In this note we discuss the conditional stability issue for the finite dimensional Calderón problem for the fractional Schrödinger equation with a finite number of measurements. More precisely, we assume that the unknown potential $ q in L^{infty}(Omega) $ in the equation $ ((- Delta)^s+ q)u = 0 mbox{ in } Omegasubset mathbb{R}^n $ satisfies the a priori assumption that it is contained in a finite dimensional subspace of $ L^{infty}(Omega) $. Under this condition we prove Lipschitz stability estimates for the fractional Calderón problem by means of finitely many Cauchy data depending on $ q $. We allow for the possibility of zero being a Dirichlet eigenvalue of the associated fractional Schrödinger equation. Our result relies on the strong Runge approximation property of the fractional Schrödinger equation.
