# Information Scrambling and Loschmidt Echo.

@article{Yan2020InformationSA, title={Information Scrambling and Loschmidt Echo.}, author={Bin Yan and Lukasz Cincio and Wojciech Zurek}, journal={Physical review letters}, year={2020}, volume={124 16}, pages={ 160603 } }

We demonstrate analytically and verify numerically that the out-of-time order correlator is given by the thermal average of Loschmidt echo signals. This provides a direct link between the out-of-time-order correlator-a recently suggested measure of information scrambling in quantum chaotic systems-and the Loschmidt echo, a well-appreciated familiar diagnostic that captures the dynamical aspect of chaotic behavior in the time domain, and is accessible to experimental studies.

## 63 Citations

Recovery of Damaged Information and the Out-of-Time-Ordered Correlators.

- Computer Science, PhysicsPhysical review letters
- 2020

It is shown that if the scrambled information is, in addition, partially damaged by a local measurement, then such a damage can still be treated by application of the time-reversed protocol.

Benchmarking Information Scrambling

- Computer SciencePhysical Review Letters
- 2022

This work provides a simple and robust approach to single out the degree of genuine scrambling from the noisy backgrounds of information scrambling, and demonstrates the protocol with simulations on IBM cloud-based quantum computers.

Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality.

- PhysicsPhysical review letters
- 2021

It is shown that this bipartite OTOC is equal to the operator entanglement of the evolution, and its interplay with entangling power is determined, and it is provided operational significance by unraveling intimate connections with average entropy production and scrambling of information at the level of quantum channels.

Minimal Model for Fast Scrambling.

- PhysicsPhysical review letters
- 2020

It is argued 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.

Quantum echo dynamics in the Sherrington-Kirkpatrick model

- PhysicsSciPost Physics
- 2020

Understanding the footprints of chaos in quantum-many-body systems has been under debate for a long time.
In this work, we study the echo dynamics of the
Sherrington-Kirkpatrick (SK) model with…

Thermofield dynamics: Quantum chaos versus decoherence

- Physics
- 2021

Quantum chaos imposes universal spectral signatures that govern the thermofield dynamics of a many-body system in isolation. The fidelity between the initial and time-evolving thermofield double…

Quantum scrambling and the growth of mutual information

- Computer Science, PhysicsQuantum Science and Technology
- 2020

It is proved that the growth of entanglement as quantified by the mutual information is lower bounded by the time-dependent change of out-of-time-ordered correlator, and the rate of increase of the Mutual information can be upper bounded bythe sum of local entropy productions and the exchange entropy arising from the flow of information between separate partitions of a quantum system.

Super-exponential growth of out-of-time-ordered correlators

- Physics
- 2020

Out-of-time-ordered correlators (OTOCs) are an effective tool in characterizing black hole chaos, many-body thermalization and quantum dynamics instability. Previous research findings have shown that…

Information Scrambling versus Decoherence—Two Competing Sinks for Entropy

- Computer Science, Physics
- 2020

This work develops key steps towards a thermodynamic description of information scrambling in open quantum systems and separates the entropy production into contributions arising from scrambling and decoherence, for which statements of the second law are derived.

Isospectral Twirling and Quantum Chaos

- PhysicsEntropy
- 2021

We show that the most important measures of quantum chaos, such as frame potentials, scrambling, Loschmidt echo and out-of-time-order correlators (OTOCs), can be described by the unified framework of…

## References

SHOWING 1-10 OF 69 REFERENCES

Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems

- PhysicsQuantum
- 2019

Characterizing the work statistics of driven complex quantum systems is generally challenging because of the exponential growth with the system size of the number of transitions involved between…

Measuring the scrambling of quantum information

- Physics
- 2016

We provide a general protocol to measure out-of-time-order correlation functions. These correlation functions are of broad theoretical interest for diagnosing the scrambling of quantum information in…

Environment-independent decoherence rate in classically chaotic systems.

- PhysicsPhysical review letters
- 2001

An exponential decay for the Loschmidt echo is predicted with a (decoherence) rate which is asymptotically given by the mean Lyapunov exponent of the classical system, and therefore independent of the perturbation strength, within a given range of strengths.

Chaos in quantum channels

- Computer Science, Physics
- 2015

The butterfly effect in quantum systems implies the information-theoretic definition of scrambling, which shows that any input subsystem must have near vanishing mutual information with almost all partitions of the output.

Gaussian Decoherence and Gaussian Echo from Spin Environments

- Physics
- 2006

We examine an exactly solvable model of decoherence -- a spin-system interacting with a collection of environment spins. We show that in this simple model (introduced some time ago to illustrate…

Decoherence as decay of the Loschmidt echo in a Lorentz gas.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002

Numerical evidence is found that, if the perturbation is within a certain range, M(t) decays exponentially with a rate 1/tau(phi) determined by the Lyapunov exponent lambda of the corresponding classical dynamics.

Semiclassical echo dynamics in the Sachdev-Ye-Kitaev model

- PhysicsPhysical Review B
- 2019

The existence of a quantum butterfly effect in the form of exponential sensitivity to small perturbations has been under debate for a long time. Lately, this question has gained increased interest…

Perturbation Independent Decay of the Loschmidt Echo in a Many-Body System.

- PhysicsPhysical review letters
- 2020

This work finds that, when the reversible interactions dominate over the perturbations, the information scrambled among up to 10^{2} spins can still be recovered, and shows the emergence of a regime of intrinsic irreversibility in accordance to a central hypothesis of irreversability.

Decoherence, chaos, and the second law.

- PhysicsPhysical review letters
- 1994

It is shown how the interaction with the environment limits distances over which quantum coherence can persist, and therefore reconciles quantum dynamics with classical Hamiltonian chaos.