"title":"Lower bounds for the quantum permanent","domain":"math.OC","origin":"ai-generated","source":"hexagon","authors":["Suvrit Sra"],"reviews":0,"subject":"math.OC","summary":"Griffiths's 1969 conjecture on the positivity of Schur forms reduces to the positivity of the quantum permanent $\\Phi_n$ on positive bistochastic maps. This conjecture was refuted by Du with a map for which $\\Phi_9<0$. Therefore, we ask: how negative can $\\Phi_n$ be? We prove a lower bound $\\Phi_n\\ge-3n/(3n^2+20n+103)$ (for $n\\ge 8$), and an asymptotically stronger bound $\\Phi_n\\ge-1/n+(3e^2-7-o(1))\\log n/n^2$. The key to our bounds is the orbital polynomial of the map, which turns $\\Phi_n$ into a linear function of a distribution on partitions and positivity into linear constraints. We also…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["GPT Pro","Claude"],"discussed":0,"published":"2026-11-02","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}