Hadamard states play a prominent role in quantum field theory in curved spacetimes. They generalize important properties of the Poincare invariant vacuum state from standard QFT. In particular, they permit the forumlation of a rigorous theory of renormalization. However, the construction of Hadamard states in generic globally hyperbolic spacetimes often presents a major obstacle. In this talk I will discuss a construction of Hadamard states in asymptotically spacetimes due to Moretti, Dappiagi and Pinamonti. At the basis of their construction is a correspondence between a quantum theory living in the interior of a lightcone and a theory intrinsically defined on its boundary. I will describe how this correspondence can be used to construct Hadamard states for the scalar field [Moretti, Dappiaggi, Pinamonti] and the electromagnetic potential [Dappiaggi, Siemssen] in asymptotically flat spacetimes.