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We prove that uniqueness for the Calder\'on problem on a Riemannian manifoldwith boundary follows from a hypothetical unique continuation property for theelliptic operator $\Delta+V+(\Lambda^{1}_{t}-q)\otimes (\Lambda^{2}_{t}-q)$defined on $\partial\mathcal{M}^{2}\times [0,1]$ where $V$ and $q$ arepotentials and $\Lambda^{i}_{t}$ is a Dirichlet-Neumann operator at depth $t$.This is done by showing that the difference of two Dirichlet-Neumann maps isequal to the Neumann boundary values of the solution to an inhomogeneousequation for said operator, where the source term is a measure supported on thediagonal of $\partial\mathcal{M}^{2}$.

The Calder\'on problem is an inverse source problem