Measurement-Induced Entanglement in Conformal Field Theory
arXiv:2508.02788 · doi:10.1103/b7sb-nhjq
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.
4.5 + 13 pages
References in corpus (34)
- Experimental quantum teleportation
- Many body localization and thermalization in quantum statistical mechanics
- Random Quantum Circuits
- Entanglement versus Correlations in Spin Systems
- Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
- Measurement-induced entanglement and teleportation on a noisy quantum processor
- Experimental Realization of a Measurement-Induced Entanglement Phase Transition on a Superconducting Quantum Processor
- Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
- Measurement as a shortcut to long-range entangled quantum matter
- Universal entanglement entropy in 2D conformal quantum critical points
- Exact emergent quantum state designs from quantum chaotic dynamics
- Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements
- Long-range entanglement from measuring symmetry-protected topological phases
- Measurements conspire nonlocally to restructure critical quantum states
- Dynamical purification and the emergence of quantum state designs from the projected ensemble
- Solvable model of deep thermalization with distinct design times
- Continuous Gaussian Measurements of the Free Boson CFT: A model for Exactly Solvable and Detectable Measurement-Induced Dynamics
- Logarithmic observables in critical percolation
- Entanglement in one-dimensional critical state after measurements
- Generalized Deep Thermalization for Free Fermions
- Measurement-altered Ising quantum criticality
- A Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity
- Probing sign structure using measurement-induced entanglement
- Holographic measurement and bulk teleportation
- Realizing the Nishimori transition across the error threshold for constant-depth quantum circuits
- Entanglement Entropy and Mutual Information of Circular Entangling Surfaces in 2 + 1-dimensional Quantum Lifshitz Model
- Holographic measurement in CFT thermofield doubles
- Entanglement entropy after selective measurements in quantum chains
- Universal structure of measurement-induced information in many-body ground states
- Entanglement swapping in critical quantum spin chains
- Entanglement Entropy of Local Operators in Quantum Lifshitz Theory
- Nonlocality of Deep Thermalization
- Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
- Observable-projected ensembles