This paper explores the preparation of tensor network states using a single round of measurements and on-site unitary feedback. The authors identify criteria on local tensors that enable deterministic state preparation and construct families of measurement-preparable states in one and two dimensions, including symmetry-breaking, symmetry-protected, and topological phases. They demonstrate how to engineer states with specific correlation lengths and entanglement properties. The paper also presents diagnostics to verify the preparability of a given tensor network state and discusses generalizations such as multiple rounds of measurements, matrix product operators, and incomplete basis measurements. The authors provide detailed constructions and examples, including the preparation of states like the AKLT, cluster, GHZ, and Néel states, and their deformations. They also explore higher-dimensional examples and the application of tensor network operators. The work highlights the rich phenomenology and connections between entanglement spectra and correlation functions in tensor network states prepared via measurement.This paper explores the preparation of tensor network states using a single round of measurements and on-site unitary feedback. The authors identify criteria on local tensors that enable deterministic state preparation and construct families of measurement-preparable states in one and two dimensions, including symmetry-breaking, symmetry-protected, and topological phases. They demonstrate how to engineer states with specific correlation lengths and entanglement properties. The paper also presents diagnostics to verify the preparability of a given tensor network state and discusses generalizations such as multiple rounds of measurements, matrix product operators, and incomplete basis measurements. The authors provide detailed constructions and examples, including the preparation of states like the AKLT, cluster, GHZ, and Néel states, and their deformations. They also explore higher-dimensional examples and the application of tensor network operators. The work highlights the rich phenomenology and connections between entanglement spectra and correlation functions in tensor network states prepared via measurement.