Measuring the scrambling of quantum information

Swingle, Brian; Bentsen, Gregory; Schleier-Smith, Monika; Hayden, Patrick

doi:10.1103/physreva.94.040302

Cited by 472 publications

(481 citation statements)

References 78 publications

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“…Experimentally, the butterfly velocity v B , and its relation to QPT, can be studied by measuring the OTOC of a QPT system. Recently, new protocols and methods, that are versatile to simulate diverse many-body systems and achievable with state-of-the-art technology, have been proposed to measure the OTOC [14,32]. Furthermore, experimental measurements of the OTOC have also been implemented [33,34].…”

Section: Discussionmentioning

confidence: 99%

“…Very importantly, as a characteristic velocity of a chaotic quantum system, v B sets a bound on the speed of the information propagation [1]. In holographic theories, the butterfly effect has extensively been studied in context [5][6][7][8][9][10][11][12][13][14][15][16][17]. In the study of high energy scattering near horizon and information scrambling of black holes it is found that the butterfly effect ubiquitously exists and is signaled by a…”

Section: Introductionmentioning

confidence: 99%

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Holographic butterfly effect at quantum critical points

Ling¹,

Liu²,

Wu³

2017

J. High Energ. Phys.

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When the Lyapunov exponent λ L in a quantum chaotic system saturates the bound λ L 2πk B T , it is proposed that this system has a holographic dual described by a gravity theory. In particular, the butterfly effect as a prominent phenomenon of chaos can ubiquitously exist in a black hole system characterized by a shockwave solution near the horizon. In this paper we propose that the butterfly velocity can be used to diagnose quantum phase transition (QPT) in holographic theories. We provide evidences for this proposal with an anisotropic holographic model exhibiting metal-insulator transitions (MIT), in which the derivatives of the butterfly velocity with respect to system parameters characterizes quantum critical points (QCP) with local extremes in zero temperature limit. We also point out that this proposal can be tested by experiments in the light of recent progress on the measurement of out-of-time-order correlation function (OTOC).

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Holographic butterfly effect at quantum critical points

Ling¹,

Liu²,

Wu³

2017

J. High Energ. Phys.

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“…One can also investigate quantum quenches as a possible probe of SYK physics by disconnecting or reconnecting the dot and wires to effectively freeze the zero modes or restore their coupling. Finally, much work has been done regarding measuring out-of-time-order correlators in cold atoms and qubit systems (see, e.g., [60][61][62][63]). Our setup offers the exciting prospect of exploiting Majorana hardware and topological quantum information ideas to measure such quantities in pursuit of the SYK model's hallmark maximal chaos.…”

Section: Let Us Now Examine a General T -Invariant Four-fermion Intermentioning

confidence: 99%

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

2017

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The Sachdev-Ye-Kitaev (SYK) model describes a collection of randomly interacting Majorana fermions that exhibits profound connections to quantum chaos and black holes. We propose a solid-state implementation based on a quantum dot coupled to an array of topological superconducting wires hosting Majorana zero modes. Interactions and disorder intrinsic to the dot mediate the desired random Majorana couplings, while an approximate symmetry suppresses additional unwanted terms. We use random-matrix theory and numerics to show that our setup emulates the SYK model (up to corrections that we quantify) and discuss experimental signatures. DOI: 10.1103/PhysRevB.96.121119 Introduction. Majorana fermions provide building blocks for many novel phenomena. As one notable example, Majorana-fermion zero modes [1,2] capture the essence of non-Abelian statistics and topological quantum computation [3,4], and correspondingly now form the centerpiece of a vibrant experimental effort [5][6][7][8][9][10][11][12][13][14][15][16]. More recently, randomly interacting Majorana fermions governed by the "Sachdev-YeKitaev (SYK) model" [17][18][19] were shown to exhibit sharp connections to chaos, quantum-information scrambling, and black holes-naturally igniting broad interdisciplinary activity (see, e.g., [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]). The goal of this Rapid Communication is to exploit hardware components of a Majorana-based topological quantum computer for a tabletop implementation of the SYK model, thus uniting these very different topics.The SYK Hamiltonian reads

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“…Interference and weak measurement have been performed with cold atoms [58], which have been proposed as platforms for realizing scrambling and quantum chaos [15,16,59]. Yet cold atoms are not necessary for measuringÃ ρ .…”

Section: Interference-based Measurement Ofã ρmentioning

confidence: 99%

“…In the context of quantum channels, F (t) is related to the tripartite information [14]. Experiments have been proposed [15][16][17] and performed [18,19] to measure F (t) with cold atoms and ions, with cavity quantum electrodynamics, and with nuclear-magnetic-resonance quantum simulators.F (t) quantifies sensitivity to initial conditions, a signature of chaos. Consider a quantum system S governed by a Hamiltonian H .…”

mentioning

confidence: 99%

Jarzynski-like equality for the out-of-time-ordered correlator

Halpern

2017

Phys. Rev. A

121

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The out-of-time-ordered correlator (OTOC) diagnoses quantum chaos and the scrambling of quantum information via the spread of entanglement. The OTOC encodes forward and reverse evolutions and has deep connections with the flow of time. So do fluctuation relations such as Jarzynski's equality, derived in nonequilibrium statistical mechanics. I unite these two powerful, seemingly disparate tools by deriving a Jarzynski-like equality for the OTOC. The equality's left-hand side equals the OTOC. The right-hand side suggests a protocol for measuring the OTOC indirectly. The protocol is platform-nonspecific and can be performed with weak measurement or with interference. Time evolution need not be reversed in any interference trial. The equality enables fluctuation relations to provide insights into holography, condensed matter, and quantum information and vice versa. DOI: 10.1103/PhysRevA.95.012120The out-of-time-ordered correlator (OTOC) F (t) diagnoses the scrambling of quantum information [1][2][3][4][5][6]: Entanglement can grow rapidly in a many-body quantum system, dispersing information throughout many degrees of freedom. F (t) quantifies the hopelessness of attempting to recover the information via local operations.Originally applied to superconductors [7], F (t) has undergone a revival recently. F (t) characterizes quantum chaos, holography, black holes, and condensed matter. The conjecture that black holes scramble quantum information at the greatest possible rate has been framed in terms of F (t) [6,8]. The slowest scramblers include disordered systems [9][10][11][12][13]. In the context of quantum channels, F (t) is related to the tripartite information [14]. Experiments have been proposed [15][16][17] and performed [18,19] to measure F (t) with cold atoms and ions, with cavity quantum electrodynamics, and with nuclear-magnetic-resonance quantum simulators.F (t) quantifies sensitivity to initial conditions, a signature of chaos. Consider a quantum system S governed by a Hamiltonian H . Suppose that S is initialized to a pure state |ψ and perturbed with a local unitary operator V . S then evolves forward in time under the unitary U = e −iH t for a duration t, is perturbed with a local unitary operator W, and evolves backward under U † . The state |ψ := U † WUV |ψ = W(t)V |ψ results. Suppose, instead, that S is perturbed with V not at the sequence's beginning, but at the end: |ψ evolves forward under U , is perturbed with W, evolves backward under U † , and is perturbed with V . The state |ψ := V U † WU |ψ = V W(t)|ψ results. The overlap between the two possible final states equals the correlator: push an ion-trap potential along some direction in space [26]. Let F := F (H f ) − F (H i ) denote the difference between the equilibrium free energies at the inverse temperature β: 1 F (H ) = − 1 β ln Z β, , wherein the partition function is Z β, := Tr(e −βH ) and = i or f . The free-energy difference has applications in chemistry, biology, and pharmacology [27]. One could measure F , in principle, by measuring th...

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Measuring the scrambling of quantum information

Cited by 472 publications

References 78 publications

Holographic butterfly effect at quantum critical points

Holographic butterfly effect at quantum critical points

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

Jarzynski-like equality for the out-of-time-ordered correlator

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