Out-of-Time-Ordered-Correlator Quasiprobabilities Robustly Witness Scrambling

Alonso, José Raúl González; Halpern, Nicole Yunger; Dressel, Justin

doi:10.1103/physrevlett.122.040404

Cited by 57 publications

(43 citation statements)

References 54 publications

(54 reference statements)

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“…In conclusion, the discussion above allows one to view the OTOCs as a measure of chaos: chaotic dynamics corresponds to OTOCs that vanish sufficiently rapidly with time. On the other hand, for a non-chaotic Hamiltonian one expects information to spread coherently: for large system sizes this results in either a slow decay or a non-vanishing asymptotics of OTOCs [46], while for small ones this causes revivals, consisting in OTOCs frequently returning close to their original value [102].…”

Section: A the Otocs And The Operator Spreadingmentioning

confidence: 99%

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Quantum chaos in the Brownian SYK model with large finite N : OTOCs and tripartite information

Sünderhauf

Piroli

et al. 2019

J. High Energ. Phys.

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We consider the Brownian SYK model of N interacting Majorana fermions, with random couplings that are taken to vary independently at each time. We study the out-of-time-ordered correlators (OTOCs) of arbitrary observables and the Rényi-2 tripartite information of the unitary evolution operator, which were proposed as diagnostic tools for quantum chaos and scrambling, respectively. We show that their averaged dynamics can be studied as a quench problem at imaginary times in a model of N qudits, where the Hamiltonian displays site-permutational symmetry. By exploiting a description in terms of bosonic collective modes, we show that for the quantities of interest the dynamics takes place in a subspace of the effective Hilbert space whose dimension grows either linearly or quadratically with N , allowing us to perform numerically exact calculations up to N = 10 6 . We analyze in detail the interesting features of the OTOCs, including their dependence on the chosen observables, and of the tripartite information. We observe explicitly the emergence of a scrambling time t * ∼ ln N controlling the onset of both chaotic and scrambling behavior, after which we characterize the exponential decay of the quantities of interest to the corresponding Haar scrambled values. CONTENTS

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Section: A the Otocs And The Operator Spreadingmentioning

confidence: 99%

“…with the elements of I a , I b and I c ordered as they appear in Eqs. (100), (101) and (102). Finally, let us consider two disjoint subsets A ∪ B = {1 .…”

Section: B Extracting Otocs and Entropiesmentioning

confidence: 99%

Quantum chaos in the Brownian SYK model with large finite N : OTOCs and tripartite information

Sünderhauf

Piroli

et al. 2019

J. High Energ. Phys.

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“…Recently out of time ordered correlators (OTOCs) have experienced a resurgence of interest from different fields of physics ranging from the black hole information problem [1] to information propagation in condensed matter systems [2][3][4][5][6][7][8][9]. The OTOC is of particular interest due to its role in witnessing the spreading or"scrambling" of locally stored quantum information across all degrees of freedom of the system, something traditional dynamical correlation functions of the form A(t)B cannot.…”

Section: Introductionmentioning

confidence: 99%

Out-of-time-order correlations in the quasiperiodic Aubry-André model

Riddell

Sørensen

2020

Phys. Rev. B

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We study out of time ordered correlators (OTOC) in a free fermionic model with a quasi-periodic potential. This model is equivalent to the Aubry-André model and features a phase transition from an extended phase to a localized phase at a non-zero value of the strength of the quasi-periodic potential. We investigate five different time-regimes of interest for out of time ordered correlators; early, wavefront, x = vBt, late time equilibration and infinite time. For the early time regime we observe a power law for all potential strengths. For the time regime preceding the wavefront we confirm a recently proposed universal form and use it to extract the characteristic velocity of the wavefront for the present model. A Gaussian waveform is observed to work well in the time regime surrounding x = vBt. Our main result is for the late time equilibration regime where we derive a finite time equilibration bound for the OTOC, bounding the correlator's distance from its late time value. The bound impose strict limits on equilibration of the OTOC in the extended regime and is valid not only for the Aubry-André model but for any quadratic model. Finally, momentum out of time ordered correlators for the Aubry-André model are studied where large values of the OTOC are observed at late times at the critical point.arXiv:1908.03292v3 [cond-mat.stat-mech]

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“…However, non-integrable Hamiltonians can have an exponentially longer recurrence time [12,47,48] that persistently scrambles the information of the initially local operators to cover the lattice. An OTOC and its QPD can witness such information-scrambling behavior [45].…”

Section: Otocs and Their Qpdsmentioning

confidence: 99%

“…Moreover, while the OTOC can also decay due to decoherence in a manner that seems qualitatively similar to the decay from information scrambling, the nonclassical features of the corresponding QPD can only diminish with decoherence. As such, the QPD robustly distinguishes such decoherence from scrambling [45], making it an attractive candidate for experimental use.…”

Section: Introductionmentioning

confidence: 99%

Optimizing measurement strengths for qubit quasiprobabilities behind out-of-time-ordered correlators

2019

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Out-of-time-ordered correlators (OTOCs) have been proposed as a tool to witness quantum information scrambling in many-body system dynamics. These correlators can be understood as averages over nonclassical multi-time quasi-probability distributions (QPDs). These QPDs have more information, and their nonclassical features witness quantum information scrambling in a more nuanced way. However, their high dimensionality and nonclassicality make QPDs challenging to measure experimentally. We focus on the topical case of a many-qubit system and show how to obtain such a QPD in the laboratory using circuits with three and four sequential measurements. Averaging distinct values over the same measured distribution reveals either the OTOC or parameters of its QPD. Stronger measurements minimize experimental resources despite increased dynamical disturbance.

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Out-of-Time-Ordered-Correlator Quasiprobabilities Robustly Witness Scrambling

Cited by 57 publications

References 54 publications

Quantum chaos in the Brownian SYK model with large finite N : OTOCs and tripartite information

Quantum chaos in the Brownian SYK model with large finite N : OTOCs and tripartite information

Out-of-time-order correlations in the quasiperiodic Aubry-André model

Optimizing measurement strengths for qubit quasiprobabilities behind out-of-time-ordered correlators

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