Dynamics of Pseudoentanglement

• URL: http://arxiv.org/abs/2403.09619v2
• Date: Wed, 25 Sep 2024 18:21:53 GMT
• Title: Dynamics of Pseudoentanglement
• Authors: Xiaozhou Feng, Matteo Ippoliti,
• Abstract summary: dynamics of quantum entanglement plays a central role in explaining the emergence of thermal equilibrium in isolated many-body systems. Recent works have introduced a notion of pseudoentanglement describing ensembles of many-body states. This prompts the question: how much entanglement is truly necessary to achieve thermal equilibrium in quantum systems?
• Score: 0.03320194947871346
• License: http://creativecommons.org/licenses/by/4.0/
• 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. 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 pseudothermalization. These models replicate all the efficiently observable predictions of thermal equilibrium, while generating only a small amount of entanglement, thus deviating from the "maximum-entropy principle" that underpins thermodynamics. 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. 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 pseudothermalization transitions.

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