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

José Raúl González Alonso, Nicole Yunger Halpern, and Justin Dressel
Phys. Rev. Lett. 122, 040404 – Published 1 February 2019
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  • Introduction.—
  • OTOCs and their quasiprobabilities.—
  • Spin chain.—
  • Decoherence.—
  • Simulation results and discussion.—
  • Conclusions and outlook.—
  • ACKNOWLEDGMENTS
    • Supplemental Material
    References

    Abstract

    Out-of-time-ordered correlators (OTOCs) have received considerable recent attention as qualitative witnesses of information scrambling in many-body quantum systems. Theoretical discussions of OTOCs typically focus on closed systems, raising the question of their suitability as scrambling witnesses in realistic open systems. We demonstrate empirically that the nonclassical negativity of the quasiprobability distribution (QPD) behind the OTOC is a more sensitive witness for scrambling than the OTOC itself. Nonclassical features of the QPD evolve with timescales that are robust with respect to decoherence and are immune to false positives caused by decoherence. To reach this conclusion, we numerically simulate spin-chain dynamics and three measurement protocols (the interferometric, quantum-clock, and weak-measurement schemes) for measuring OTOCs. We target experiments based on quantum-computing hardware such as superconducting qubits and trapped ions.

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    • Received 23 June 2018

    DOI:https://doi.org/10.1103/PhysRevLett.122.040404

    © 2019 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Many-body localizationOpen quantum systems & decoherenceQuantum aspects of black holesQuantum correlations in quantum informationQuantum entanglement
    Interdisciplinary PhysicsGravitation, Cosmology & AstrophysicsCondensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

    Authors & Affiliations

    José Raúl González Alonso1,*, Nicole Yunger Halpern2, and Justin Dressel1,3

    • 1Schmid College of Science and Technology, Chapman University, Orange, California 92866, USA
    • 2Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125, USA
    • 3Institute for Quantum Studies, Chapman University, Orange, California 92866, USA

    • *Corresponding author. gonzalezalonso@chapman.edu

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    Vol. 122, Iss. 4 — 1 February 2019

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    Images

    • Figure 1
      Figure 1

      Evolution of measured OTOC, F(t)=⟨W†(t)V†W(t)V⟩, with and without decoherence. Values measured with three different protocols are compared against the ideal value: interferometric FI(t), weak FW(t), and quantum clock FC(t). To simulate near-term experiments, the system consists of N=5 spins in an Ising chain with (a) a transverse field and (b) a transverse and a longitudinal field, with parameters detailed in the text. The system starts in a Gibbs state ρT=Z−1exp(−H/T) with T/J=1 and Z=Tr[exp(−H/T)]. The system undergoes environmental dephasing of each qubit with a decay constant of T2*=130  μs. The local operators W=σ1z and V=σNz. These plots highlight the difficulties in unambiguously distinguishing between (a) nonscrambling and (b) scrambling Hamiltonians in an experimental setting with decoherence.

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    • Figure 2
      Figure 2

      Evolution of measured Rep˜t with and without decoherence, using the sequential-weak-measurement protocol. The QPD, p˜t(v1,w2,v2,w3)=Tr(Πw3W(t)Πv2VΠw2W(t)Πv1Vρ), underlies the OTOC, F(t)=∑v1w2v2*w3*p˜t(v1,w2,v2,w3), where V=∑vΠv and W=∑wΠw. Of the 16 QPD values, four examples are shown. The numeric labels in the legend have the form abcd, where v1=(−1)a, w2=(−1)b, v2=(−1)c, and w3=(−1)d. The shaded regions show nonclassical behavior of the QPD.

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    • Figure 3
      Figure 3

      Total nonclassicality, N˜(t)=∑|p˜t(v1,w2,v2,w3)|−1, of the QPD, p˜t, showing sensitivity to decoherence for (a) integrable and (b) scrambling systems. Comparing two timescales can reveal scrambling. The duration between the onset of nonclassicality (t˜*∼10  μs) and the first maximum (tm∼20  μs) is roughly constant across both plots. The area between tm and the next zero (tz) is shaded. For the integrable Hamiltonian, tz−tm∼tm−t˜*∼10  μs. For the nonintegrable Hamiltonian, tz−tm remains an order of magnitude larger (tz−tm∼100  μs), even with decoherence. In the decoherence-free scrambling case, N˜(t) remains nonzero for at least four orders of magnitude of time longer than in the nonscrambling case.

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