Dynamics of Pseudoentanglement

Abstract

The dynamics of quantum entanglement plays a central role in explaining the emergence of thermal equilibrium in isolated many-body systems. However, entanglement is notoriously hard to measure. Recent works have introduced a notion of pseudoentanglement describing ensembles of many-body states that, while only weakly entangled, cannot be efficiently distinguished from states with much higher entanglement, such as random states in the Hilbert space. This prompts the question: how much entanglement is truly necessary to achieve thermal equilibrium in quantum systems? In this work we address this question by introducing random circuit models of quantum dynamics that, at late times, equilibrate to pseudoentangled ensembles -- a phenomenon we name ensemble pseudothermalization. These models replicate all the efficiently observable predictions of thermal equilibrium, while generating only a small (and tunable) amount of entanglement. We examine (i) how a pseudoentangled ensemble on a small subsystem spreads to the whole system as a function of time, and (ii) how a pseudoentangled ensemble can be generated from an initial product state. We map the above problems onto a family of classical Markov chains on subsets of the computational basis. The mixing times of such Markov chains are related to the time scales at which the states produced from the dynamics become indistinguishable from Haar-random states at the level of each statistical moment, or number of copies. Based on a combination of rigorous bounds and conjectures supported by numerics, we argue that each Markov chain's relaxation time and mixing time have different asymptotic behavior in the limit of large system size. This is a necessary condition for a cutoff phenomenon: an abrupt dynamical transition to equilibrium. We thus conjecture that our random circuits give rise to asymptotically sharp distinguishability transitions.

16 pages main text + 8 pages appendix. 9 figures. v2: thoroughly updated presentation, added subsection VI.B on 'Implications', added note on recent results on spectral gaps of random circuits. v3: reformatted for JHEP, minor changes

References in corpus (52)

• Quantum entanglement
• Thermalization and its mechanism for generic isolated quantum systems
• Topological entanglement entropy
• Many body localization and thermalization in quantum statistical mechanics
• Entanglement entropy and conformal field theory
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Quantum Resource Theories
• Measuring entanglement entropy through the interference of quantum many-body twins
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Quantum thermalization through entanglement in an isolated many-body system
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Generalized Gibbs ensemble in integrable lattice models
• Identifying Topological Order by Entanglement Entropy
• Probing entanglement entropy via randomized measurements
• Random Quantum Circuits
• Chaos and complexity by design
• The randomized measurement toolbox
• Scalable probes of measurement-induced criticality
• Avalanches and many-body resonances in many-body localized systems
• Observation of measurement-induced quantum phases in a trapped-ion quantum computer
• Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
• Matrix product simulations of non-equilibrium steady states of quantum spin chains
• Measurement-induced entanglement and teleportation on a noisy quantum processor
• Markovian baths and quantum avalanches
• A review of Quantum Cellular Automata
• Pseudorandom States, Non-Cloning Theorems and Quantum Money
• Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton
• Models of quantum complexity growth
• Anomalous Subdiffusion from Subsystem Symmetries
• Exact emergent quantum state designs from quantum chaotic dynamics
• Operator growth and eigenstate entanglement in an interacting integrable Floquet system
• Measurement-induced phase transitions in quantum automaton circuits
• Dynamical purification and the emergence of quantum state designs from the projected ensemble
• Proof of Aldous' spectral gap conjecture
• Entanglement dynamics in hybrid quantum circuits
• Solvable model of deep thermalization with distinct design times
• Local gap threshold for frustration-free spin systems
• Classical Shadows for Quantum Process Tomography on Near-term Quantum Computers
• Probing post-measurement entanglement without post-selection
• Generalized Deep Thermalization for Free Fermions
• Pseudomagic Quantum States
• Quantum State Complexity in Computationally Tractable Quantum Circuits
• Finite-time teleportation phase transition in random quantum circuits
• Quantum many-body systems in thermal equilibrium
• A Cutoff Phenomenon for Quantum Markov Chains
• Complete Hilbert-Space Ergodicity in Quantum Dynamics of Generalized Fibonacci Drives
• Transport properties of a boundary-driven one-dimensional gas of spinless fermions
• Deep thermalization in constrained quantum systems
• Postselection-free learning of measurement-induced quantum dynamics
• Black holes often saturate entanglement entropy the fastest
• Cutoff phenomenon and entropic uncertainty for random quantum circuits

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