Quantum chaos and the correspondence principle

Wang, Jiaozi; Benenti, Giuliano; Casati, Giulio; Wang, Wenge

doi:10.1103/physreve.103.l030201

Cited by 44 publications

(32 citation statements)

References 41 publications

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“…On the other hand, as we shown in Ref. [25], a proper averaging (of the logarithms of OTOC) restores the role of OTOC as a diagnostic of chaotic dynamics, as…”

Section: A Out-of-time-ordered Correlationsupporting

confidence: 54%

“…7 and 8: in those figures the growth rate decreases with , while here it is -independent. map [25], in which we substitute the cusps in the potential V (x) of the original triangle map by small circle arcs of radius r:…”

Section: Comparison With Chaotic Casementioning

confidence: 99%

“…For that purpose, we can consider the quantum dynamics in the time domain and study the out-of-time-ordered correlator (OTOC) [10][11][12][13] or the number of harmonics of the phase-space Wigner distribution function [14][15][16][17][18][19][20][21][22]. Indeed, for chaotic dynamics the short-time behavior of both quantities exhibits an exponential increase at a rate which is determined by the largest Lyapunov exponent of the underlying classical dynamics [23][24][25]. Therefore, number of harmonics and OTOC can distinguish classically chaotic systems from those which are only mixing or ergodic.…”

Section: Introductionmentioning

confidence: 99%

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Statistical and dynamical properties of the quantum triangle map

Wang,

Benenti,

Casati

et al. 2022

Preprint

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We study the statistical and dynamical properties of the quantum triangle map, whose classical counterpart can exhibit ergodic and mixing dynamics, but is never chaotic. Numerical results show that ergodicity is a sufficient condition for spectrum and eigenfunctions to follow the prediction of Random Matrix Theory, even though the underlying classical dynamics is not chaotic. On the other hand, dynamical quantities such as the out-of-time-ordered correlator (OTOC) and the number of harmonics, exhibit a growth rate vanishing in the semiclassical limit, in agreement with the fact that classical dynamics has zero Lyapunov exponent. Our finding show that, while spectral statistics can be used to detect ergodicity, OTOC and number of harmonics are diagnostics of chaos.

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“…On the other hand, as we shown in Ref. [25], a proper averaging (of the logarithms of OTOC) restores the role of OTOC as a diagnostic of chaotic dynamics, as…”

Section: A Out-of-time-ordered Correlationsupporting

confidence: 54%

Section: Comparison With Chaotic Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Statistical and dynamical properties of the quantum triangle map

Wang,

Benenti,

Casati

et al. 2022

Preprint

Self Cite

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show abstract

“…To the best of our knowledge, this is the first example of a genuine many-body setup in which such discrepancy is observed. Previous studies dealt only with single-body examples with classical counterparts [35][36][37][38][39][40][41].…”

Section: Discussion and Outlookmentioning

confidence: 99%

Quantum Chaos and Circuit Parameter Optimization

Kim¹,

Oz²,

Rosa³

2022

Preprint

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We explore quantum chaos diagnostics of variational circuit states at random parameters and study their correlation with the circuit expressibility and the optimization of control parameters. By measuring the operator spreading coefficient and the eigenvalue spectrum of the modular Hamiltonian of the reduced density matrix, we identify the universal structure of random matrix models in high-depth circuit states. We construct different layer unitaries corresponding to the GOE and GUE distributions and quantify their VQA performance. Our study also highlights a potential tension between the OTOC and BGS-type diagnostics of quantum chaos.

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“…Starting from the behavior of the spectral statistics of the generating Hamiltonian [1] to dynamical signatures of chaos like hypersensitivity of system dynamics to perturbation [2,3] and the dynamical generation of quantum correlations, such as quantum entanglement [4][5][6][7][8][9][10], and quantum discord [11,12]. Recently, out-of-time ordered correlators have also been used to probe quantum chaos [13][14][15][16][17][18][19][20]. The signatures of chaos are not only explored in the semiclassical limit but also in the deep quantum regime [19,21,22].…”

Section: Introductionmentioning

confidence: 99%

Revisiting the role of chaos in quantum tomography

Sahu,

PG,

Madhok

2022

Preprint

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Does chaos in the dynamics enable information gain in quantum tomography or impedes it? We address this question by considering continuous measurement tomography in which the measurement record is obtained as a sequence of expectation values of a Hermitian observable evolving under the repeated application of the Floquet map of the quantum kicked top. For a given dynamics and Hermitian observables, we observe completely opposite behavior in the tomography of well-localized spin coherent states compared to random states. As the chaos in the dynamics increases, the reconstruction fidelity of spin coherent states decreases. This contrasts with the previous results connecting information gain in tomography of random states with the degree of chaos in the dynamics that drives the system. The rate of information gain and hence the fidelity obtained in tomography depends not only on the degree of chaos in the dynamics and to what extent it causes the initial observable to spread in various directions of the operator space but, more importantly, how well these directions are aligned with the density matrix to be estimated. Our study also gives an operational interpretation for operator spreading in terms of fidelity gain in an actual quantum information tomography protocol.

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Quantum chaos and the correspondence principle

Cited by 44 publications

References 41 publications

Statistical and dynamical properties of the quantum triangle map

Statistical and dynamical properties of the quantum triangle map

Quantum Chaos and Circuit Parameter Optimization

Revisiting the role of chaos in quantum tomography

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