Subspace constraints for joint measurability

The structure of quantum effects, positive operators of norm at most one, played a central role in the work of Paul Busch on uncertainty, complementarity, and joint measurability in quantum measurement theory. Here we focus on one aspect of this structure, called "strength of an effect along a ray" [Lett. Math. Phys. 47 329 (1999)], presenting a few observations not explicit in the existing literature. In fact, the strength function turns out to be useful for characterising positivity and complementarity of quantum effects of a suitable block matrix form, and for studying extensions of joint measurements defined on a subspace of codimension one.