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Hierarchy of Linear Light Cones with Long-Range Interactions

Tran, Minh C. and Chen, Chi-Fang and Ehrenberg, Adam and Guo, Andrew Y. and Deshpande, Abhinav and Hong, Yifan and Gong, Zhe-Xuan and Gorshkov, Alexey V. and Lucas, Andrew (2020) Hierarchy of Linear Light Cones with Long-Range Interactions. Physical Review X, 10 (3). Art. No. 031009. ISSN 2160-3308.

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In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently separated spacetime points approximately commute—given a many-body state |ψ⟩, O_x(t)O_y|ψ⟩≈O_yO_x(t)|ψ⟩ with arbitrarily small errors—so long as |x−y|≳vt, where v is finite. Yet, most nonrelativistic physical systems realized in nature have long-range interactions: Two degrees of freedom separated by a distance r interact with potential energy V(r)∝1/r^α. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: At the same α, some quantum information processing tasks are constrained by a linear light cone, while others are not. In one spatial dimension, this linear light cone exists for every many-body state |ψ⟩ when α>3 (Lieb-Robinson light cone); for a typical state |ψ⟩ chosen uniformly at random from the Hilbert space when α>5/2 (Frobenius light cone); and for every state of a noninteracting system when α>2 (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones—and their tightness—also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that universal quantum state transfer, as well as many-body quantum chaos, is bounded by the Frobenius light cone and, therefore, is poorly constrained by all Lieb-Robinson bounds.

Item Type:Article
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URLURL TypeDescription Paper InPhysics : Viewpoint
Chen, Chi-Fang0000-0001-5589-7896
Ehrenberg, Adam0000-0002-3167-6519
Deshpande, Abhinav0000-0002-6114-1830
Gorshkov, Alexey V.0000-0003-0509-3421
Additional Information:© 2020 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Received 11 February 2020; revised 1 May 2020; accepted 29 May 2020; published 13 July 2020. We thank Ana Maria Rey for useful discussions. M. C. T., A. Y. G., A. D., A. E., and A. V. G. acknowledge support by the DoE ASCR Quantum Testbed Pathfinder program (Grant No. DE-SC0019040), DoE ASCR FAR-QC (Grant No. DE-SC0020312), NSF Physics Frontier Center QC program, AFOSR Multidisciplinary University Research Initiative, AFOSR, ARO Multidisciplinary University Research Initiative, DoE BES Materials and Chemical Sciences Research for Quantum Information Science program (Grant No. DE-SC0019449), ARL CDQI, and NSF Physics Frontier Center at JQI. C.-F. C. is supported by the Millikan graduate fellowship at Caltech. A. Y. G. is supported by the NSF Graduate Research Fellowship Program under Grant No. DGE-1840340. A. E. also acknowledges funding from the DoD. Z.-X. G. is supported by the NSF RAISE-TAQS program under Grant No. CCF-1839232.
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0019040
Department of Energy (DOE)DE-SC0020312
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Army Research Office (ARO)UNSPECIFIED
Department of Energy (DOE)DE-SC0019449
Army Research LaboratoryUNSPECIFIED
Caltech Millikan FellowshipUNSPECIFIED
NSF Graduate Research FellowshipDGE-1840340
Department of DefenseUNSPECIFIED
Subject Keywords:Quantum Physics, Quantum Information
Issue or Number:3
Record Number:CaltechAUTHORS:20200713-104200613
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104354
Deposited By: Tony Diaz
Deposited On:13 Jul 2020 18:42
Last Modified:13 Jul 2020 20:58

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