Landscape of Tensor Network States Preparable from Measurement

Measurements and feedback have emerged as powerful resources for creating many-body quantum states. However, a detailed understanding of what is possible is restricted to fixed-point representatives of phases of matter. In this talk, we go beyond this, characterizing more general patterns of many-body entanglement that can be deterministically created from measurement. In 1D, a complete framework is developed for the case where a single round of measurements is the only entangling operation. Specifically, we completely classify the space of 1D preparable quantum states (forming a strict subset of all matrix product states), and characterize their physical constraints. In doing so, we find an intriguing physical trade-off between the richness of the preparable entanglement spectrum and correlation functions, naturally implying a powerful no-go theorem for preparing certain quantum states. Moreover, our classification enables one to search for and engineer preparable quantum states with a range of desired correlation lengths and entanglement properties. We conclude by charting out generalizations, such as higher dimensional examples, considering multiple rounds of measurements, and implementing matrix product operators. At a high level, our 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.