Measurement-Induced Phase Transitions in the Dynamics of Entanglement

Abstract

We define dynamical universality classes for many-body systems whose unitary evolution is punctuated by projective measurements. In cases where such measurements occur randomly at a finite rate $p$ for each degree of freedom, we show that the system has two dynamical phases: `entangling' and `disentangling'. The former occurs for $p$ smaller than a critical rate $p_c$, and is characterized by volume-law entanglement in the steady-state and `ballistic' entanglement growth after a quench. By contrast, for $p>p_c$ the system can sustain only area-law entanglement. At $p=p_c$ the steady state is scale-invariant and, in 1+1D, the entanglement grows logarithmically after a quench. To obtain a simple heuristic picture for the entangling-disentangling transition, we first construct a toy model that describes the zeroth Rényi entropy in discrete time. We solve this model exactly by mapping it to an optimization problem in classical percolation. The generic entangling-disentangling transition can be diagnosed using the von Neumann entropy and higher Rényi entropies, and it shares many qualitative features with the toy problem. We study the generic transition numerically in quantum spin chains, and show that the phenomenology of the two phases is similar to that of the toy model, but with distinct `quantum' critical exponents, which we calculate numerically in $1+1$D. We examine two different cases for the unitary dynamics: Floquet dynamics for a nonintegrable Ising model, and random circuit dynamics. We obtain compatible universal properties in each case, indicating that the entangling-disentangling phase transition is generic for projectively measured many-body systems. We discuss the significance of this transition for numerical calculations of quantum observables in many-body systems.

17+4 pages, 16 figures; updated discussion and results for mutual information; graphics error fixed

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• Local Information Flow in Quantum Quench Dynamics
• Entanglement transitions from restricted Boltzmann machines
• Hardness of observing strong-to-weak symmetry breaking
• Embedding memory-efficient stochastic simulators as quantum trajectories
• Double-trace deformation in Keldysh field theory
• Interaction-induced transition in quantum many-body detection probability
• Phase transitions induced by standard and predetermined measurements in transmon arrays
• Multipartite entanglement structure of monitored quantum circuits
• Probing prethermal nonergodicity through measurement outcomes of monitored quantum dynamics
• Multifractality in monitored single-particle dynamics
• Entangling power, gate typicality, and measurement-induced phase transitions
• Semiclassical Quantum Trajectories in the Monitored Lipkin-Meshkov-Glick Model
• Measurement-induced phase transitions for free fermions in a quasiperiodic potential
• Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements
• Local spreading of stabilizer Rényi entropy in a brickwork random Clifford circuit
• Topology and Spectrum in Measurement-Induced Phase Transitions
• Localization induced by spatially uncorrelated subohmic baths in one dimension
• Measurement-induced phase transition in periodically driven free-fermionic systems
• Absorbing State Phase Transition with Clifford Circuits
• Conformal symmetry in quasi-free Markovian open quantum systems
• Random Quantum Circuits with Time-Reversal Symmetry
• Universality in the tripartite information after global quenches: spin flip and semilocal charges
• Extending Classically Simulatable Bounds of Clifford Circuits with Nonstabilizer States via Framed Wigner Functions
• Purification Dynamics in a Continuous-time Hybrid Quantum Circuit Model
• Entanglement transitions in the quantum Ising chain: A comparison between different unravelings of the same Lindbladian
• Coherent Information Phase Transition in a Noisy Quantum Circuit
• Telling different unravelings apart via nonlinear quantum-trajectory averages
• Effect of the readout efficiency of quantum measurement on the system entanglement
• Variational post-selection for ground states and thermal states simulation
• Solvable Quantum Circuits in Tree+1 Dimensions
• Exact spectral gaps of random one-dimensional quantum circuits
• Monitored Fluctuating Hydrodynamics
• Transport and integrability-breaking in non-Hermitian many-body quantum systems
• Non-Hermitian Multipole Skin Effects Challenge Localization
• Origin and Limit of the Recovery of Damaged Information by Time Reversal
• The planted directed polymer: inferring a random walk from noisy images
• Rise and fall of nonstabilizerness via random measurements
• Reaction-diffusion dynamics in a Fibonacci chain: Interplay between classical and quantum behavior
• Mesoscopic Fluctuations and Multifractality at and across Measurement-Induced Phase Transition
• Quantized dynamics in closed quantum systems
• Entanglement dynamics of monitored noninteracting fermions on graphics processing units
• Quench dynamics of entanglement entropy under projective charge measurements: the free fermion case
• Hierarchy of emergent cluster states by measurement from symmetry-protected-topological states with large symmetry to subsystem cat state
• Quantum trajectories for the variational description of closed systems: a case study with Gaussian states
• Measurement-Driven Transitions between Area Law Phases
• Entanglement Dynamics of Random GUE Hamiltonians
• Chaos controlled and disorder driven phase transitions induced by breaking permutation symmetry
• Universal time evolution of string order parameter in quantum critical systems with boundary invertible or non-invertible symmetry breaking
• Motion from Measurement: The Role of Symmetry of Quantum Measurements
• Quantum dynamics of monitored free fermions: Evolution of quantum correlations and scaling at measurement-induced phase transition
• Instability of the engineered dark state in two-band fermions under number-conserving dissipative dynamics
• Random displacements in critical Rydberg atom arrays
• Quantum-limited generalized measurement for tunnel-coupled condensates
• Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling
• Dissipation-Induced Steady States in Topological Superconductors: Mechanisms and Design Principles
• Quantum Entanglement Phase Transitions and Computational Complexity: Insights from Ising Models
• Enhanced localization in the prethermal regime of continuously measured many-body localized systems
• Entanglement of bosonic systems under monitored evolution
• Uncovering measurement-induced entanglement via directional adaptive dynamics and incomplete information
• Entanglement phases and phase transitions in monitored free fermion system due to localizations
• Absorption to Fluctuating Bunching States in Non-Unitary Boson Dynamics
• Exact, Average, and Broken Symmetries in a Simple Adaptive Monitored Circuit
• Emergent deterministic entanglement dynamics in monitored infinite-range bosonic systems
• Wehrl Entropy and Entanglement Complexity of Quantum Spin Systems
• Out-of-equilibrium quantum dynamics of fermionic gases in the presence of localized particle loss
• Multipartite Greenberger-Horne-Zeilinger Entanglement in Monitored Random Clifford Circuits
• Parallel Quantum Signal Processing Via Polynomial Factorization
• Measurement-invisible quantum correlations in scrambling dynamics
• Relaxation Critical Dynamics in Measurement-induced Phase Transitions
• Absorbing state phase transitions beyond directed percolation in dissipative quantum state preparation
• Detecting Measurement-Induced Entanglement Transitions With Unitary Mirror Circuits
• Aperiodic Dissipation as a Mechanism for Steady-State Localization
• Spectral Statistics of Non-Hermitian Matrices and Dissipative Quantum Chaos
• Entanglement behavior and localization properties in monitored fermion systems
• Error Mitigation Thresholds in Noisy Random Quantum Circuits
• Identifying Entanglement Phases with Bipartite Projected Ensembles
• $\nu$-QSSEP: A toy model for entanglement spreading in stochastic diffusive quantum systems
• Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States
• Quantum Darwinism-encoding transitions on expanding trees
• Positive bias makes tensor-network contraction tractable
• Long-range multipartite entanglement near measurement-induced transitions
• Field theory of charge sharpening in symmetric monitored quantum circuits
• Measurement-induced criticality in extended and long-range unitary circuits
• Temperature dependence of energy transport in the ${\mathbb{Z}}_3$ chiral clock model
• Gauge freedoms in unravelled quantum dynamics: When do different continuous measurements yield identical quantum trajectories?
• Transitions of the Lyapunov spectrum and entanglement entropy in monitored quantum dynamics with homogeneous unitary gates
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• Post-measurement Quantum Monte Carlo
• Exact solution to a Bhatnagar-Gross-Krook-type equation for quantum lattice gases with dephasing noise
• Measurement-Induced Phase Transition in a Disordered XX Spin Chain: A Real-Space Renormalization Group Study
• Measurement-Induced Entanglement in Conformal Field Theory
• Entanglement transitions in a boundary-driven open quantum many-body system
• Symmetry and Topology of Monitored Quantum Dynamics
• Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics
• Symmetry Properties of Quantum Dynamical Entropy
• Localization of information driven by stochastic resetting
• Coherence-induced deep thermalization transition in random permutation quantum dynamics
• Short-time simulation of quantum dynamics by Pauli measurements
• Plaquette Models, Cellular Automata, and Measurement-induced Criticality
• Fractal structure of multipartite entanglement in monitored quantum circuits
• Entanglement transition in unitary system-bath dynamics
• Threefold Way for Typical Entanglement
• Neural network enhanced cross entropy benchmark for monitored circuits
• Stacked quantum Ising systems and quantum Ashkin-Teller model
• Complexity of Quantum Trajectories
• Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits
• Multipartite entanglement structures in quantum stabilizer states
• Computable measures of non-Markovianity for Gaussian free fermion systems
• Quantum evolution with random phase scattering
• Multiparty Entanglement Microscopy of Quantum Ising models in 1d, 2d and 3d
• Universal Aspects of High-Temperature Relaxation Dynamics in Random Spin Models
• Symmetric tensor scars with tunable entanglement from volume to area law
• Markovian to non-Markovian phase transition in the operator dynamics of a mobile impurity
• Competing automorphisms and disordered Floquet codes
• Nonequilibrium Critical Scaling of a Squeezing Phase Transition
• Mixed-state learnability transitions in monitored noisy quantum dynamics
• Phase transitions in (2 + 1)D subsystem-symmetric monitored quantum circuits
• Deterministic quantum trajectory via imaginary time evolution
• Quantum conditional mutual information as a probe of measurement-induced entanglement phase transitions
• Replica Keldysh field theory of quantum-jump processes: General formalism and application to imbalanced and inefficient fermion counting
• Entanglement transition and suppression of critical phase of thermofield double state in monitored quantum circuit with unitary $R$ matrix gates
• Controlled Zeno-Induced Localization of Free Fermions in a Quasiperiodic Chain
• Non-commutative Index of Measurement-only Entanglement Phase Transition
• Phase Transition of Topological Index driven by Dephasing
• Non-invasive mid-circuit measurement and reset on atomic qubits
• Work Statistics and Quantum Trajectories: No-Click Limit and non-Hermitian Hamiltonians
• Destruction and recovery of the entanglement entropy of a many-body quantum system after a single measurement
• Entropy and singular-value moments of products of truncated random unitary matrices
• Measurement resolution enhanced coherence for lattice fermions
• Robustness of a state with Ising topological order against local projective measurements
• Disordered purification phase transition in hybrid random circuits
• Disappearance of measurement-induced phase transition in a quantum spin system for large sizes
• Exact large deviations and emergent long-range correlations in sequential quantum East circuits
• Error detection without post-selection in adaptive quantum circuits
• Information Bounds on phase transitions in disordered systems
• Tri-unitary quantum circuits
• Generation of Volume-Law Entanglement by Local-Measurement-Only Quantum Dynamics
• Entanglement entropy scaling laws from fluctuations of non-conserved quantities
• Control-driven critical fluctuations across quantum trajectories
• Measurement-induced entanglement in noisy 2D random circuits
• Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions
• Engineering entanglement geometry via spacetime-modulated measurements
• Entanglement Growth from Entangled States: A Unified Perspective on Entanglement Generation and Transport
• Frustration-Free Control and Absorbing-State Transport in Entangled State Preparation
• Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings
• Entanglement Phase Transition in Chaotic non-Hermitian Systems
• Inverse Superconductor-Insulator Transition in Weakly Monitored Josephson Junction Arrays
• Nonunitary gates using measurements only
• Non-Markovianity Benefits Quantum Dynamics Simulation
• Moments of Quantum Channel Ensembles
• Diagnosing chaos with projected ensembles of process tensors
• Noisy Monitored Quantum Circuits
• Roughening Transition in Quantum Circuits
• Computational Complexity and Simulability of Non-Hermitian Quantum Dynamics
• Measurement-and Feedback-Driven Non-Equilibrium Phase Transitions on a Quantum Processor
• Scaling Laws of Quantum Information Lifetime in Monitored Quantum Dynamics