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arXiv:1803.10772 · Physical Review X

Disentangling Scrambling and Decoherence via Quantum Teleportation

Beni Yoshida, Norman Y. Yao

Published Jan 9, 2019• 134 citations
arXivHTMLPDF

Abstract

Out-of-time-order correlation (OTOC) functions provide a powerful theoretical tool for diagnosing chaos and the scrambling of information in strongly interacting, quantum systems.However, their direct and unambiguous experimental measurement remains an essential challenge.At its core, this challenge arises from the fact that the effects of both decoherence and experimental noise can mimic that of information scrambling, leading to decay of OTOCs.Here, we analyze a quantum teleportation protocol that explicitly enables one to differentiate between scrambling and decoherence.Moreover, we demonstrate that within this protocol, one can extract a precise "noise" parameter which quantitatively captures the nonscramblinginduced decay of OTOCs.Using this parameter, we prove explicit bounds on the true value of the OTOC.Our results open the door to experimentally measuring quantum scrambling with built-in verifiability.

DOI
10.1103/physrevx.9.011006

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Out-of-time-order correlation (OTOC) functions provide a powerful theoretical tool for diagnosing chaos and the scrambling of information in strongly interacting, quantum systems.However, their direct and unambiguous experimental measurement remains an essential challenge.At its core, this challenge arises from the fact that the effects of both decoherence and experimental noise can mimic that of information scrambling, leading to decay of OTOCs.Here, we analyze a quantum teleportation protocol that explicitly enables one to differentiate between scrambling and decoherence.Moreover, we demonstrate that within this protocol, one can extract a precise "noise" parameter which quantitatively captures the nonscramblinginduced decay of OTOCs.Using this parameter, we prove explicit bounds on the true value of the OTOC.Our results open the door to experimentally measuring quantum scrambling with built-in verifiability.
Out-of-time-ordered correlation functions (OTOCs) play a crucial role in the study of thermalization, entanglement, and quantum chaos, as they quantify the scrambling of quantum information due to complex interactions. As a consequence of their out-of-time-ordered nature, OTOCs are difficult to measure experimentally. Here we propose an OTOC measurement protocol that does not rely on the reversal of time evolution and is easy to implement in a range of experimental settings. The protocol accounts for both pure and mixed initial states, and is applicable to systems that interact with environmental degrees of freedom. We demonstrate the application of our protocol by the characterization of scrambling in a periodically driven spin that exhibits quantum chaos.
We propose and analyze a protocol to study quantum information scrambling using statistical correlations between measurements, which are performed after evolving a quantum system from randomized initial states.We prove that the resulting correlations precisely capture the so-called out-of-time-ordered correlators and can be used to probe chaos in strongly interacting, many-body systems.Our protocol requires neither reversing time evolution nor auxiliary degrees of freedom, and it can be realized in state-of-the-art quantum simulation experiments.
Scrambling, the delocalization of initially localized quantum information, is commonly characterized by the out-of-time ordered correlator (OTOC). Employing the OTOC-Renyi-2 entropy theorem we derive a quantum speed limit for the OTOC, which sets an lower bound for the rate with which information can be scrambled. This bound becomes particularly tractable by describing the scrambling of information in a closed quantum system as an effective decoherence process of an open system interacting with an environment. We prove that decay of the OTOC can be bounded by the strength of the system-environment coupling and two-point environmental correlation functions. We validate our analytic bound numerically using the non-integrable transverse field Ising model. Our results provide a universal and model-agnostic quantitative framework for understanding the dynamical limits of information spreading across quantum many-body physics, condensed matter, and engineered quantum platforms.
Abstract Out-of-time-order correlators (OTOCs) have emerged as the preeminent theoretical and experimental probe of quantum information scrambling — the delocalization of quantum information across many-body degrees of freedom. Here we present a comprehensive computational study of OTOCs across three paradigmatic models: the Sachdev-Ye-Kitaev (SYK) model, the non-integrable transverse-field Ising chain, and random unitary circuits. Through exact diagonalization and large-N analytics, we extract Lyapunov exponents, scrambling times, and butterfly velocities, demonstrating that all chaotic systems studied approach, but do not saturate, the Maldacena-Shenker-Stanford (MSS) bound λ_L ≤ 2π/β. Crucially, we introduce the Spectral Out-of-Time-Order Correlator (SOTOC), a novel frequency-domain diagnostic that decomposes information scrambling into its constituent spectral modes. The SOTOC achieves a 32% improvement in Lyapunov exponent extraction precision over conventional log-linear fitting and maintains robust performance at noise levels σ > 0.30, where traditional methods fail. Our phase diagram reveals a sharp transition in scrambling dynamics at h/J ≈ 1.0 in the TFIM, coinciding with the onset of quantum chaos as measured by level-spacing statistics. These results establish SOTOC as a practical and theoretically grounded tool for probing scrambling in near-term quantum devices and holographic systems.
Quantum information scrambling has received tremendous attention owing to its key concept in the fields of quantum chaos and quantum gravity. Here, with exploiting a fully controllable superconducting quantum processor, we study the verified scrambling in a 1D spin chain by an analog superconducting quantum simulator with the signs and values of individual driving and coupling terms fully controllable. By engineering opposite Hamiltonians on two subsystems, we measure the temporal and spatial patterns of out-of-time ordered correlators (OTOC), with the Hamiltonian mismatch and the decoherence extracted quantitatively from the scrambling dynamics, providing a benchmarking tool for probing not only the spatial but the temporal patterns of scrambling dynamics in many-body systems. Our work demonstrates the superconducting system with strong controllability as a powerful quantum simulator.
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 interacting quantum systems and have recently received particular attention in the study of chaos and black holes within holographic duality. Measuring them requires an echo-type sequence in which the sign of a many-body Hamiltonian is reversed. We illustrate our protocol by detailing an implementation employing cold atoms and cavity quantum electrodynamics to probe spin models with nonlocal interactions. To verify the feasibility of the scheme with current technology, we analyze the effects of dissipation in a chaotic kicked-top model. Finally, we propose a number of other experimental platforms where similar out-of-time-order correlation functions can be measured.