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HandWiki. Lieb-Robinson Bounds. Encyclopedia. Available online: https://encyclopedia.pub/entry/30466 (accessed on 23 September 2026).
HandWiki. Lieb-Robinson Bounds. Encyclopedia. Available at: https://encyclopedia.pub/entry/30466. Accessed September 23, 2026.
HandWiki. "Lieb-Robinson Bounds" Encyclopedia, https://encyclopedia.pub/entry/30466 (accessed September 23, 2026).
HandWiki. (2022, October 20). Lieb-Robinson Bounds. In Encyclopedia. https://encyclopedia.pub/entry/30466
HandWiki. "Lieb-Robinson Bounds." Encyclopedia. Web. 20 October, 2022.
Lieb-Robinson Bounds
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The Lieb-Robinson bound is a theoretical upper limit on the speed at which information can propagate in non-relativistic quantum systems. It demonstrates that information cannot travel instantaneously in quantum theory, even when the relativity limits of the speed of light are ignored. The existence of such a finite speed was discovered mathematically by Elliott H. Lieb and Derek W. Robinson (de) in 1972. It turns the locality properties of physical systems into the existence of, and upper bound for this speed. The bound is now known as the Lieb-Robinson bound and the speed is known as the Lieb-Robinson velocity. This velocity is always finite but not universal, depending on the details of the system under consideration. For finite-range, e.g. nearest-neighbor, interactions, this velocity is a constant independent of the distance travelled. In long-range interacting systems, this velocity remains finite, but it can increase with the distance travelled. In the study of quantum systems such as quantum optics, quantum information theory, atomic physics, and condensed matter physics, it is important to know that there is a finite speed with which information can propagate. The theory of relativity shows that no information, or anything else for that matter, can travel faster than the speed of light. When non-relativistic mechanics is considered, however, (Newton's equations of motion or Schrödinger's equation of quantum mechanics) it had been thought that there is then no limitation to the speed of propagation of information. This is not so for certain kinds of quantum systems of atoms arranged in a lattice, often called quantum spin systems. This is important conceptually and practically, because it means that, for short periods of time, distant parts of a system act independently. One of the practical applications of Lieb-Robinson bounds is quantum computing. Current proposals to construct quantum computers built out of atomic-like units mostly rely on the existence of this finite speed of propagation to protect against too rapid dispersal of information. 

condensed matter quantum computers physical systems

References

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