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arXiv:1806.02807 · Nature

Verified quantum information scrambling

K. A. Landsman, Caroline Figgatt, Thomas Schuster, Norbert M. Linke, Beni Yoshida, Norman Y. Yao, Christopher R. Monroe

Published Mar 6, 2019• 368 citations
arXivHTMLPDF
DOI
10.1038/s41586-019-0952-6

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Quantum information scrambling is the spread of local information into correlation throughout the entire quantum many-body system. This concept has become a central topic in different contexts. In this work, we restate the connection between anyon condensation and topological quantum information scrambling in quantum Hall interfaces. We consider the interface between the Abelian Halperin-330 state and the non-Abelian Read-Rezayi state. We verify explicitly that the interface can be fully gapped. This allows the transmutation of local pseudospin information carried by an Abelian anyon into topological information stored entirely by the anyons in the non-Abelian quantum Hall liquid, with no scrambled information stored at the interface. In combination with our previous work [K. K. W. Ma and K. Yang, Phys. Rev. B 105, 045306 (2022)], our results demonstrate the dependence of the scrambling mechanism on the gapfulness of the interface. Possible Andreev-like reflection of non-Abelian anyons in the fully gapped interface is also discussed.
Abstract Quantum information scrambling refers to the loss of local recoverability of quantum information, which has found widespread attention from high energy physics to quantum computing. In the present analysis we propose a possible starting point for the development of a comprehensive framework for the thermodynamics of scrambling. To this end, we prove that the growth of entanglement as quantified by the mutual information is lower bounded by the time-dependent change of out-of-time-ordered correlator. We further show that the rate of increase of the mutual information can be upper bounded by the sum of local entropy productions, and the exchange entropy arising from the flow of information between separate partitions of a quantum system. Our results are illustrated for the ion trap system, that was recently used to verify information scrambling in an experiment, and for the Sachdev–Ye–Kitaev model.