Lieb-Robinson bounds

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.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 was thought that there is then no limitation to the speed of propagation of information. The fact that this is not so, for certain kinds of quantum systems of atoms arranged in a lattice (often called quantum spin systems), is important conceptually and also practically because it means that for short periods of time distant parts of the system act independently.The surprising existence of such a finite speed of propagation (up to exponentially small error terms) was discovered mathematicallyin the 1972 paper. It turns the locality properties of physical systems into the existence of an upper bound forthis speed. The bound is known as the Lieb-Robinson bound and the speed is known as the Lieb-Robinson velocity. The velocity is not universal, because it depends on thedetails of the system under consideration, but for each system there is a finite velocity.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.Review articles can be found in the following references, for example,