Out-of-time order correlators (OTOCs) are crucial tools for studying quantum chaos as they show distinct scrambling behavior for chaotic Hamiltonians. We calculate the OTOC and analyze the quantum information scrambling in atom-field and spin-spin interaction models, which are open-system models and exhibit non-Markovian behavior. We also examine the Loschmidt echo for these models and comment on their chaotic nature. The commutator growth of two local operators, which is upper bounded by the Lieb-Robinson bound, is studied for these models, and the patterns of scrambling are investigated.
Out-of-time order correlators (OTOCs) are crucial tools for studying quantum chaos as they show distinct scrambling behavior for chaotic Hamiltonians. We calculate the OTOC and analyze the quantum information scrambling in atom-field and spin-spin interaction models, which are open-system models and exhibit non-Markovian behavior. We also examine the Loschmidt echo for these models and comment on their chaotic nature. The commutator growth of two local operators, which is upper bounded by the Lieb-Robinson bound, is studied for these models, and the patterns of scrambling are investigated.
Quantum information scrambling, typically explored in closed quantum systems, describes the spread of initially localized information throughout a system and can be quantified by measures such as the Loschmidt echo (LE) and out-of-time-order correlator (OTOC). In this paper, we explore information scrambling in the presence of dissipation by generalizing the concepts of LE and OTOC to open quantum systems governed by Lindblad dynamics. We investigate the universal dynamics of the generalized LE across regimes of weak and strong dissipation. In the weak dissipation regime, we identify a universal structure, while in the strong dissipation regime, we observe a distinctive two-local-minima structure, which we interpret through an analysis of the Lindblad spectrum. Furthermore, we establish connections between the thermal averages of LE and OTOC and prove a general relation between OTOC and Rényi entropy in open systems. Finally, we propose an experimental protocol for measuring OTOC in open systems. These findings provide deeper insights into information scrambling under dissipation and pave the way for experimental studies in open quantum systems.
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.
Out-of-time-order correlators (OTOCs) serve as a proxy for quantum information scrambling, which refers to the process where information stored locally disperses across the many-body degrees of freedom in a quantum system, rendering it inaccessible to local probes. Most experimental implementations of OTOCs to probe information scrambling rely on indirect measurements based on global observables, using techniques such as Loschmidt echoes andmultiple quantum coherences, via time-reversal evolutions. In this article, we establish a direct connection between OTOCs with global and local observables in the context of NMR experiments, where the observable is the total magnetization of the system. We conduct a numerical analysis to quantify the differences in the evolution of both magnitudes, evaluating the excitation dynamics in spin ring systems with 8 to 16 spins, using a many-body Hamiltonian and long-range interactions. Our analysis decomposes the global echo into a sum of local echoes and cross-contributions, leading to local and global OTOCs. The results indicate that, after an initial transient period, local OTOCs determine the global ones. We observe that the difference between the average of local OTOCs and the global one, as well as their fluctuations, becomes negligible as the system size increases. Thus, for large homogeneous systems, global and local OTOCs become equivalent. This behavior aligns with that observed in highly interacting or chaotic systems in several experiments.
Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators.Operator growth is a manifestation of information scrambling and can be diagnosed by out-of-time-order correlators (OTOCs).However, the behavior of OTOCs of local operators in generic chaotic local Hamiltonians remains poorly understood, with some semiclassical and large-N models exhibiting exponential growth of OTOCs and a sharp chaos wave front and other random circuit models showing a diffusively broadened wave front.In this paper, we propose a unified physical picture for scrambling in chaotic local Hamiltonians.We construct a random time-dependent Hamiltonian model featuring a large-N limit where the OTOC obeys a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) type equation and exhibits exponential growth and a sharp wave front.We show that quantum fluctuations manifest as noise (distinct from the randomness of the couplings in the underlying Hamiltonian) in the FKPP equation and that the noise-averaged OTOC exhibits a crossover to a diffusively broadened wave front.At small N, we demonstrate that operator growth dynamics, averaged over the random couplings, can be efficiently simulated for all time using matrix product state techniques.To show that time-dependent randomness is not essential to our conclusions, we push our previous matrix product operator methods to very large size and show that data for a timeindependent Hamiltonian model are also consistent with a diffusively broadened wave front.
We investigate the integrability-to-chaos transition and information scrambling in Ising spin networks via a graph-theoretic formulation. Modeling spins as vertices and interactions as edges encoded by adjacency matrices across path, Erdos-Renyi, and Watts-Strogatz topologies, we demonstrate that long-range couplings and heterogeneous degree distributions markedly accelerate quantum information propagation. The Hamiltonian comprises local and normalized non-local interactions; tuning the non-local coupling and field heterogeneity drives integrability breaking. To quantify scrambling, we employ bipartite mutual and tripartite information. Increasing non-local interactions drives tripartite information to large negative values, signaling deep information scrambling. The squared commutators constructed from out-of-time-order correlators (OTOCs) exhibit early-time exponential growth; equivalently, the OTOC four-point functions themselves decay exponentially, yielding quantum Lyapunov exponents that scale systematically with parameters governing the chaotic regime. Complementing this, Krylov complexity reveals rapid operator growth in the chaotic phase, synchronizing with OTOC and mutual information dynamics. Spectrally, the transition manifests as a shift from Poissonian to Wigner-Dyson level spacing statistics. The spectral form factor (SFF) exhibits the characteristic slope-dip-ramp-plateau structure, enabling the extraction of Thouless and Heisenberg times. Crucially, a reduced Thouless time strongly correlates with accelerated information and operator scrambling. Ultimately, this work establishes a unified framework bridging network topology with information-theoretic, operator, and spectral diagnostics, offering insights into thermalization and non-equilibrium dynamics in quantum many-body systems.
Abstract How does quantum chaos lead to rapid scrambling of information as well as errors across a system when one introduces perturbations in the dynamics? What are its consequences for the reliability of quantum simulations and quantum information processing? We employ continuous measurement quantum tomography as a paradigm to study these questions. The measurement record is generated as a sequence of expectation values of a Hermitian observable evolving under repeated application of the Floquet map of the quantum kicked top. Interestingly, we find that the reconstruction fidelity initially increases regardless of the degree of chaos or the strength of perturbations in the dynamics. For random states, when the measurement record is obtained from a random initial observable, the subsequent drop in the fidelity obtained is inversely correlated to the degree of chaos in the dynamics. More importantly, this also gives us an operational interpretation of Loschmidt echo for operators by connecting it to the performance of quantum tomography. We define a quantity to capture the scrambling of errors, an out-of-time-ordered correlator (OTOC) between two operators under perturbed and unperturbed system dynamics that serves as a signature of chaos and quantifies the spread of errors. Our results demonstrate not only a fundamental link between Loschmidt echo and scrambling of errors, as captured by OTOCs, but that such a link can have operational consequences in quantum information processing.