An n-dimensional quantum observable in quantum structures is a kind of a σ-homomorphism defined on the Borel σ-algebra of $\mathbb R^{n}$ with values in a monotone σ-complete effect algebra or in a σ-complete MV-algebra. It defines an n-dimensional spectral resolution that is a mapping from $\mathbb R^{n}$ into the quantum structure which is a monotone, left-continuous mapping with non-negative increments and which is going to 0 if one variable goes to $-\infty $ and it goes to 1 if all variables go to $+\infty $ . The basic question is to show when an n-dimensional spectral resolution entails an n-dimensional quantum observable. We show cases when this is possible and we apply the result to existence of three different kinds of joint observables.