Incompatibility in General Probabilistic Theories, Generalized Spectrahedra, and Tensor Norms

In this work, we investigate measurement incompatibility in general probabilistic theories (GPTs). We show several equivalent characterizations of compatible measurements. The first is terms the positivity associated maps. second relates compatibility to inclusion certain generalized spectrahedra. For this, extend theory free spectrahedra ordered vector spaces. third characterization connects dichotomic measurements ratio tensor crossnorms Banach use these study amount present different GPTs, i.e. their regions. centrally symmetric that degree given as injective and projective norm product This allows us completely characterize regions obtain optimal universal bounds on 1-summing constants Moreover, find new maximal more than three qubit