Fast Scrambling Research Articles

Black holes, complex curves, and graph theory: Revising a conjecture by Kasner

The ratios 8/9=22/3≈0.9428 and 3/2≈0.866 appear in various contexts of black hole physics, as values of the charge-to-mass ratio Q/M or the rotation parameter a/M for Reissner-Nordström and Kerr black holes, respectively. In this work, in the Reissner-Nordström case, I relate these ratios with the quantization of the horizon area, or equivalently of the entropy. Furthermore, these ratios are related to a century-old work of Kasner, in which he conjectured that certain sequences arising from complex analysis may have a quantum interpretation. These numbers also appear in the case of Kerr black holes, but the explanation is not as straightforward. The Kasner ratio may also be relevant for understanding the random matrix and random graph approaches to black hole physics, such as fast scrambling of quantum information, via a bound related to Ramanujan graph. Intriguingly, some other pure mathematical problems in complex analysis, notably complex interpolation in the unit disk, appear to share some mathematical expressions with the black hole problem and thus also involve the Kasner ratio.

Operator growth and spread complexity in open quantum systems

Commonly, the notion of “quantum chaos” refers to the fast scrambling of information throughout complex quantum systems undergoing unitary evolution. Motivated by the Krylov complexity and the operator growth hypothesis, we demonstrate that the entropy of the population distribution for an operator in time is a useful way to capture the complexity of the internal information dynamics of a system when subject to an environment and is, in principle, agnostic to the specific choice of operator basis. We demonstrate its effectiveness for the Sachdev-Ye-Kitaev (SYK) model, examining the dynamics of the system in both its Krylov basis and the basis of operator strings. We prove that the former basis minimises spread complexity while the latter is an eigenbasis for high dissipation. In both cases, we probe the long-time dynamics of the model and the phenomenological effects of decoherence on the complexity of the dynamics.

Improving metrology with quantum scrambling in a spin-1 Bose-Einstein condensate coupled to a cavity

Spinor Bose-Einstein condensate is an ideal candidate for implementing the many-body entanglement, quantum measurement and quantum information processing owing to its inherent spin-mixing dynamics. Here we present a system of an 87Rb atomic spin-1 Bose-Einstein condensate coupled to an optical ring cavity, in which cavity-mediated nonlinear interactions give rise to saddle points in the semiclassical phase space, providing a general mechanism for exponential fast scrambling and metrological gain augment. We theoretically study metrological gain and fidelity out-of-time-ordered correlator based on time-reversal protocols and demonstrate that exponential rapid scrambling dynamics can enhance quantum metrology. In addition, we use the out-of-time-ordered correlator to probe dynamical phase transitions. This work is useful to understand the intrinsic relation between the concepts from different subfields of quantum science.

Quantum theory of three-dimensional de Sitter space

We sketch the construction of a quantum model of three-dimensional de Sitter space, based on the covariant entropy principle and the observation that semiclassical physics suggests the possibility of a consistent theory of a finite number of unstable massive particles with purely gravitational interactions. Our model is holographic, finite, unitary, causal, plausibly exhibits fast scrambling, and qualitatively reproduces features of semiclassical de Sitter physics. In an appendix we outline some calculations that might lead to further tests of the model. Published by the American Physical Society 2024

Exploiting Newly Designed Fractional-Order 3D Lorenz Chaotic System and 2D Discrete Polynomial Hyper-Chaotic Map for High-Performance Multi-Image Encryption

Chaos-based image encryption has become a prominent area of research in recent years. In comparison to ordinary chaotic systems, fractional-order chaotic systems tend to have a greater number of control parameters and more complex dynamical characteristics. Thus, an increasing number of researchers are introducing fractional-order chaotic systems to enhance the security of chaos-based image encryption. However, their suggested algorithms still suffer from some security, practicality, and efficiency problems. To address these problems, we first constructed a new fractional-order 3D Lorenz chaotic system and a 2D sinusoidally constrained polynomial hyper-chaotic map (2D-SCPM). Then, we elaborately developed a multi-image encryption algorithm based on the new fractional-order 3D Lorenz chaotic system and 2D-SCPM (MIEA-FCSM). The introduction of the fractional-order 3D Lorenz chaotic system with the fourth parameter not only enables MIEA-FCSM to have a significantly large key space but also enhances its overall security. Compared with recent alternatives, the structure of 2D-SCPM is simpler and more conducive to application implementation. In our proposed MIEA-FCSM, multi-channel fusion initially reduces the number of pixels to one-sixth of the original. Next, after two rounds of plaintext-related chaotic random substitution, dynamic diffusion, and fast scrambling, the fused 2D pixel matrix is eventually encrypted into the ciphertext one. According to numerous experiments and analyses, MIEA-FCSM obtained excellent scores for key space (2541), correlation coefficients (<0.004), information entropy (7.9994), NPCR (99.6098%), and UACI (33.4659%). Significantly, MIEA-FCSM also attained an average encryption rate as high as 168.5608 Mbps. Due to the superiority of the new fractional-order chaotic system, 2D-SCPM, and targeted designs, MIEA-FCSM outperforms many recently reported leading image encryption algorithms.

Dynamical transition from localized to uniform scrambling in locally hyperbolic systems.

Fast scrambling of quantum correlations, reflected by the exponential growth of out-of-time-order correlators (OTOCs) on short pre-Ehrenfest time scales, is commonly considered as a major quantum signature of unstable dynamics in quantum systems with a classical limit. In two recent works [Phys.Rev. Lett. 123, 160401 (2019)0031-900710.1103/PhysRevLett.123.160401] and [Phys. Rev.Lett. 124, 140602 (2020)10.1103/PhysRevLett.124.140602], a significant difference in the scrambling rate of integrable (many-body) systems was observed, depending on the initial state being semiclassically localized around unstable fixed points or fully delocalized (infinite temperature). Specifically, the quantum Lyapunov exponent λ_{q} quantifying the OTOC growth is given, respectively, by λ_{q}=2λ_{s} or λ_{q}=λ_{s} in terms of the stability exponent λ_{s} of the hyperbolic fixed point. Here we show that a wave packet, initially localized around this fixed point, features a distinct dynamical transition between these two regions. We present an analytical semiclassical approach providing a physical picture of this phenomenon, and support our findings by extensive numerical simulations in the whole parameter range of locally unstable dynamics of a Bose-Hubbard dimer. Our results suggest that the existence of this crossover is a hallmark of unstable separatrix dynamics in integrable systems, thus opening the possibility to distinguish the latter, on the basis of this particular observable, from genuine chaotic dynamics generally featuring uniform exponential growth of the OTOC.

Fast prescramblers

We consider the process of diffusion or "pre-scrambling" of information in a quantum system. We define a measure for this spreading or "pre-scrambling" of the wavefunction in terms of a minimum probability threshold for the states in the system's Hilbert space. We illustrate our findings on the example of a prototype model with enhanced memory capacity. We conjecture: (1) The fastest pre-scramblers require a time logarithmic in the number of degrees of freedom. (2) The investigated enhanced memory capacity model is a fast pre-scrambler. (3) (Fast) pre-scrambling occurs not later than (fast) scrambling. (4) Fast scramblers are fast pre-scramblers. (5) Black holes are fast pre-scramblers.

Signatures of the interplay between chaos and local criticality on the dynamics of scrambling in many-body systems.

Fast scrambling, quantified by the exponential initial growth of out-of-time-ordered correlators (OTOCs), is the ability to efficiently spread quantum correlations among the degrees of freedom of interacting systems and constitutes a characteristic signature of local unstable dynamics. As such, it may equally manifest both in systems displaying chaos or in integrable systems around criticality. Here we go beyond these extreme regimes with an exhaustive study of the interplay between local criticality and chaos right at the intricate phase-space region where the integrability-chaos transition first appears. We address systems with a well-defined classical (mean-field) limit, as coupled large spins and Bose-Hubbard chains, thus allowing for semiclassical analysis. Our aim is to investigate the dependence of the exponential growth of the OTOCs, defining the quantum Lyapunov exponent λ_{q} on quantities derived from the classical system with mixed phase space, specifically the local stability exponent of a fixed point λ_{loc} as well as the maximal Lyapunov exponent λ_{L} of the chaotic region around it. By extensive numerical simulations covering a wide range of parameters we give support to a conjectured linear dependence 2λ_{q}=aλ_{L}+bλ_{loc}, providing a simple route to characterize scrambling at the border between chaos and integrability.

Fast scrambling of mutual information in Kerr-AdS5

We compute the disruption of mutual information in a TFD state dual to a Kerr black hole with equal angular momenta in AdS5 due to an equatorial shockwave. The shockwave respects the axi-symmetry of the Kerr geometry with specific angular momenta {mathcal{L}}_{phi_1} & {mathcal{L}}_{phi_2} . The sub-systems considered are hemispheres in the left and the right dual CFTs with the equator of the S3 as their boundary. We compute the change in the mutual information by determining the growth of the HRT surface at late times. We find that at late times leading up to the scrambling time the minimum value of the instantaneous Lyapunov index {lambda}_L^{left(min right)} is bounded by kappa =frac{2pi {T}_H}{left(1-mu {mathcal{L}}_{+}right)} and is found to be greater than 2πTH in certain regimes with TH and μ denoting the black hole’s temperature and the horizon angular velocity respectively while {mathcal{L}}_{+} = {mathcal{L}}_{phi_1} + {mathcal{L}}_{phi_2} . We also find that for non-extremal geometries the null perturbation obeys {mathcal{L}}_{+} < μ−1 for it to reach the outer horizon from the AdS boundary. The scrambling time at very late times is given by κτ* ≈ log mathcal{S} where mathcal{S} is the Kerr entropy. We also find that the onset of scrambling is delayed due to a term proportional to log(1 − {mu mathcal{L}}_{+} )−1 which is not extensive and does not scale with the entropy of Kerr black hole.

Beyond quantum chaos in emergent dual holography

Black holes are well known to be fast scramblers, responsible for physics of quantum chaos in dual holography. Recently, the Euclidean wormhole has been proposed to play a central role in the chaotic behavior of the spectral form factor. Furthermore, this phenomena was reinterpreted based on an effective field theory approach for quantum chaos. Since the graded nonlinear $\ensuremath{\sigma}$-model approach can describe not only the Wigner-Dyson level statistics but also its Poisson distribution, it is natural to ask whether the dual holography can touch the Poisson regime beyond the quantum chaos. In this study, we investigate disordered strongly coupled conformal field theories in the large central-charge limit. An idea is to consider a quenched average for metric fluctuations and to take into account the renormalization group flow of the metric-tensor distribution function from the UV to the IR boundary. Here, renormalization effects at a given disorder configuration are described by the conventional dual holography. We uncover that the renormalized distribution function shows a power-law behavior universally, interpreted as an infinite randomness fixed point.

Fast scrambling dynamics and many-body localization transition in an all-to-all disordered quantum spin model

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 behaviors that are distinct from that of local models. The operator scrambling grows almost equally fast in the two phases. In the thermal phase, we show that fast scrambling is exhibited without appealing to the semiclassical limit. We also briefly discuss the experimental realization of the model using superconducting qubit quantum simulators.

Unexpected Acid-Triggered Formation of Reversibly Photoswitchable Stenhouse Salts from Donor-Acceptor Stenhouse Adducts.

Donor-acceptor Stenhouse adducts (DASAs) are reversibly photoswitchable dyes, which are able to interconvert between a red/NIR absorbing triene-like state and a colorless cyclic state. Although optically attractive for multiple applications, their low solubility and lack of photoswitching in water impede their use in aqueous environments. We developed water-soluble DASAs based on indoline as donor and methyl, or trifluoromethyl, pyrazolone-based acceptors. In acetonitrile, photophysical analysis and photochemical studies, accounted with a three-state kinetic model, confirmed the reversible photoswitching mechanism previously proposed. In water, the colorless cyclic state is a thermodynamic sink at neutral pH values. In contrast, in acidic conditions, we observed a fast scrambling of DASAs' end-group resulting in the in situ formation of Stenhouse salts (StS), which are in turn capable of reversible photoswitching. We believe that this unexpected result is of interest not only for the future design of DASAs with improved stability, but also for further development and applications of StS as photoswitchable probes.

Measurement-induced phase transitions in sparse nonlocal scramblers

Measurement-induced phase transitions arise due to a competition between the scrambling of quantum information in a many-body system and local measurements. In this work we investigate these transitions in different classes of fast scramblers, systems that scramble quantum information as quickly as is conjectured to be possible -- on a timescale proportional to the logarithm of the system size. In particular, we consider sets of deterministic sparse couplings that naturally interpolate between local circuits that slowly scramble information and highly nonlocal circuits that achieve the fast-scrambling limit. We find that circuits featuring sparse nonlocal interactions are able to withstand substantially higher rates of local measurement than circuits with only local interactions, even at comparable gate depths. We also study the quantum error-correcting codes that support the volume-law entangled phase and find that our maximally nonlocal circuits yield codes with nearly extensive contiguous code distance. Use of these sparse, deterministic circuits opens pathways towards the design of noise-resilient quantum circuits and error correcting codes in current and future quantum devices with minimum gate numbers.

Long-range-ordered phase in a quantum Heisenberg chain with interactions beyond nearest neighbors

Spin ensembles coupled to optical cavities provide a powerful platform for engineering synthetic quantum matter. Recently, we demonstrated that cavity mediated infinite range interactions can induce fast scrambling in a Heisenberg $XXZ$ spin chain (Phys. Rev. Research {\bf 2}, 043399 (2020)). In this work, we analyze the kaleidoscope of quantum phases that emerge in this system from the interplay of these interactions. Employing both analytical spin-wave theory as well as numerical DMRG calculations, we find that there is a large parameter regime where the continuous $U(1)$ symmetry of this model is spontaneously broken and the ground state of the system exhibits $XY$ order. This kind of symmetry breaking and the consequent long range order is forbidden for short range interacting systems by the Mermin-Wagner theorem. Intriguingly, we find that the $XY$ order can be induced by even an infinitesimally weak infinite range interaction. Furthermore, we demonstrate that in the $U(1)$ symmetry broken phase, the half chain entanglement entropy violates the area law logarithmically. Finally, we discuss a proposal to verify our predictions in state-of-the-art quantum emulators.

Deterministic Fast Scrambling with Neutral Atom Arrays.

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-neighbor 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(logN) parallel applications of nearest-neighbor gates. These tools enable direct experimental access to fast scrambling dynamics in a highly controlled and programmable way and can be harnessed to produce highly entangled states with varied applications.

Signature of universal fast scrambling in the transient response of a driven mott insulator system

The scrambling rate λ s, a measure of the early growth of decoherence in an interacting quantum system, has been conjectured to have a universal saturation bound, λ s ⩽ 2πk B T/ℏ, where T is the temperature. This decoherence arises from the spread of quantum information over a large number of untracked degrees of freedom. The commonly studied indicator of scrambling is the out of time-ordered correlator (OTOC) of noncommuting quantum operators, in-turn related to generalized uncertainty relations, and reminiscent of the Lyapunov exponent of classically chaotic systems. From a practical measurement point of view, other quantities besides OTOCs, that are also sensitive to these generalized uncertainty relations, may capture the scrambling behavior. Here, using a large- Keldysh field theory approach, we show that the nonequilibrium current response of a Mott insulator system consisting of a mesoscopic quantum dot array, when subjected to an electric field quench, reveals this phenomenon on account of number-phase uncertainty. Both ac and dc field quenches are considered. The passage from the initial Mott insulator phase with well-defined charge excitations, to the final nonequilibrium steady current state, is revealed in the transient current response that has Bloch-like oscillations. We find that the amplitude of these oscillations decreases at the universal rate, 2πk B T/ℏ, associated with fast scramblers. Our Mott insulator model provides a new example of a fast scrambler in addition to the known ones such as extremal black holes and the Sachdev–Ye–Kitaev (SYK) model.

Black hole interior in unitary gauge construction

A quantum system with a black hole accommodates two widely different, though physically equivalent, descriptions. In one description, based on global spacetime of general relativity, the existence of the interior region is manifest, while understanding unitarity requires nonperturbative quantum gravity effects such as replica wormholes. The other description adopts a manifestly unitary, or holographic, description, in which the interior emerges effectively as a collective phenomenon of fundamental degrees of freedom. In this paper we study the latter approach, which we refer to as the unitary gauge construction. In this picture, the formation of a black hole is signaled by the emergence of a surface (stretched horizon) possessing special dynamical properties: quantum chaos, fast scrambling, and low energy universality. These properties allow for constructing interior operators, as we do explicitly, without relying on details of microscopic physics. A key role is played by certain coarse modes in the zone region (hard modes), which determine the degrees of freedom relevant for the emergence of the interior. We study how the interior operators can or cannot be extended in the space of microstates and analyze irreducible errors associated with such extension. This reveals an intrinsic ambiguity of semiclassical theory formulated with a finite number of degrees of freedom. We provide an explicit prescription of calculating interior correlators in the effective theory, which describes only a finite region of spacetime. We study the issue of state dependence of interior operators in detail and discuss a connection of the resulting picture with the quantum error correction interpretation of holography.

Dirac fast scramblers

We introduce a family of Gross-Neveu-Yukawa models with a large number of fermion and boson flavors as higher dimensional generalizations of the Sachdev-Ye-Kitaev model. The models may be derived from local lattice couplings and give rise to Lorentz invariant critical solutions in 1+1 and 2+1 dimensions. These solutions imply anomalous dimensions of both bosons and fermions tuned by the number ratio of boson to fermion flavors. In 1+1 dimension the solution represents a stable critical phase, while in 2+1 dimension it governs a quantum phase transition. We compute the out of time order correlators in the 1+1 dimensional model, showing that it exhibits growth with the maximal Lyapunov exponent $\lambda_L=2\pi T$ in the low temperature limit.

Absence of Fast Scrambling in Thermodynamically Stable Long-Range Interacting Systems.

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 is extensive in terms of system size and the thermodynamic limit is well defined. We rigorously demonstrate that the OTOC shows a polynomial growth over time as long as α>D and the necessary scrambling time over a distance R is larger than t≳R^{[(2α-2D)/(2α-D+1)]}.

Fast scrambling without appealing to holographic duality

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 rapid decline of the OTOC is accompanied by a fast growth of the entanglement entropy, as well as a swift change in the magnetization. Finally, potential realizations of our model are proposed in current experimental setups. Our work establishes a promising route to create fast scramblers.