@article{TEXTUAL,
      recid = {14676},
      author = {Sahay, Rahul and Verresen, Ruben},
      title = {Classifying One-Dimensional Quantum States Prepared by a  Single Round of Measurements},
      journal = {PRX Quantum},
      address = {2025-02-13},
      number = {TEXTUAL},
      abstract = {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.},
      url = {http://knowledge.uchicago.edu/record/14676},
}