On Polytopes and Convex Sets Associated with Graphical Models in Classical and Quantum...
Talkat Quantum Physics and Statistical Causal Models (Simons Institute workshop, 2022) · 2022-04-27..04-29
summary
Defines the local marginal polytope and shows it is typically strictly larger than the true marginal polytope, proves that points in the larger set correspond to valid configurations in graph covers (double, triple, n‑fold; one toy double cover yields 32 edge choices), and connects that gap to why the sum-product algorithm (loopy belief propagation) gives good but suboptimal decodings used for LDPC codes in 5G. Extends the same polytope/cover machinery to normal factor graphs and quantum mass functions to reframe Bell‑type paradoxes and decoherence.
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