  We consider states of holographic conformal field theories constructed by
adding sources for local operators in the Euclidean path integral, with the aim
of investigating the extent to which arbitrary bulk coherent states can be
represented by such Euclidean path-integrals in the CFT. We construct the
associated dual Lorentzian spacetimes perturbatively in the sources. Extending
earlier work, we provide explicit formulae for the Lorentzian fields to first
order in the sources for general scalar field and metric perturbations in
arbitrary dimensions. We check the results by holographically computing the
Lorentzian one-point functions for the sourced operators and comparing with a
direct CFT calculation. We present evidence that at the linearized level,
arbitrary bulk initial data profiles can be generated by an appropriate choice
of Euclidean sources. However, in order to produce initial data that is very
localized, the amplitude must be taken small at the same time otherwise the
required sources diverge, invalidating the perturbative approach.
