Scrambling of Algebras in Open Quantum Systems

TL;DR

This paper introduces an algebraic out-of-time-ordered correlator (OTOC) framework to analyze information scrambling in open quantum systems, highlighting the interplay between environmental decoherence and local scrambling.

Contribution

It generalizes the algebraic OTOC approach from closed to open quantum systems, providing new insights into the competition between decoherence and scrambling.

Findings

Analytical characterization of information scrambling in open systems.

Numerical simulations linking scrambling to many-body scars.

Identification of decoherence-free subspaces stability.

Abstract

Many quantitative approaches to the dynamical scrambling of information in quantum systems involve the study of out-of-time-ordered correlators (OTOCs). In this paper, we introduce an algebraic OTOC ($\mathcal{A}$-OTOC) that allows us to study information scrambling of generalized quantum subsystems under quantum channels. For closed quantum systems, this algebraic framework was recently employed to unify quantum information-theoretic notions of operator entanglement, coherence-generating power, and Loschmidt echo. The main focus of this work is to provide a natural generalization of these techniques to open quantum systems. We first show that, for unitary dynamics, the $\mathcal{A}$-OTOC quantifies a generalized notion of information scrambling, namely between a subalgebra of observables and its commutant. For open quantum systems, on the other hand, we find a competition between the global environmental decoherence and the local scrambling of information. We illustrate this interplay by analytically studying various illustrative examples of algebras and quantum channels. To complement our analytical results, we perform numerical simulations of two paradigmatic systems: the PXP model and the Heisenberg XXX model, under dephasing. Our numerical results reveal connections with many-body scars and the stability of decoherence-free subspaces.