Measurement-Induced Entanglement in Conformal Field Theory

TL;DR

This paper investigates how local measurements affect entanglement in quantum-critical states described by conformal field theories, revealing universal and conformally invariant measurement-induced entanglement in Tomonaga-Luttinger liquids.

Contribution

It provides an exact analytical study of measurement-induced entanglement in Tomonaga-Luttinger liquids using replica trick and boundary conformal field theory techniques.

Findings

Measurement-induced entanglement is universal and conformally invariant.

Exact computation of MIE in Tomonaga-Luttinger liquids matches numerical results.

Physical quantum measurements produce fundamentally different entanglement than forced measurement outcomes.

Abstract

Local measurements can radically reshape patterns of many-body entanglement, especially in long-range entangled quantum-critical states. Yet, analytical results addressing the effects of measurements on many-body states remain scarce, and measurements are often approximated as forcing specific measurement outcomes. We study measurement-induced entanglement (MIE) in Tomonaga-Luttinger liquids, a broad family of 1+1d quantum critical states described at low energies by compact free boson conformal field theories (CFT). Measuring the local charge operator, we show that the MIE is entirely universal, conformally invariant, and depends on the operator content of the CFT. Using a replica-trick to address the randomness of the measurement outcomes, we compute the MIE exactly for Tomonaga-Luttinger liquids, in very good agreement with matrix-product state calculations. We show that the MIE for physical quantum measurements is fundamentally different from the entanglement induced by forcing measurement outcomes, and has a natural interpretation in terms of Born averaging over conformally-invariant boundary conditions.