Lieb-Robinson Bounds and the Generation of Correlations and Topological Quantum Order
Open accessAbstract
The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light cone with exponentially decaying tails. We discuss several consequences of this result in the context of quantum information theory. First, we show that the information that leaks out to spacelike separated regions is negligible and that there is a finite speed at which correlations and entanglement can be distributed. Second, we discuss how these ideas can be used to prove lower bounds on the time it takes to convert states without topological quantum order to states with that property. Finally, we show that the rate at which entropy can be created in a block of spins scales like the boundary of that block.
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Strongly entangled models in more than one dimension are computationally hard, with examples including fermionic models, frustrated models, and disordered models.
“Generally speaking, computationally hard are those 'strongly entangled' models in more than 1D such as”
From Can one trust quantum simulators? (2012) · cites this paper as [90]
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- Authors
- Bravyi, S., Hastings, M. B., & Verstraete, F.
- Affiliations
- IBM Research - Thomas J. Watson Research Center (US)
- Los Alamos National Laboratory (US)
- California Institute of Technology (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2006-07-31
- Volume
- 97
- Issue
- 5
- Pages
- 050401-050401
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1977658351
- Cited by
- 664
- References
- 25
- Citations by year
- 2026: 22 · 2025: 57 · 2024: 65 · 2023: 45 · 2022: 47 · 2021: 48 · 2020: 30 · 2019: 41 · 2018: 35 · 2017: 31 · 2016: 44 · 2015: 32 · 2014: 25 · 2013: 27 · 2012: 24
- FWCI
- 12.19
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Ghent University Academic Bibliography (Ghent University) (submittedVersion, other-oa)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (9907949, W-7405-ENG-36)
- U.S. Department of Energy (W-7405, W-7405-ENG-36)
- Gordon and Betty Moore Foundation
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- Lieb-Robinson bound, quantum correlations, entanglement propagation, topological quantum order, quantum state conversion, entropy production, quantum information, spin systems
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