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Scrambling of algebras in open quantum systems

Faidon Andreadakis*, Namit Anand†, and Paolo Zanardi‡

  • Department of Physics and Astronomy and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA

  • *fandread@usc.edu
  • †namitana@usc.edu
  • ‡zanardi@usc.edu
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Phys. Rev. A 107, 042217 – Published 21 April, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.042217

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 (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 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 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.

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Phys. Rev. A 107, 042217– Published 21 April, 2023
  • Received 19 November 2022
  • Accepted 28 March 2023
Article part of CHORUS
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