We study quantum information scrambling in spin models with both long-range all-to-all and short-range interactions. We argue that a simple global, spatially homogeneous interaction together with local chaotic dynamics is sufficient to give rise to fast scrambling, which describes the spread of quantum information over the entire system in a time that is logarithmic in the system size. This is illustrated in two tractable models: (1) a random circuit with Haar random local unitaries and a global interaction and (2) a classical model of globally coupled non-linear oscillators. We use exact numerics to provide further evidence by studying the time evolution of an out-of-time-order correlator and entanglement entropy in spin chains of intermediate sizes. Our results pave the way towards experimental investigations of fast scrambling and aspects of quantum gravity with quantum simulators.
We study the quantum thermalization and information scrambling dynamics of an experimentally realizable quantum spin model with homogeneous XX-type all-to-all interactions and random local potentials. We identify the thermalization-localization transition by changing the disorder strength, under a proper all-to-all interaction strength. The scrambling dynamics in the localization phase shows novel behaviors distinct from that of local models. The operator scrambling grows almost equally fast in both phases. In the thermal phase, we show there exhibits fast scrambling without appealing to the s…
I consider a spin chain with nearest-neighbor and next nearest-neighbor interactions. I show that the Hamiltonian obtained by specifying the desired combination of symmetry blocks is a fast scrambler. This is a smaller model than the "minimal model" by Belyansky et al..
Given a quantum many-body system with few-body interactions, how rapidly can quantum information be hidden during time evolution? The fast scrambling conjecture is that the time to thoroughly mix information among N degrees of freedom grows at least logarithmically in N. We derive this inequality for generic quantum systems at infinite temperature, bounding the scrambling time by a finite decay time of local quantum correlations at late times. Using Lieb-Robinson bounds, generalized Sachdev-Ye-Kitaev models, and random unitary circuits, we propose that a logarithmic scrambling time can be achi…
Motivated by the question of whether all fast scramblers are holographically dual to quantum gravity, we study the dynamics of a non-integrable spin chain model composed of two ingredients - a nearest neighbor Ising coupling, and an infinite range $XX$ interaction. Unlike other fast scrambling many-body systems, this model is not known to be dual to a black hole. We quantify the spreading of quantum information using an out-of time-ordered correlator (OTOC), and demonstrate that our model exhibits fast scrambling for a wide parameter regime. Simulation of its quench dynamics finds that the rap…
Out-of-time-order correlation functions provide a proxy for diagnosing chaos in quantum systems. We propose and analyze an interferometric scheme for their measurement, using only local quantum control and no reverse time evolution. Our approach utilizes a combination of Ramsey interferometry and the recently demonstrated ability to directly measure Renyi entropies. To implement our scheme, we present a pair of cold-atom-based experimental blueprints; moreover, we demonstrate that within these systems, one can naturally realize the transverse-field Sherrington-Kirkpatrick (TFSK) model, which e…
Fast scramblers are dynamical quantum systems that produce many-body entanglement on a timescale that grows logarithmically with the system size $N$. We propose and investigate a family of deterministic, fast scrambling quantum circuits realizable in near-term experiments with arrays of neutral atoms. We show that three experimental tools -- nearest-neighbour Rydberg interactions, global single-qubit rotations, and shuffling operations facilitated by an auxiliary tweezer array -- are sufficient to generate nonlocal interaction graphs capable of scrambling quantum information using only $O(\log…
In this study, we investigate out-of-time-order correlators (OTOCs) in systems with power-law decaying interactions such as $R^{-α}$, where $R$ is the distance. In such systems, the fast scrambling of quantum information or the exponential growth of information propagation can potentially occur according to the decay rate $α$. In this regard, a crucial open challenge is to identify the optimal condition for $α$ such that fast scrambling cannot occur. In this study, we disprove fast scrambling in generic long-range interacting systems with $α>D$ ($D$: spatial dimension), where the total energy …
The information loss problem in black hole evaporation is one of fundamental issues. Its resolution requires more profound understanding of information storage mechanism in quantum systems. In this Letter, we argue that when multiple unknown parameters are stored in large entangled qudits, strong chaos generated by fast scrambling in high temperature limit yields an ordered information storage structure with decoupled quantum information capsules (QICs). A rotational isometry emerges in the quantum Fisher information metric. The isometry is expected to be observed in future experiments on cold…
In this paper we revisit the gravitational eikonal amplitudes of two scattering spinning particles and inspect their scrambling power in the spin spaces that is quantified through the tripartite information. We found that in the non-relativistic limit and a special high-energy limit the leading contribution is a quantity that is universal and theory independent. The minimal coupling is singled out with minimal scrambling in a different high momenta limit. We also inspected the initial state dependence of entanglement generation and found that the spin coherent state with vanishing spin may not…
We study information scrambling, as diagnosed by the out-of-time order correlations (OTOCs), in a system of large spins collectively interacting via spatially inhomogeneous and incommensurate exchange couplings. The model is realisable in a cavity QED system in the dispersive regime. Fast scrambling, signalled by an exponential growth of the OTOCs, is observed when the couplings do not factorise into the product of a pair of local interaction terms, and at the same time the state of the spins points initially coplanar to the equator of the Bloch sphere. When one of these conditions is not real…
Quantum information scrambling under many-body dynamics is of fundamental interest. The tripartite mutual information can quantify the scrambling via its negative value. Here, we first study the quench dynamics of tripartite mutual information in a non-integrable Ising model where the strong and weak thermalization are observed with different initial states. We numerically show that the fastest scrambling can occur when the energy density of the chosen initial state possesses the maximum density of states. We then present an experimental protocol for observing weak and strong thermalization in…
We introduce a minimal model for realizing a fast-to-slow scrambling transition mediated by an auxiliary central qubit (c-qubit). The c-qubit is coupled to a spin-$1/2$ Ising model with local Ising interactions and tunable c-qubit-spin coupling. Each spin becomes next-nearest neighbor to all others through the c-qubit, which mediates effective all-to-all interactions. As the interaction with the c-spin increases, we find a surprising transition from super-ballistic scrambling and information growth to continuously restricted sub-ballistic entanglement and operator growth. This slow growth occu…
Scrambling of quantum information is the process by which information initially stored in the local degrees of freedom of a quantum many-body system spreads over its many-body degrees of freedom, becoming inaccessible to local probes and thus apparently lost. Scrambling and entanglement are key concepts reconciling seemingly unrelated behaviors including thermalization of isolated quantum systems and information loss in black holes, and have revolutionized our understanding of non-equilibrium phenomena. Here, we demonstrate that a family of fidelity out-of-time-order correlators (FOTOCs), rece…
Black holes are conjectured to be the fastest information scramblers, and within holographic duality, the speed of quantum information scrambling of thermal states of quantum systems is at the heart of studies of chaos and black hole dynamics. Here, considering the Ising interaction on the thermal state of spin chains with Dzyaloshinskii-Moriya (DM) interaction and measuring the out-of-time-order correlation functions, we study the effect of DM interaction on the speed of scrambling the quantum information. On the contrary to its advantages in quantum information and metrology such as exciting…
Many proposed quantum mechanical models of black holes include highly nonlocal interactions. The time required for thermalization to occur in such models should reflect the relaxation times associated with classical black holes in general relativity. Moreover, the time required for a particularly strong form of thermalization to occur, sometimes known as scrambling, determines the time scale on which black holes should start to release information. It has been conjectured that black holes scramble in a time logarithmic in their entropy, and that no system in nature can scramble faster. In this…
We demonstrate that a holographic model of the Einstein-Podolsky-Rosen pair exhibits fast scrambling. Strongly entangled quark and antiquark in $\mathcal{N}=4$ super Yang-Mills theory are considered. Their gravity dual is a fundamental string whose endpoints are uniformly accelerated in opposite direction. We slightly increase the acceleration of the endpoint and show that it quickly destroys the correlation between the quark and antiquark. The proper time scale of the destruction is $τ_\ast\sim β\ln S$ where $β$ is the inverse Unruh temperature and $S$ is the entropy of the accelerating quark…
Collective behavior strongly influences the charging dynamics of quantum batteries (QBs). Here, we study the impact of nonlocal correlations on the energy stored in a system of $N$ QBs. A unitary charging protocol based on a Sachdev-Ye-Kitaev (SYK) quench Hamiltonian is thus introduced and analyzed. SYK models describe strongly interacting systems with nonlocal correlations and fast thermalization properties. Here, we demonstrate that, once charged, the average energy stored in the QB is very stable, realizing an ultraprecise charging protocol. By studying fluctuations of the average energy st…
We propose an experimentally realizable quantum spin model that exhibits fast scrambling, based on non-local interactions which couple sites whose separation is a power of 2. By controlling the relative strengths of deterministic, non-random couplings, we can continuously tune from the linear geometry of a nearest-neighbor spin chain to an ultrametric geometry in which the effective distance between spins is governed by their positions on a tree graph. The transition in geometry can be observed in quench dynamics, and is furthermore manifest in calculations of the entanglement entropy. Between…
We study holographic entanglement and information scrambling in de-Sitter (dS) space in the context of the DS/dS correspondence. We find that our previously identified non-local entanglement structure of dS vacua can be extended out of the time-reflection symmetric slice. We extend the geometry to a two-sided configuration and calculate the zero-time mutual information between two intervals on different sides when there is a localized shock wave in the bulk. Interestingly, we find that the information scrambling time saturates the fast scrambler bound proposed by Sekino and Susskind and that t…
Proof of a Universal Speed Limit on Fast Scrambling in Quantum Systems
Joint Quantum Institute and Department of Physics, University of Maryland（马里兰大学联合量子研究所与物理系）；Condensed Matter Theory Center, Department of Physics, University of Maryland（马里兰大学凝聚态理论中心与物理系）
Information scrambling, characterized by the out-of-time-ordered correlator (OTOC), has attracted much attention, as it sheds new light on chaotic dynamics in quantum many-body systems. The scale invariance, which appears near the quantum critical region in condensed matter physics, is considered to be important for the fast decay of the OTOC. In this paper, we focus on the one-dimensional spin-1/2 XXZ model, which exhibits quantum criticality in a certain parameter region, and investigate the relationship between scrambling and the scale invariance. We quantify scrambling by the averaged OTOC…
Strongly long-range interacting quantum systems---those with interactions decaying as a power-law $1/r^α$ in the distance $r$ on a $D$-dimensional lattice for $α\le D$---have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. As a first step towards rectifying this problem, we prove two new Lieb-Robins…
Recently, physicists have started applying quantum information theory to black holes. This led to the conjecture that black holes are the fastest scramblers of information, and that they scramble it in time order M log M, where M is the mass of the black hole in natural units. As stated above, the conjecture is not completely defined, as there are several possible definitions of scrambling times. It appears that not all papers that refer to this conjecture interpret it the same way. We consider a definition of scrambling time stronger than the one given in the paper that first proposed this co…
In this letter we propose a general principle for how to build up a quantum neural network with high learning efficiency. Our stratagem is based on the equivalence between extracting information from input state to readout qubit and scrambling information from the readout qubit to input qubits. We characterize the quantum information scrambling by operator size growth, and by Haar random averaging over operator sizes, we propose an averaged operator size to describe the information scrambling ability for a given quantum neural network architectures, and argue this quantity is positively correl…
Quantum scrambling measured by out-of-time-ordered correlator (OTOC) has an important role in understanding the physics of black holes and evaluating quantum chaos. It is known that Rydberg atom has been a general interest due to its extremely favourable properties for building a quantum simulator. Fast and efficient quantum simulators can be developed by studying quantum scrambling in related systems. Here we present a general quantum circuit to theoretically implement an interferometric protocol which is a technique proposed to measure OTOC functions. We apply this circuit to measure OTOC an…
Two seemingly distinct notions regarding black holes have captured the imagination of theoretical physicists over the past decade: First, black holes are conjectured to be fast scramblers of information, a notion that is further supported through connections to quantum chaos and decay of mutual information via AdS/CFT holography. Second, black hole information paradox has motivated exotic quantum structure near horizons of black holes (e.g., gravastars, fuzzballs, or firewalls) that may manifest themselves through delayed gravitational wave echoes in the aftermath of black hole formation or me…
The entanglement evolution after a quantum quench became one of the tools to distinguish integrable versus chaotic (non-integrable) quantum many-body dynamics. Following this line of thoughts, here we propose that the revivals in the entanglement entropy provide a finite-size diagnostic benchmark for the purpose. Indeed, integrable models display periodic revivals manifested in a dip in the block entanglement entropy in a finite system. On the other hand, in chaotic systems, initial correlations get dispersed in the global degrees of freedom (information scrambling) and such a dip is suppresse…
Scrambling is a process by which the state of a quantum system is effectively randomized due to the global entanglement that "hides" initially localized quantum information. In this work, we lay the mathematical foundations of studying randomness complexities beyond scrambling by entanglement properties. We do so by analyzing the generalized (in particular Rényi) entanglement entropies of designs, i.e. ensembles of unitary channels or pure states that mimic the uniformly random distribution (given by the Haar measure) up to certain moments. A main collective conclusion is that the Rényi entang…
We study a family of weighted random walks on complete graphs. These `democratic walks' turn out to be explicitly solvable, and we find the hierarchy window for which the characteristic time scale saturates the so-called fast scrambling conjecture. We show that these democratic walks describe well the properties of information spreading in systems in which every degree of freedom interacts with every other degree of freedom, such as Matrix or infinite range models. The argument is based on the analysis of suitably defined `Information fields' ($\mathcal{I}$), which are shown to evolve stochast…
We study from the perspective of quantum information scrambling an acoustic black hole modelled by two semi-infinite, stationary, one dimensional condensates, connected by a spatial step-like discontinuity, and flowing respectively at subsonic and supersonic velocities. We develop a simple analytical treatment based on Bogolyubov theory of quantum fluctuations which is sufficient to derive analogue Hawking emission, and we compute out-of-time order correlations (OTOCs) of the Bose density field. We find that sonic black holes are slow scramblers contrary to their astrophysical counterparts: th…
We study the scrambling of quantum information in local random unitary circuits by focusing on the tripartite information proposed by Hosur et al. We provide exact results for the averaged Rényi-$2$ tripartite information in two cases: (i) the local gates are Haar random and (ii) the local gates are dual-unitary and randomly sampled from a single-site Haar-invariant measure. We show that the latter case defines a one-parameter family of circuits, and prove that for a "maximally chaotic" subset of this family quantum information is scrambled faster than in the Haar-random case. Our approach is …
