Analytic construction of dimension-dependent steering witnesses from generalized equiangular measurements

We construct a dimension-dependent family of generalized equiangular measurements that gives explicit steering witnesses in every prime dimension dgeq5. The construction consists of d-1 mutually unbiased measurements and an additional normalized family of 2d-1 Hermitian operators depending on a parameter tau. Positivity of the latter family is the main technical problem. We show that the noncentral operators reduce to three-dimensional invariant blocks, while the remaining central operator is exactly solvable in a two-dimensional subspace. Two unitarily equivalent 3times3 matrix representations describe the same active spectrum, but yield different Gershgorin enclosures because Gershgorin bounds are basis dependent. Combining the stronger endpoint from each representation gives a fully analytic asymmetric interval for tau that guarantees a valid POVM. Combining this POVM with the d-1 MUMs yields an explicit GEAM. Finally, using a maximally entangled realization and the local-hidden-state bound previously derived for generalized equiangular measurements, we obtain an explicit steering inequality and a sufficient criterion guaranteeing quantum violation in every prime dimension dgeq5.