SciPost Physics

SciPost Phys. 7, 024 (2019) · published 23 August 2019

• doi: 10.21468/SciPostPhys.7.2.024
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Abstract

We study the entanglement entropy of the quantum trajectories of a free fermion chain under continuous monitoring of local occupation numbers. We propose a simple theory for entanglement entropy evolution from disentangled and highly excited initial states. It is based on generalized hydrodynamics and the quasi-particle pair approach to entanglement in integrable systems. We test several quantitative predictions of the theory against extensive numerics and find good agreement. In particular, the volume law entanglement is destroyed by the presence of arbitrarily weak measurement.

• Dolgirev et al., Non-Gaussian correlations imprinted by local dephasing in fermionic wires
  Phys. Rev. B 102, 100301 (2020) [Crossref]
• Buchhold et al., Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions
  Phys. Rev. X 11, 041004 (2021) [Crossref]
• Sierant et al., Controlling Entanglement at Absorbing State Phase Transitions in Random Circuits
  Phys. Rev. Lett. 130, 120402 (2023) [Crossref]
• Zhang et al., Nonuniversal entanglement level statistics in projection-driven quantum circuits
  Phys. Rev. B 101, 235104 (2020) [Crossref]
• Szyniszewski et al., Universality of Entanglement Transitions from Stroboscopic to Continuous Measurements
  Phys. Rev. Lett. 125, 210602 (2020) [Crossref]
• Carollo et al., Entangled multiplets and spreading of quantum correlations in a continuously monitored tight-binding chain
  Phys. Rev. B 106, L220304 (2022) [Crossref]
• Turkeshi et al., Measurement-induced entanglement transitions in the quantum Ising chain: From infinite to zero clicks
  Phys. Rev. B 103, 224210 (2021) [Crossref]
• Müller et al., Measurement-Induced Dark State Phase Transitions in Long-Ranged Fermion Systems
  Phys. Rev. Lett. 128, 010605 (2022) [Crossref]
• Agrawal et al., Entanglement and Charge-Sharpening Transitions in U(1) Symmetric Monitored Quantum Circuits
  Phys. Rev. X 12, 041002 (2022) [Crossref]
• Shkolnik et al., Measurement induced criticality in quasiperiodic modulated random hybrid circuits
  Phys. Rev. B 108, 184204 (2023) [Crossref]
• Sierant et al., Universal Behavior beyond Multifractality of Wave Functions at Measurement-Induced Phase Transitions
  Phys. Rev. Lett. 128, 130605 (2022) [Crossref]
• Barratt et al., Field Theory of Charge Sharpening in Symmetric Monitored Quantum Circuits
  Phys. Rev. Lett. 129, 120604 (2022) [Crossref]
• Wu et al., Spontaneous symmetry breaking and localization in nonequilibrium steady states of interactive quantum systems
  Science Bulletin 68, 2010 (2023) [Crossref]
• Feng et al., Boundary-sensitive Lindbladians and relaxation dynamics
  Phys. Rev. B 109, 014313 (2024) [Crossref]
• Liu et al., Non-unitary dynamics of Sachdev-Ye-Kitaev chain
  SciPost Phys. 10, 048 (2021) [Crossref]
• Zhou et al., Nonunitary entanglement dynamics in continuous-variable systems
  Phys. Rev. B 104, L180301 (2021) [Crossref]
• Wasak et al., Quantum-Zeno Fermi polaron in the strong dissipation limit
  Phys. Rev. Research 3, 013086 (2021) [Crossref]
• Dajka, Currents in a Quantum Nanoring Controlled by Non-Classical Electromagnetic Field
  Entropy 23, 652 (2021) [Crossref]
• Klobas et al., Entanglement dynamics in Rule 54: Exact results and quasiparticle picture
  SciPost Phys. 11, 107 (2021) [Crossref]
• Leontica et al., Purification dynamics in a continuous-time hybrid quantum circuit model
  Phys. Rev. B 108, 174308 (2023) [Crossref]
• Altland et al., Dynamics of measured many-body quantum chaotic systems
  Phys. Rev. Research 4, L022066 (2022) [Crossref]
• Yamaguchi et al., Feedback-cooled Bose-Einstein condensation: Near and far from equilibrium
  Phys. Rev. A 107, 063306 (2023) [Crossref]
• Lu et al., Spacetime duality between localization transitions and measurement-induced transitions
  PRX Quantum 2, 040319 (2021) [Crossref]
• Lunt et al., Measurement-induced entanglement transitions in many-body localized systems
  Phys. Rev. Research 2, 043072 (2020) [Crossref]
• Zhou et al., Entanglement Membrane in Chaotic Many-Body Systems
  Phys. Rev. X 10, 031066 (2020) [Crossref]
• Hashizume et al., Measurement-induced phase transitions in sparse nonlocal scramblers
  Phys. Rev. Research 4, 013174 (2022) [Crossref]
• Turkeshi et al., Enhanced entanglement negativity in boundary-driven monitored fermionic chains
  Phys. Rev. B 106, 024304 (2022) [Crossref]
• Chaudhari et al., Zeno crossovers in the entanglement speed of spin chains with noisy impurities
  J. Stat. Mech. 2022, 103101 (2022) [Crossref]
• Fleckenstein et al., Non-Hermitian topology in monitored quantum circuits
  Phys. Rev. Research 4, L032026 (2022) [Crossref]
• Li et al., Conformal invariance and quantum nonlocality in critical hybrid circuits
  Phys. Rev. B 104, 104305 (2021) [Crossref]
• Jin et al., From Stochastic Spin Chains to Quantum Kardar-Parisi-Zhang Dynamics
  Phys. Rev. Lett. 125, 040603 (2020) [Crossref]
• Fuji et al., Measurement-induced quantum criticality under continuous monitoring
  Phys. Rev. B 102, 054302 (2020) [Crossref]
• Iaconis et al., Multifractality in nonunitary random dynamics
  Phys. Rev. B 104, 214307 (2021) [Crossref]
• Ladewig et al., Monitored open fermion dynamics: Exploring the interplay of measurement, decoherence, and free Hamiltonian evolution
  Phys. Rev. Research 4, 033001 (2022) [Crossref]
• L. M. Lezama et al., Logarithmic, noise-induced dynamics in the Anderson insulator
  SciPost Phys. 12, 174 (2022) [Crossref]
• Civolani et al., Engineering Transport via Collisional Noise: A Toolbox for Biology Systems
  Entropy 26, 20 (2023) [Crossref]
• Zhou, Entanglement phase transitions in non-Hermitian quasicrystals
  Phys. Rev. B 109, 024204 (2024) [Crossref]
• Kagamihara et al., Rényi entanglement entropy after a quantum quench starting from insulating states in a free boson system
  Phys. Rev. A 107, 033305 (2023) [Crossref]
• Szyniszewski et al., Disordered monitored free fermions
  Phys. Rev. B 108, 165126 (2023) [Crossref]
• Zhang, Perturbative Page curve induced by external impulse
  J. High Energ. Phys. 2023, 56 (2023) [Crossref]
• Jin et al., Semiclassical theory of quantum stochastic resistors
  Phys. Rev. Research 5, 013033 (2023) [Crossref]
• Ravindranath et al., Robust Oscillations and Edge Modes in Nonunitary Floquet Systems
  Phys. Rev. Lett. 130, 230402 (2023) [Crossref]
• Lunt et al., Measurement-induced criticality and entanglement clusters: A study of one-dimensional and two-dimensional Clifford circuits
  Phys. Rev. B 104, 155111 (2021) [Crossref]
• Ippoliti et al., Postselection-Free Entanglement Dynamics via Spacetime Duality
  Phys. Rev. Lett. 126, 060501 (2021) [Crossref]
• Jin et al., Interplay between transport and quantum coherences in free fermionic systems
  J. Phys. A: Math. Theor. 54, 404001 (2021) [Crossref]
• Jin et al., Kardar-Parisi-Zhang Physics and Phase Transition in a Classical Single Random Walker under Continuous Measurement
  Phys. Rev. Lett. 129, 260603 (2022) [Crossref]
• Fidkowski et al., How Dynamical Quantum Memories Forget
  Quantum 5, 382 382 (2021) [Crossref]
• Zhang et al., Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics
  Quantum 6, 723 723 (2022) [Crossref]
• Moghaddam et al., Exponential Shortcut to Measurement-Induced Entanglement Phase Transitions
  Phys. Rev. Lett. 131, 020401 (2023) [Crossref]
• Alba et al., Spreading of correlations in Markovian open quantum systems
  Phys. Rev. B 103, L020302 (2021) [Crossref]
• Medina et al., Entanglement transitions from restricted Boltzmann machines
  Phys. Rev. B 104, 104205 (2021) [Crossref]
• Capizzi et al., Symmetry resolved relative entropies and distances in conformal field theory
  J. High Energ. Phys. 2021, 195 (2021) [Crossref]
• Sierant et al., Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains
  Quantum 6, 638 638 (2022) [Crossref]
• Block et al., Measurement-Induced Transition in Long-Range Interacting Quantum Circuits
  Phys. Rev. Lett. 128, 010604 (2022) [Crossref]
• Lee et al., Entanglement Phase Transition Due to Reciprocity Breaking without Measurement or Postselection
  PRX Quantum 5, 010313 (2024) [Crossref]
• Fava et al., Nonlinear Sigma Models for Monitored Dynamics of Free Fermions
  Phys. Rev. X 13, 041045 (2023) [Crossref]
• Alberton et al., Entanglement Transition in a Monitored Free-Fermion Chain: From Extended Criticality to Area Law
  Phys. Rev. Lett. 126, 170602 (2021) [Crossref]
• Snizhko et al., Weak-Measurement-Induced Asymmetric Dephasing: Manifestation of Intrinsic Measurement Chirality
  Phys. Rev. Lett. 127, 170401 (2021) [Crossref]
• Fujimoto et al., Dynamical Scaling of Surface Roughness and Entanglement Entropy in Disordered Fermion Models
  Phys. Rev. Lett. 127, 090601 (2021) [Crossref]
• Parez et al., Quasiparticle dynamics of symmetry-resolved entanglement after a quench: Examples of conformal field theories and free fermions
  Phys. Rev. B 103, L041104 (2021) [Crossref]
• Boorman et al., Diagnostics of entanglement dynamics in noisy and disordered spin chains via the measurement-induced steady-state entanglement transition
  Phys. Rev. B 105, 144202 (2022) [Crossref]
• Li et al., Statistical mechanics of quantum error correcting codes
  Phys. Rev. B 103, 104306 (2021) [Crossref]
• Cheng et al., Efficient Sampling of Noisy Shallow Circuits Via Monitored Unraveling
  PRX Quantum 4, 040326 (2023) [Crossref]
• Doggen et al., Generalized quantum measurements with matrix product states: Entanglement phase transition and clusterization
  Phys. Rev. Research 4, 023146 (2022) [Crossref]
• Xing et al., Interactions and integrability in weakly monitored Hamiltonian systems
  Phys. Rev. B 109, L060302 (2024) [Crossref]
• Sharma et al., Measurement-induced criticality in extended and long-range unitary circuits
  SciPost Phys. Core 5, 023 (2022) [Crossref]
• Nahum et al., Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory
  PRX Quantum 2, 010352 (2021) [Crossref]
• Kalsi et al., Three-fold way of entanglement dynamics in monitored quantum circuits
  J. Phys. A: Math. Theor. 55, 264009 (2022) [Crossref]
• Russomanno et al., Entanglement transitions and quantum bifurcations under continuous long-range monitoring
  Phys. Rev. B 108, 104313 (2023) [Crossref]
• Bastianello et al., Entanglement spreading and quasiparticle picture beyond the pair structure
  SciPost Phys. 8, 045 (2020) [Crossref]
• Iaconis et al., Measurement-induced phase transitions in quantum automaton circuits
  Phys. Rev. B 102, 224311 (2020) [Crossref]
• Granet et al., Volume-Law to Area-Law Entanglement Transition in a Nonunitary Periodic Gaussian Circuit
  Phys. Rev. Lett. 130, 230401 (2023) [Crossref]
• Lami et al., Continuously monitored quantum systems beyond Lindblad dynamics
  New J. Phys. 26, 023041 (2024) [Crossref]
• Tang et al., Quantum criticality in the nonunitary dynamics of (2+1) -dimensional free fermions
  Phys. Rev. B 103, 174303 (2021) [Crossref]
• Van Regemortel et al., Monitoring-induced entanglement entropy and sampling complexity
  Phys. Rev. Research 4, L032021 (2022) [Crossref]
• Sierant et al., Entanglement and Absorbing State Transitions in (d+1)-Dimensional Stabilizer Circuits
  Acta Phys. Pol. A 144, 474 (2023) [Crossref]
• Khor et al., Measurement-induced chirality: Diffusion and disorder
  Phys. Rev. B 108, 214305 (2023) [Crossref]
• Potter et al.,
  , 211 (2022) [Crossref]
• Jin et al., Exact description of quantum stochastic models as quantum resistors
  Phys. Rev. Research 4, 013109 (2022) [Crossref]
• Behrends et al., Surface codes, quantum circuits, and entanglement phases
  Phys. Rev. Research 6, 013137 (2024) [Crossref]
• Yang et al., Keldysh nonlinear sigma model for a free-fermion gas under continuous measurements
  Phys. Rev. Research 5, 033174 (2023) [Crossref]
• Basu et al., Fisher zeros and persistent temporal oscillations in nonunitary quantum circuits
  Phys. Rev. Research 4, 013018 (2022) [Crossref]
• Rossini et al., Coherent and dissipative dynamics at quantum phase transitions
  Physics Reports 936, 1 (2021) [Crossref]
• Zhou, Entanglement Phase Transitions in Non-Hermitian Kitaev Chains
  Entropy 26, 272 (2024) [Crossref]
• Kolodrubetz, Optimality of Lindblad unfolding in measurement phase transitions
  Phys. Rev. B 107, L140301 (2023) [Crossref]
• Kumar et al., Boundary transfer matrix spectrum of measurement-induced transitions
  Phys. Rev. B 109, 014303 (2024) [Crossref]
• Yamashika et al., Time evolution of entanglement entropy after quenches in two-dimensional free fermion systems: A dimensional reduction treatment
  Phys. Rev. B 109, 125122 (2024) [Crossref]
• Ferreira et al., Transport and Nonreciprocity in Monitored Quantum Devices: An Exact Study
  Phys. Rev. Lett. 132, 136301 (2024) [Crossref]
• Van Regemortel et al., Entanglement Entropy Scaling Transition under Competing Monitoring Protocols
  Phys. Rev. Lett. 126, 123604 (2021) [Crossref]
• Nahum et al., Entanglement and dynamics of diffusion-annihilation processes with Majorana defects
  Phys. Rev. Research 2, 023288 (2020) [Crossref]
• Su et al., Dynamics and phases of nonunitary Floquet transverse-field Ising model
  Phys. Rev. Research 6, 013131 (2024) [Crossref]
• Parez et al., Exact quench dynamics of symmetry resolved entanglement in a free fermion chain
  J. Stat. Mech. 2021, 093102 (2021) [Crossref]
• Murciano et al., Measurement-Altered Ising Quantum Criticality
  Phys. Rev. X 13, 041042 (2023) [Crossref]
• Bentsen et al., Measurement-induced purification in large- N hybrid Brownian circuits
  Phys. Rev. B 104, 094304 (2021) [Crossref]
• Wiersema et al., Measurement-induced entanglement phase transitions in variational quantum circuits
  SciPost Phys. 14, 147 (2023) [Crossref]
• Stefanov et al., Key for a Hidden Quantum State
  Phys. Rev. Lett. 129, 083603 (2022) [Crossref]
• Li et al., Measurement-driven entanglement transition in hybrid quantum circuits
  Phys. Rev. B 100, 134306 (2019) [Crossref]
• Carollo et al., Dissipative quasiparticle picture for quadratic Markovian open quantum systems
  Phys. Rev. B 105, 144305 (2022) [Crossref]
• Pöpperl et al., Localization, fractality, and ergodicity in a monitored qubit
  Phys. Rev. Research 6, 013313 (2024) [Crossref]
• Barratt et al., Transitions in the Learnability of Global Charges from Local Measurements
  Phys. Rev. Lett. 129, 200602 (2022) [Crossref]
• Tang et al., Measurement-induced phase transition: A case study in the nonintegrable model by density-matrix renormalization group calculations
  Phys. Rev. Research 2, 013022 (2020) [Crossref]
• Zabalo et al., Infinite-randomness criticality in monitored quantum dynamics with static disorder
  Phys. Rev. B 107, L220204 (2023) [Crossref]
• Zhang et al., Emergent Replica Conformal Symmetry in Non-Hermitian SYK2Chains
  Quantum 5, 579 579 (2021) [Crossref]
• Piccitto et al., Entanglement transitions in the quantum Ising chain: A comparison between different unravelings of the same Lindbladian
  Phys. Rev. B 105, 064305 (2022) [Crossref]
• Chiriacò et al., Diagrammatic method for many-body non-Markovian dynamics: Memory effects and entanglement transitions
  Phys. Rev. B 108, 075151 (2023) [Crossref]
• Choo et al., Thermal and dissipative effects on the heating transition in a driven critical system
  SciPost Phys. 13, 104 (2022) [Crossref]
• Ashida et al., Non-Hermitian physics
  Advances in Physics 69, 249 (2020) [Crossref]
• Fisher et al., Random Quantum Circuits
  Annu. Rev. Condens. Matter Phys. 14, 335 (2023) [Crossref]
• Majumdar et al., Localization induced by spatially uncorrelated subohmic baths in one dimension
  Phys. Rev. B 108, 205138 (2023) [Crossref]
• Wang et al., Linear response theory of entanglement entropy
  Physica A: Statistical Mechanics and its Applications 599, 127437 127437 (2022) [Crossref]
• Lopez-Piqueres et al., Mean-field entanglement transitions in random tree tensor networks
  Phys. Rev. B 102, 064202 (2020) [Crossref]
• Jubb, Causal state updates in real scalar quantum field theory
  Phys. Rev. D 105, 025003 (2022) [Crossref]
• Sang et al., Measurement-protected quantum phases
  Phys. Rev. Research 3, 023200 (2021) [Crossref]
• Mori et al., Universal Survival Probability for a d -Dimensional Run-and-Tumble Particle
  Phys. Rev. Lett. 124, 090603 (2020) [Crossref]
• Doggen et al., Evolution of many-body systems under ancilla quantum measurements
  Phys. Rev. B 107, 214203 (2023) [Crossref]
• Zhang, Quantum entanglement in the Sachdev—Ye—Kitaev model and its generalizations
  Front. Phys. 17, 43201 (2022) [Crossref]
• Ziolkowska et al., Yang-Baxter integrable Lindblad equations
  SciPost Phys. 8, 044 (2020) [Crossref]
• Sang et al., Entanglement Negativity at Measurement-Induced Criticality
  PRX Quantum 2, 030313 (2021) [Crossref]
• Biella et al., Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition
  Quantum 5, 528 528 (2021) [Crossref]
• Carisch et al., Quantifying measurement-induced quantum-to-classical crossover using an open-system entanglement measure
  Phys. Rev. Research 5, L042031 (2023) [Crossref]
• Lavasani et al., Topological Order and Criticality in (2+1)D Monitored Random Quantum Circuits
  Phys. Rev. Lett. 127, 235701 (2021) [Crossref]
• Bao et al., Theory of the phase transition in random unitary circuits with measurements
  Phys. Rev. B 101, 104301 (2020) [Crossref]
• Ippoliti et al., Learnability Transitions in Monitored Quantum Dynamics via Eavesdropper’s Classical Shadows
  PRX Quantum 5, 020304 (2024) [Crossref]
• Wampler et al., Stirring by Staring: Measurement-Induced Chirality
  Phys. Rev. X 12, 031031 (2022) [Crossref]
• Kawabata et al., Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
  Phys. Rev. X 13, 021007 (2023) [Crossref]
• Coppola et al., Wigner dynamics for quantum gases under inhomogeneous gain and loss processes with dephasing
  Phys. Rev. A 107, 052213 (2023) [Crossref]
• Ippoliti et al., Entanglement Phase Transitions in Measurement-Only Dynamics
  Phys. Rev. X 11, 011030 (2021) [Crossref]
• Gullans et al., Quantum Coding with Low-Depth Random Circuits
  Phys. Rev. X 11, 031066 (2021) [Crossref]
• Majidy et al., Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits
  Phys. Rev. B 108, 054307 (2023) [Crossref]
• Ruidas et al., Semiclassical Limit of a Measurement-Induced Transition in Many-Body Chaos in Integrable and Nonintegrable Oscillator Chains
  Phys. Rev. Lett. 132, 030402 (2024) [Crossref]
• Lunt et al.,
  , 251 (2022) [Crossref]
• Li et al., Decodable hybrid dynamics of open quantum systems with Z2 symmetry
  Phys. Rev. B 108, 214302 (2023) [Crossref]
• Mori, Floquet States in Open Quantum Systems
  Annu. Rev. Condens. Matter Phys. 14, 35 (2023) [Crossref]
• Rossini et al., Measurement-induced dynamics of many-body systems at quantum criticality
  Phys. Rev. B 102, 035119 (2020) [Crossref]
• Modak et al., Entanglement revivals as a probe of scrambling in finite quantum systems
  J. Stat. Mech. 2020, 083110 (2020) [Crossref]
• Lavasani et al., Measurement-induced topological entanglement transitions in symmetric random quantum circuits
  Nat. Phys. 17, 342 (2021) [Crossref]
• Poboiko et al., Measurement-Induced Phase Transition for Free Fermions above One Dimension
  Phys. Rev. Lett. 132, 110403 (2024) [Crossref]
• Nahum et al., Renormalization group for measurement and entanglement phase transitions
  Phys. Rev. B 108, 104203 (2023) [Crossref]
• Mochizuki et al., Absorption to fluctuating bunching states in nonunitary boson dynamics
  Phys. Rev. Research 6, 013004 (2024) [Crossref]
• Iadecola et al., Measurement and Feedback Driven Entanglement Transition in the Probabilistic Control of Chaos
  Phys. Rev. Lett. 131, 060403 (2023) [Crossref]
• Dajka, Geometric speed limit for fermionic dimer as a hallmark of Coulomb interaction
  Quantum Inf Process 23, 93 (2024) [Crossref]
• Young et al., Feedback-stabilized dynamical steady states in the Bose-Hubbard model
  Phys. Rev. Research 3, 043075 (2021) [Crossref]
• Wang et al., Scaling laws for non-Hermitian skin effect with long-range couplings
  Phys. Rev. B 108, 085418 (2023) [Crossref]
• Yamamoto et al., Localization properties in disordered quantum many-body dynamics under continuous measurement
  Phys. Rev. B 107, L220201 (2023) [Crossref]
• Turkeshi et al., Entanglement transitions from stochastic resetting of non-Hermitian quasiparticles
  Phys. Rev. B 105, L241114 (2022) [Crossref]
• Lóio et al., Purification timescales in monitored fermions
  Phys. Rev. B 108, L020306 (2023) [Crossref]
• Turkeshi et al., Measurement-induced criticality in (2+1) -dimensional hybrid quantum circuits
  Phys. Rev. B 102, 014315 (2020) [Crossref]
• Preisser et al., Comparing bipartite entropy growth in open-system matrix-product simulation methods
  Phys. Rev. A 108, 012616 (2023) [Crossref]
• Jian et al., Criticality and entanglement in nonunitary quantum circuits and tensor networks of noninteracting fermions
  Phys. Rev. B 106, 134206 (2022) [Crossref]
• Tirrito et al., Full counting statistics as probe of measurement-induced transitions in the quantum Ising chain
  SciPost Phys. 15, 096 (2023) [Crossref]
• Kells et al., Topological transitions in weakly monitored free fermions
  SciPost Phys. 14, 031 (2023) [Crossref]
• Maimbourg et al., Bath-Induced Zeno Localization in Driven Many-Body Quantum Systems
  Phys. Rev. Lett. 126, 120603 (2021) [Crossref]
• Alba et al., Hydrodynamics of quantum entropies in Ising chains with linear dissipation
  J. Phys. A: Math. Theor. 55, 074002 (2022) [Crossref]
• Chen et al., Emergent conformal symmetry in nonunitary random dynamics of free fermions
  Phys. Rev. Research 2, 033017 (2020) [Crossref]
• Garratt et al., Measurements Conspire Nonlocally to Restructure Critical Quantum States
  Phys. Rev. X 13, 021026 (2023) [Crossref]
• Piccitto et al., Entanglement dynamics with string measurement operators
  SciPost Phys. Core 6, 078 (2023) [Crossref]
• Tsitsishvili et al., Measurement induced transitions in non-Markovian free fermion ladders
  SciPost Phys. Core 7, 011 (2024) [Crossref]
• Li et al., Cross Entropy Benchmark for Measurement-Induced Phase Transitions
  Phys. Rev. Lett. 130, 220404 (2023) [Crossref]
• Bastianello et al., Generalized hydrodynamics with dephasing noise
  Phys. Rev. B 102, 161110 (2020) [Crossref]
• Coppola et al., Growth of entanglement entropy under local projective measurements
  Phys. Rev. B 105, 094303 (2022) [Crossref]
• Pöpperl et al., Measurements on an Anderson chain
  Phys. Rev. B 107, 174203 (2023) [Crossref]
• Poboiko et al., Theory of Free Fermions under Random Projective Measurements
  Phys. Rev. X 13, 041046 (2023) [Crossref]
• Botzung et al., Engineered dissipation induced entanglement transition in quantum spin chains: From logarithmic growth to area law
  Phys. Rev. B 104, 184422 (2021) [Crossref]
• Merritt et al., Entanglement transitions with free fermions
  Phys. Rev. B 107, 064303 (2023) [Crossref]
• Carollo et al., Entanglement statistics in Markovian open quantum systems: A matter of mutation and selection
  Phys. Rev. E 102, 030104 (2020) [Crossref]
• Klocke et al., Topological order and entanglement dynamics in the measurement-only XZZX quantum code
  Phys. Rev. B 106, 104307 (2022) [Crossref]
• Feng et al., Absence of logarithmic and algebraic scaling entanglement phases due to the skin effect
  Phys. Rev. B 107, 094309 (2023) [Crossref]
• Dias et al., Quantum noise as a symmetry-breaking field
  Phys. Rev. B 108, L060302 (2023) [Crossref]
• Choi et al., Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
  Phys. Rev. Lett. 125, 030505 (2020) [Crossref]
• Gopalakrishnan et al., Entanglement and Purification Transitions in Non-Hermitian Quantum Mechanics
  Phys. Rev. Lett. 126, 170503 (2021) [Crossref]
• Ferté et al., Solvable Model of Quantum-Darwinism-Encoding Transitions
  Phys. Rev. Lett. 132, 110201 (2024) [Crossref]
• Shirakawa et al., Discretized quantum adiabatic process for free fermions and comparison with the imaginary-time evolution
  Phys. Rev. Research 3, 013004 (2021) [Crossref]
• Majumdar et al., Bath-induced phase transition in a Luttinger liquid
  Phys. Rev. B 107, 165113 (2023) [Crossref]