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arXiv:2408.12089 · Physical review. E

Information scrambling in bosonic Gaussian dynamics

Ali Mollabashi, Saleh Rahimi-Keshari

Published Aug 18, 2025• 2 citations
arXivHTMLPDF

Abstract

We investigate the dynamics of information scrambling in bosonic systems undergoing Gaussian unitary evolution associated with quadratic Hamiltonians. For initial Gaussian states, we observe the disappearance of the memory effect in the entanglement dynamics of disjoint blocks under Gaussian random local dynamics. In addition, we show that randomness in the Hamiltonian causes the tripartite mutual information to saturate at relatively large negative values. Therefore, despite being integrable, these systems exhibit information-scrambling diagnostics that mirror those observed in chaotic systems. We note, however, that random quadratic Hamiltonians can have a component exhibiting Wigner-Dyson energy-level statistics; for non-Gaussian states within the corresponding subspace, these systems can display chaotic behavior. Our results provide insight into the Gaussian dynamics of continuous-variable systems, which are useful and available resources for quantum information processing.

DOI
10.1103/wvpl-jdgk

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We investigate the dynamics of information scrambling in bosonic systems undergoing Gaussian unitary evolution associated with quadratic Hamiltonians. For initial Gaussian states, we observe the disappearance of the memory effect in the entanglement dynamics of disjoint blocks under Gaussian random local dynamics. In addition, we show that randomness in the Hamiltonian causes the tripartite mutual information to saturate at relatively large negative values. Therefore, despite being integrable, these systems exhibit information-scrambling diagnostics that mirror those observed in chaotic systems. We note, however, that random quadratic Hamiltonians can have a component exhibiting Wigner-Dyson energy-level statistics; for non-Gaussian states within the corresponding subspace, these systems can display chaotic behavior. Our results provide insight into the Gaussian dynamics of continuous-variable systems, which are useful and available resources for quantum information processing.
We study the role of randomness in the scrambling of quantum information within integrable free-fermionic systems. Considering quadratic Hamiltonians with varying degrees of randomness, we analyze entanglement-based measures to characterize the scrambling structure. We show that the memory effect in the entanglement of disjoint subsystems of Gaussian states vanishes when the local couplings are random, indicating information delocalization. The tripartite mutual information exhibits negative saturation values similar to those in chaotic systems, albeit with a smaller magnitude, revealing weaker scrambling under integrable quadratic dynamics. Despite integrability, spectral analyses reveal that local random models display a spectral-form-factor ramp and a partial crossover in the single-particle level-spacing ratio from Poisson-like to Wigner--Dyson-like behavior within a certain range of random couplings. These results demonstrate that randomness can act as a minimal ingredient for inducing information scrambling in integrable quadratic fermionic models.
A bstract We investigate minimal two-body Hamiltonians with random interactions that generate spectra resembling those of Gaussian random matrices, a phenomenon we term quadratic quantum chaos . Unlike integrable two-body fermionic systems, the corresponding hard-core boson models exhibit genuinely chaotic dynamics, closely paralleling the Sachdev-Ye-Kitaev (SYK) model in its spin representation. This chaotic behavior is diagnosed through spectral statistics and measures of operator growth, including Krylov complexity and the late-time decay of higher-order out-of-time-ordered correlators (OTOCs); the latter reveals the emergence of freeness in the sense of free probability. Moreover, the fractal dimension and Stabilizer Rényi entropy of a representative mid-spectrum eigenstate show finite-size deviations yet converge toward Haar-randomness as the system size increases. This convergence, constrained by local interactions, highlights the “weakly chaotic” character of these eigenstates. Owing to their simplicity and bosonic nature, these minimal models may constitute promising and resource-efficient candidates for probing quantum chaos and information scrambling on near-term quantum devices.
The study of information scrambling in many-body systems has sharpened our understanding of quantum chaos, complexity, and gravity. Here, we extend the framework for exploring information scrambling to infinite-dimensional continuous variable (CV) systems. Unlike their discrete variable cousins, continuous variable systems exhibit two complementary domains of information scrambling: (i) scrambling in the phase space of a single mode and (ii) scrambling across multiple modes of a many-body system. Moreover, for each of these domains, we identify two distinct types of scrambling; genuine scrambling, where an initial operator localized in phase space spreads out, and quasiscrambling, where a local ensemble of operators distorts but the overall phase space volume remains fixed. To characterize these behaviors, we introduce a CV out-of-time-order correlation (OTOC) function based upon displacement operators and offer a number of results regarding the CV analog for unitary designs. Finally, we investigate operator spreading and entanglement growth in random local Gaussian circuits; to explain the observed behavior, we propose a simple hydrodynamical model that relates the butterfly velocity, the growth exponent, and the diffusion constant. Experimental realizations of continuous variable scrambling as well as its characterization using CV OTOCs will be discussed.
Information scrambling is a hallmark of quantum chaos and thermalization in isolated quantum many-body systems. We investigate scrambling dynamics in the all-to-all interacting spin Sachdev-Ye-Kitaev (SYK)-qqq model using both pure- and mixed-state entanglement measures. We show that von-Neumann and Rényi entropies exhibit rapid growth followed by saturation near Haar-random values, signaling efficient scrambling. The scrambling rate reveals a nontrivial dependence on the interaction order, system size, and Hamiltonian scaling. We further employ mixed-state entanglement as a powerful probe of information scrambling. We numerically find a universal relation between the Rényi-1/2 mutual information and entanglement negativity for minimal interaction order in the early growth regime. Furthermore, entanglement negativity displays a Page-curve-like behavior under unequal subsystem partitioning, characterized by the birth, spread, and eventual death of quantum correlations. Our results provide a generic description of information scrambling using entanglement dynamics in all-to-all interacting spin systems with multi-body interactions.
A closed quantum system never forgets its initial state, but the encoded information can get scrambled and become inaccessible without measuring a large fraction of all the system degrees of freedom. This scrambling can be diagnosed by studying the spatial spreading of initially local operators under the Heisenberg time evolution, and the decay of the out-of-time-ordered correlators (OTOC). What insights can OTOCs provide to understand the dynamics of quantum many-body systems? What are the characteristic behaviors of OTOCs during the time evolution? How is information scrambling affected by the dissipation in open quantum many-body systems? We first study slow scrambling in many-body localized systems via calculating various correlators, two-point retarded correlators and OTOCs. Comparing with retarded correlators, OTOCs provide more information about the dynamics. We find that disorder slows and partially halts the onset of information scrambling. Instead of ballistic spreading, propagation of information forms a logarithmic light cone. Next, we study the finite-size scaling of OTOCs at late times in generic thermalizing quantum many-body systems. When energy is conserved, the late-time saturation value of the OTOC of generic traceless local operators scales as an inverse polynomial in the system size. This is in contrast to the inverse exponential scaling expected for chaotic dynamics without energy conservation. We also study information scrambling in open quantum many-body systems. We define a dissipative version of OTOC and study its behaviors in a prototypical chaotic quantum chain with dissipation. We find that dissipation leads to not only the overall decay of the scrambled information due to leaking, but also structural changes so that the information light cone can only reach a finite distance even when the effect of overall decay is removed. Finally, we construct a family of local Hamiltonians for understanding the asymmetric information scrambling. Our models live on a one-dimensional lattice and exhibit asymmetric butterfly light cone between the left and right spatial directions.
We systematically investigate scrambling (or delocalizing) processes of quantum information encoded in quantum many-body systems by using numerical exact diagonalization. As a measure of scrambling, we adopt the tripartite mutual information (TMI) that becomes negative when quantum information is delocalized. We clarify that scrambling is an independent property of the integrability of Hamiltonians; TMI can be negative or positive for both integrable and nonintegrable systems. This implies that scrambling is a separate concept from conventional quantum chaos characterized by nonintegrability. Specifically, we argue that there are a few exceptional initial states that do not exhibit scrambling, and show that such exceptional initial states have small effective dimensions. Furthermore, we calculate TMI in the Sachdev-Ye-Kitaev (SYK) model, a fermionic toy model of quantum gravity. We find that disorder does not make scrambling slower but makes it smoother in the SYK model, in contrast to many-body localization in spin chains.