Measuring out-of-time-ordered correlation functions without reversing time evolution

Abstract

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.

12 pages, 6 figures. Updated figure labels and author affiliation. Made a few minor edits to the main text

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• Probing Hilbert Space Fragmentation with Strongly Interacting Rydberg Atoms
• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
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• Fast scrambling dynamics and many-body localization transition in an all-to-all disordered quantum spin model
• Probing scrambling and operator size distributions using random mixed states and local measurements
• Quantum Signatures of Chaos in Anisotropic Quantum Rabi Model
• Learning out-of-time-ordered correlators with classical kernel methods
• Information acquisition, scrambling, and sensitivity to errors in quantum chaos