On the structure of higher order quantum maps

Quantum 10, 2090 (2026). https://doi.org/10.22331/q-2026-05-05-2090 We study higher order quantum maps in the context of a *-autonomous category of affine subspaces. We show that types of higher order maps can be identified with certain Boolean functions that we call type functions. By an extension of this identification, the algebraic structure of Boolean functions is inherited by some sets of quantum objects including higher order maps. Using the Mobius transform, we assign to each type functi