{"id":"hexagon/2611.00094","pdf":"https://hexagonmath.org/pdf/2611.00094v1","url":"https://hexagonmath.org/abs/2611.00094v1","tags":["math-ph","msc:81P16","decoherence functionals","decoherent histories","optimal transport","quantum postselection","signed measures"],"score":0,"title":"Classical Extensions and Strongly Positive Realizations of Decoherent History Probabilities","domain":"quant-ph","source":"hexagon","authors":["Zhenyu Sun"],"reviews":0,"subject":"quant-ph","summary":"Probabilities on several decoherent families of histories may agree on shared events yet admit no classical extension to the Boolean algebra that the families generate. We characterize the strongly positive decoherence functionals that realize given local probabilities on a finite algebra. A covariance decomposition allows any signed extension to be prescribed at any attainable rank and gives the resulting increase in minimum trace. For two contexts, agreement on their intersection suffices for a strongly positive realization. On the bipartite graph of context atoms, the minimum negative…","category":"research","comments":0,"disputed":false,"division":"physics","mentions":0,"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}