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arXiv:2405.03810 · New Journal of Physics

Bipartite OTOC in open quantum systems: information scrambling and irreversibility

Baibhab Bose, Devvrat Tiwari, Subhashish Banerjee

Published Sep 1, 2024• 3 citations
arXivHTMLPDF

Abstract

Abstract The field of information scrambling has seen significant growth over the last decade, where the out-of-time-ordered correlator (OTOC) has emerged as a prominent tool to probe it. In this work, we use bipartite OTOC, a particular form of OTOC, to study information scrambling in the atom–field interaction models and the model of the Ising spin chain interacting with a tilted magnetic field. This is done considering the effects of open quantum systems. A relationship between information scrambling, using bipartite OTOC, and irreversibility, using entropy production, is probed under unitary dynamics. The equivalence of bipartite OTOC with operator entanglement is explicitly shown for the Ising model.

DOI
10.1088/1367-2630/ad77ee

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Out-of-time-ordered correlators (OTOCs) have been extensively studied in recent years as a diagnostic of quantum information scrambling. In this paper, we study quantum information-theoretic aspects of the regularized finite-temperature OTOC. We introduce analytical results for the bipartite regularized OTOC (BROTOC): the regularized OTOC averaged over random unitaries supported over a bipartition. We show that the BROTOC has several interesting properties, for example, it quantifies the purity of the associated thermofield double state and the operator purity of the analytically continued time-evolution operator. At infinite-temperature, it reduces to one minus the operator entanglement of the time-evolution operator. In the zero-temperature limit and for nondegenerate Hamiltonians, the BROTOC probes the groundstate entanglement. By computing long-time averages, we show that the equilibration value of the BROTOC is intimately related to eigenstate entanglement. Finally, we numerically study the equilibration value of the BROTOC for various physically relevant Hamiltonian models and comment on its ability to distinguish integrable and chaotic dynamics.

arXiv:2111.07086•Quantum•Jun 27, 2022•13 citations
Abstract The field of information scrambling has seen significant growth over the last decade, where the out-of-time-ordered correlator (OTOC) has emerged as a prominent tool to probe it. In this work, we use bipartite OTOC, a particular form of OTOC, to study information scrambling in the atom–field interaction models and the model of the Ising spin chain interacting with a tilted magnetic field. This is done considering the effects of open quantum systems. A relationship between information scrambling, using bipartite OTOC, and irreversibility, using entropy production, is probed under unitary dynamics. The equivalence of bipartite OTOC with operator entanglement is explicitly shown for the Ising model.
The information scrambling phenomena in an open quantum system modeled by Ising spin chains coupled to Lipkin-Meshkov-Glick (LMG) baths are observed via an interferometric method for obtaining out-of-time-ordered correlators ($\mathcal{F}\ensuremath{-}\mathrm{OTOC}$). We also use an anisotropic bath connecting to a system of tilted field Ising spin chains in order to confirm that such situations are suitable for the emergence of ballistic spreading of information manifested in the light cones in the $\mathcal{F}\ensuremath{-}\mathrm{OTOC}$ profiles. Bipartite OTOC is also calculated for a bipartite open system, and its behavior is compared with that of the $\mathcal{F}\ensuremath{-}\mathrm{OTOC}$ of a two-spin open system to get a picture of what these measures reveal about the nature of scrambling in different parameter regimes. Additionally, the presence of distinct phases in the LMG model motivated an independent analysis of its scrambling properties, where $\mathcal{F}\ensuremath{-}\mathrm{OTOC}$ diagnostics revealed that quantum chaos emerges exclusively in the symmetry-broken phase.
In recent years, the out-of-time-order correlator (OTOC) has emerged as a diagnostic tool for information scrambling in quantum many-body systems. Here, we present exact analytical results for the OTOC for a typical pair of random local operators supported over two regions of a bipartition. Quite remarkably, we show that this "bipartite OTOC" is equal to the operator entanglement of the evolution, and we determine its interplay with entangling power. Furthermore, we compute long-time averages of the OTOC and reveal their connection with eigenstate entanglement. For Hamiltonian systems, we uncover a hierarchy of constraints over the structure of the spectrum and elucidate how this affects the equilibration value of the OTOC. Finally, we provide operational significance to this bipartite OTOC by unraveling intimate connections with average entropy production and scrambling of information at the level of quantum channels.
Out-of-time-ordered correlators (OTOCs) have been extensively used over the past few years to study information scrambling and quantum chaos in many-body systems. In this paper, we extend the formalism of the averaged bipartite OTOC of Styliaris et al. [Phys. Rev. Lett. 126, 030601 (2021)] to the case of open quantum systems. The dynamics is no longer unitary but it is described by more general quantum channels (trace preserving, completely positive maps). This ``open bipartite OTOC'' can be treated in an exact analytical fashion and is shown to amount to a distance between two quantum channels. Moreover, our analytical form unveils competing entropic contributions from information scrambling and environmental decoherence such that the latter can obfuscate the former. To elucidate this subtle interplay, we analytically study special classes of quantum channels, namely, dephasing channels, entanglement-breaking channels, and others. Finally, as a physical application we numerically study dissipative many-body spin chains and show how the competing entropic effects can be used to differentiate between integrable and chaotic regimes.
How fast quantum information scrambles such that it becomes inaccessible by local probes turns out to be central to various fields. Motivated by recent works on spin systems with nonlocal interactions, we study information scrambling in different variants of the Ising model. Our work reveals that nonlocal interactions can induce operator dynamics not precisely captured by out-of-time-order correlators (OTOCs). In particular, the operator size exhibits a slowdown in systems with generic power-law interactions despite a highly nonlinear light cone. A recently proposed microscopic model for fast scrambling does not show this slowdown, which uncovers a distinct analogy between a local operator under unitary evolution and the entanglement entropy following a quantum quench. Our work gives new insights on scrambling properties of systems in reach of current quantum simulation platforms and complements results on possibly observing features of quantum gravity in the laboratory.
Out-of-time-ordered correlators (OTOCs) have been extensively studied in recent years as a diagnostic of quantum information scrambling. In this paper, we study quantum information-theoretic aspects of the regularized finite-temperature OTOC. We introduce analytical results for the bipartite regularized OTOC (BROTOC): the regularized OTOC averaged over random unitaries supported over a bipartition. We show that the BROTOC has several interesting properties, for example, it quantifies the purity of the associated thermofield double state and the operator purity of the analytically continued time-evolution operator. At infinite-temperature, it reduces to one minus the operator entanglement of the time-evolution operator. In the zero-temperature limit and for nondegenerate Hamiltonians, the BROTOC probes the groundstate entanglement. By computing long-time averages, we show that the equilibration value of the BROTOC is intimately related to eigenstate entanglement. Finally, we numerically study the equilibration value of the BROTOC for various physically relevant Hamiltonian models and comment on its ability to distinguish integrable and chaotic dynamics.
Out-of-time-ordered correlators (OTOCs) have been extensively studied in recent years as a diagnostic of quantum information scrambling. In this paper, we study quantum information-theoretic aspects of the regularized finite-temperature OTOC. We introduce analytical results for the bipartite regularized OTOC (BROTOC): the regularized OTOC averaged over random unitaries supported over a bipartition. We show that the BROTOC has several interesting properties, for example, it quantifies the purity of the associated thermofield double state and the operator purity of the analytically continued time-evolution operator. At infinite-temperature, it reduces to one minus the operator entanglement of the time-evolution operator. In the zero-temperature limit and for nondegenerate Hamiltonians, the BROTOC probes the groundstate entanglement. By computing long-time averages, we show that the equilibration value of the BROTOC is intimately related to eigenstate entanglement. Finally, we numerically study the equilibration value of the BROTOC for various physically relevant Hamiltonian models and comment on its ability to distinguish integrable and chaotic dynamics.