  Measurements and feedback have emerged as powerful resources for creating
many-body quantum states. However, a detailed understanding has been restricted
to fixed-point representatives of phases of matter. Here, we go beyond this and
characterize the patterns of many-body entanglement that can be
deterministically created from measurement. Focusing on one spatial dimension,
a framework is developed for the case where a single round of measurements is
the only entangling operation. We show this creates matrix product states and
identify necessary and sufficient tensor conditions for preparability, which
uniquely determine the preparation protocol. We use these conditions to both
classify preparable quantum states and characterize their physical constraints.
In particular, we find a trade-off between the richness of the preparable
entanglement spectrum and correlation functions, which leads to a no-go theorem
for preparing certain quantum states. More broadly, we connect properties of
the preparation protocol to the resulting phase of matter, including trivial,
symmetry-breaking, and symmetry-protected topological phases -- for both
uniform and modulated symmetries. This work offers a resource-theoretic
perspective on preparable quantum entanglement and shows how to systematically
create states of matter, away from their fixed points, in quantum devices.
