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. This is based on two recent works with Ruben Verresen [arXiv:2404.17087; arXiv:2404.16753].