Universal structure of measurement-induced information in many-body ground states

Unlike unitary dynamics, measurements of a subsystem can induce long-range entanglement via quantum teleportation. The amount of measurement-induced entanglement or mutual information depends jointly on the measurement basis and the entanglement structure of the state (before measurement), and has operational significance for whether the state is a resource for measurement-based quantum computing, as well as for the computational complexity of simulating the state using quantum or classical computers. In this paper, we examine entropic measures of measurement-induced entanglement (MIE) and information (MII) for the ground states of quantum many-body systems in one and two spatial dimensions. From numerical and analytic analysis of a variety of models encompassing critical points, quantum Hall states, string-net topological orders, and Fermi liquids, we identify universal features of the long-distance structure of MIE and MII that depend only on the underlying phase or critical universality class of the state. We argue that, whereas in 1D the leading contributions to long-range MIE and MII are universal, in 2D, the existence of a teleportation transition for finite-depth circuits implies that trivial 2D states can exhibit long-range MIE, and the universal features lie in subleading corrections. We introduce modified MIE measures that directly extract these universal contributions. As a corollary, we show that the leading contributions to strange correlators, used to numerically identify topological phases, are in fact nonuniversal in two or more dimensions, and explain how our modified constructions enable one to isolate universal components. We discuss the implications of these results for classical- and quantum- computational simulation of quantum materials.