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About this paper
Mihály Weiner
A geometric framework is developed for comparing classical, quantum, and general probabilistic state-discrimination behavior across every nonempty subfamily of a fixed state list. The work exactly characterizes the GPT and classical profile regions, solves the three-state case, and establishes a quantitative separation with the witness β: classical profiles satisfy β≤0, quantum profiles obey β≤(3√15−9)/4≈0.6547, while unrestricted GPTs reach β=1.
Key insights
- Classical profiles are exactly normalized coverage functions, with classicality determined by nonnegative Möbius coefficients and corresponding facet inequalities.
- For three hypotheses, the functional β=t−x−y−z captures the first classical–quantum–GPT separation: classical profiles have β≤0, whereas GPT profiles can reach β=1.
- Uniform-prior profiles can conceal nonclassicality: a quantum example has a classically reproducible discrete profile but violates a classical inequality when arbitrary prior weights are allowed.
Summary by alphaXiv.
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