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

• URL: http://arxiv.org/abs/2312.11615v2
• Date: Wed, 8 May 2024 14:57:04 GMT
• Title: Universal structure of measurement-induced information in many-body ground states
• Authors: Zihan Cheng, Rui Wen, Sarang Gopalakrishnan, Romain Vasseur, Andrew C. Potter,
• Abstract summary: We study measures of measurement-induced entanglement (MIE) and information (MII) for the ground-states of quantum many-body systems. 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 implies that trivial $2d$ states can exhibit long-range MIE.
• Score: 1.0621665950143144
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 work, 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 sub-leading 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 non-universal 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.

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