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Measurement-Induced Entanglement in Conformal Field Theory
Kabir Khanna1,2, Romain Vasseur1
1University of Geneva, Department of Theoretical Physics, 24 quai Ernest-Ansermet, 1211 Genève, Switzerland.
None:
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. Using a replica trick to address the randomness of the measurement outcomes, we compute exactly the entanglement induced by measuring the local charge operator 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.
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