Diagrammatic method for many-body non-Markovian dynamics: memory effects and entanglement transitions

Abstract

We study the quantum dynamics of a many-body system subject to coherent evolution and coupled to a non-Markovian bath. We propose a technique to unravel the non-Markovian dynamics in terms of quantum jumps, a connection that was so far only understood for single-body systems. We develop a systematic method to calculate the probability of a quantum trajectory, and formulate it in a diagrammatic structure. We find that non-Markovianity renormalizes the probability of realizing a quantum trajectory, and that memory effects can be interpreted as a perturbation on top of the Markovian dynamics. We show that the diagrammatic structure is akin to that of a Dyson equation, and that the probability of the trajectories can be calculated analytically. We then apply our results to study the measurement-induced entanglement transition in random unitary circuits. We find that non-Markovianity does not significantly shift the transition, but stabilizes the volume law phase of the entanglement by shielding it from transient strong dissipation.

References in corpus (102)

• Decoherence Free Subspaces for Quantum Computation
• Measure for the Degree of Non-Markovian Behavior of Quantum Processes in Open Systems
• Non-Markovian dynamics in open quantum systems
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Entanglement and non-Markovianity of quantum evolutions
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Quantum trajectories and open many-body quantum systems
• Operator Spreading in Random Unitary Circuits
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Assessing non-Markovian dynamics
• 1/f noise: implications for solid-state quantum information
• Measurement-driven entanglement transition in hybrid quantum circuits
• Keldysh Field Theory for Driven Open Quantum Systems
• Theory of the phase transition in random unitary circuits with measurements
• Quantum Computing Using Dissipation to Remain in a Decoherence-Free Subspace
• Measurement-induced criticality in random quantum circuits
• Strong dissipation inhibits losses and induces correlations in cold molecular gases
• Dynamical purification phase transitions induced by quantum measurements
• Observation of a dynamical topological phase transition
• Universal Fault-Tolerant Computation on Decoherence-Free Subspaces
• On the degree of non-Markovianity of quantum evolution
• Concepts of quantum non-Markovianity: a hierarchy
• Entanglement transition in a monitored free fermion chain -- from extended criticality to area law
• Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
• Dynamical Critical Phenomena in Driven-Dissipative Systems
• Stochastic wave function method for non-Markovian quantum master equations
• Non-Markovian quantum jumps
• Entanglement in a fermion chain under continuous monitoring
• Scalable probes of measurement-induced criticality
• Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
• Emergent statistical mechanics of entanglement in random unitary circuits
• Concatenating Decoherence Free Subspaces with Quantum Error Correcting Codes
• Observation of measurement-induced quantum phases in a trapped-ion quantum computer
• Entanglement phase transitions in measurement-only dynamics
• Measurement-induced topological entanglement transitions in symmetric random quantum circuits
• Statistical mechanics of quantum error correcting codes
• Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
• Unconventional magnetism via optical pumping of interacting spin systems
• Measurement-induced criticality in (2+1)-d hybrid quantum circuits
• Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems
• Experimental Realization of a Measurement-Induced Entanglement Phase Transition on a Superconducting Quantum Processor
• Universal non-equilibrium properties of dissipative Rydberg gases
• Genuine quantum trajectories for non-Markovian processes
• Measurement-induced dark state phase transitions in long-ranged fermion systems
• Entanglement Transitions from Stochastic Resetting of Non-Hermitian Quasiparticles
• Nonequilibrium many-body steady states via Keldysh formalism
• Entanglement and purification transitions in non-Hermitian quantum mechanics
• SYK meets non-Hermiticity II: measurement-induced phase transition
• Entanglement Transition in the Projective Transverse Field Ising Model
• Efficient classical simulation of random shallow 2D quantum circuits
• Observation of the photon-blockade breakdown phase transition
• Fate of measurement-induced phase transition in long-range interactions
• Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains
• Universality of entanglement transitions from stroboscopic to continuous measurements
• Emergent conformal symmetry in non-unitary random dynamics of free fermions
• Open system dynamics with non-Markovian quantum jumps
• Growth of entanglement entropy under local projective measurements
• Quantum critical regime in a quadratically-driven nonlinear photonic lattice
• Interaction-induced impeding of decoherence and anomalous diffusion
• Driven Markovian Quantum Criticality
• Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition
• An alternative non-Markovianity measure by divisibility of dynamical map
• Theory of Initialization-Free Decoherence-Free Subspaces and Subsystems
• Efficient classical simulation of noisy random quantum circuits in one dimension
• Entanglement Negativity at Measurement-Induced Criticality
• Measurement-induced phase transitions in $(d+1)$-dimensional stabilizer circuits
• Measurement-induced criticality and entanglement clusters: a study of 1D and 2D Clifford circuits
• Emergence of glass-like dynamics for dissipative and strongly interacting bosons
• Volume-to-Area Law Entanglement Transition in a non-Hermitian Free Fermionic Chain
• Open system quantum dynamics with correlated initial states, not completely positive maps and non-Markovianity
• Pure-state quantum trajectories for general non-Markovian systems do not exist
• Quantum error correction in the presence of spontaneous emission
• Measurement-Induced Power-Law Negativity in an Open Monitored Quantum Circuit
• Quantum criticality in the nonunitary dynamics of $(2+1)$-dimensional free fermions
• Two-time Correlations Probing the Dynamics of Dissipative Many-Body Quantum Systems: Aging and Fast Relaxation
• Monitored Open Fermion Dynamics: Exploring the Interplay of Measurement, Decoherence, and Free Hamiltonian Evolution
• Exotic attractors of the non-equilibrium Rabi-Hubbard model
• Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics
• Engineered dissipation induced entanglement transition in quantum spin chains: from logarithmic growth to area law
• A solvable family of driven-dissipative many-body systems
• Quantum Computation using Decoherence-Free States of the Physical Operator Algebra
• Transient trapping into metastable states in systems with competing orders
• Tensor network based machine learning of non-Markovian quantum processes
• Measuring and using non-markovianity
• Topological order and entanglement dynamics in the measurement-only XZZX quantum code
• Non-equilibrium fixed points of coupled Ising models
• Exploring quantum phases by driven dissipation
• Many-body quantum state diffusion for non-Markovian dynamics in strongly interacting systems
• Cluster representations and the Wolff algorithm in arbitrary external fields
• Entanglement, non-Markovianity, and causal non-separability
• Non-Markovian Quantum Dynamics in Strongly Coupled Multimode Cavities Conditioned on Continuous Measurement
• Transient superconductivity without superconductivity
• Measurement-Induced Phase Transition in a Quantum Spin System
• Rate operator unravelling for open quantum system dynamics
• Characterizing (non-)Markovianity through Fisher Information
• Polarity dependent heating at the phase interface in metal-insulator transitions
• Negative absolute conductivity in photoexcited metals
• Non-Markovian dynamics under time-translation symmetry
• Quantifying Non-Markovianity in Open Quantum Dynamics
• How to design quantum-jump trajectories via distinct master equation representations

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• Measurement induced transitions in non-Markovian free fermion ladders
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• The impact of different unravelings in a monitored system of free fermions
• Entanglement enhancement induced by noise in inhomogeneously monitored systems
• Nonstabilizerness in the unitary and monitored quantum dynamics of XXZ-staggered and SYK models
• Quantum trajectories for time-local non-Lindblad master equations
• Complexity of spin configurations dynamics due to unitary evolution and periodic projective measurements
• Generalizing measurement-induced phase transitions to information exchange symmetry breaking
• Generalized Rate Operator Quantum Jumps via Realization-Dependent Transformations
• Entanglement transitions induced by quantum-data collection
• Noise Classification in Three-Level Quantum Networks by Machine Learning
• Entanglement behavior and localization properties in monitored fermion systems
• Markovian to non-Markovian phase transition in the operator dynamics of a mobile impurity
• Entanglement transition in unitary system-bath dynamics
• Noisy Monitored Quantum Circuits