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

Styliaris, Georgios; Anand, Namit; Zanardi, Paolo

doi:10.1103/physrevlett.126.030601

Cited by 59 publications

(72 citation statements)

References 91 publications

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“…Another interesting measure to which the Isospectral twirling technique can be applied is quantum coherence [168][169][170][171][172][173][174][175][176][177][178][179][180][181][182]. Quantum coherence enters various aspects of the study of quantum mechanical systems, ranging from quantum chaos [133], to signature of quantum phase transitions [183] and as a resource in quantum thermodynamics [184].…”

Section: Coherence and Wigner-yanase-dyson Skew Information 341 Cohmentioning

confidence: 99%

Random matrix theory of the isospectral twirling

et al. 2021

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We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref. [1]. The relevant ensembles of Hamiltonians are those defined by salient spectral probability distributions. The Gaussian Unitary Ensembles (GUE) describes a class of quantum chaotic Hamiltonians, while spectra corresponding to the Poisson and Gaussian Diagonal Ensemble (GDE) describe non chaotic, integrable dynamics. We compute the Isospectral twirling of several classes of important quantities in the analysis of quantum many-body systems: Frame potentials, Loschmidt Echos, OTOCs, Entanglement, Tripartite mutual information, coherence, distance to equilibrium states, work in quantum batteries and extension to CP-maps. Moreover, we perform averages in these ensembles by random matrix theory and show how these quantities clearly separate chaotic quantum dynamics from non chaotic ones.

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Section: Coherence and Wigner-yanase-dyson Skew Information 341 Cohmentioning

confidence: 99%

Random matrix theory of the isospectral twirling

et al. 2021

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“…OTOC has received significant attention in recent times with its applicability ranging from quantum information theory to condensed matter physics to quantum gravity. Very recently, OTOC has found its application in the context of open quantum systems as the coupling of the system with a dissipative or dephasing bath naturally leads to information scrambling [33,34]. Motivated by this, in this section we derive QRT like formula for OTOC correlators.…”

Section: Qrt For Out-of-time-ordered Correlatorsmentioning

confidence: 99%

Quantum Regression theorem for multi-time correlators : A detailed analysis in the Heisenberg Picture

Khan,

Agarwalla,

Jain

2021

Preprint

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Quantum regression theorem is a very useful result in open quantum system and extensively used for computing multi-point correlation functions. Traditionally it is derived for two-time correlators in the Markovian limit employing the Schrödinger picture. In this paper we make use of the Heisenberg picture to derive quantum regression theorems for multi-time correlation functions which in the special limit reduce to the well known two-time regression theorem. For multi-time correlation function we find that the regression theorem takes the same form as it takes for two-time correlation function with a mild restriction that one of the times should be greater than all the other time variables. Interestingly, the Heisenberg picture also allows us to derive analogue of regression theorem for out-of-time-ordered correlators (OTOCs). We further extend our study for the case of non-Markovian dynamics and report the modifications to the standard quantum regression theorem. We illustrate all of the above results using the paradigmatic dissipative spin-boson model.

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“…The onset of chaotic dynamics is at the center of many important phenomena in quantum many-body systems, from thermalization in a closed system [1][2][3][4][5][6][7][8][9][10][11] to scrambling of information in quantum channels [12][13][14][15][16][17], black hole dynamics [18][19][20][21], entanglement complexity [22,23], to pseudorandomness in quantum circuits [24][25][26][27][28], and finally, the complexity of quantum evolutions [29][30][31][32]. Several probes of quantum chaos have been studied in recent years [33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Isospectral Twirling and Quantum Chaos

Leone

Oliviero

Hamma

2021

Entropy

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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 the isospectral twirling, namely the Haar average of a k-fold unitary channel. We show that such measures can then always be cast in the form of an expectation value of the isospectral twirling. In literature, quantum chaos is investigated sometimes through the spectrum and some other times through the eigenvectors of the Hamiltonian generating the dynamics. We show that thanks to this technique, we can interpolate smoothly between integrable Hamiltonians and quantum chaotic Hamiltonians. The isospectral twirling of Hamiltonians with eigenvector stabilizer states does not possess chaotic features, unlike those Hamiltonians whose eigenvectors are taken from the Haar measure. As an example, OTOCs obtained with Clifford resources decay to higher values compared with universal resources. By doping Hamiltonians with non-Clifford resources, we show a crossover in the OTOC behavior between a class of integrable models and quantum chaos. Moreover, exploiting random matrix theory, we show that these measures of quantum chaos clearly distinguish the finite time behavior of probes to quantum chaos corresponding to chaotic spectra given by the Gaussian Unitary Ensemble (GUE) from the integrable spectra given by Poisson distribution and the Gaussian Diagonal Ensemble (GDE).

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

Cited by 59 publications

References 91 publications

Random matrix theory of the isospectral twirling

Random matrix theory of the isospectral twirling

Quantum Regression theorem for multi-time correlators : A detailed analysis in the Heisenberg Picture

Isospectral Twirling and Quantum Chaos

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