About: 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 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

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rdfs:label	Lieb–Robinson bounds (en)
rdfs:comment	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 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 (en)
dct:subject	Limits of computation Quantum information theory
Wikipage page ID	42610902 (xsd:integer)
Wikipage revision ID	1117831131 (xsd:integer)
Link from a Wikipage to another Wikipage	Limits of computation Quantum computer Quantum information theory Quantum mechanics Schrödinger's equation Basis (linear algebra) Derek W. Robinson Lie product formula Operator norm Quantum optics Elliott H. Lieb Gaussian quadrature Condensed matter physics Quantum information theory Linear operator Hamiltonian (quantum mechanics) Speed Expectation value (quantum mechanics) Theory of relativity Hilbert space Atomic physics Special relativity Speed of light Information Newtonian mechanics Self-adjoint operator Lindblad equation Observable Quantum dissipation Translation-invariant dbr:Wikt:finite
sameAs	Lieb–Robinson bounds Lieb–Robinson bounds
dbp:wikiPageUsesTemplate	dbt:Anchor dbt:Expert_needed dbt:NumBlk dbt:Reflist dbt:When dbt:EquationRef dbt:EquationNote
has abstract	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 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. (en)
prov:wasDerivedFrom	wikipedia-en:Lieb–Robinson_bounds?oldid=1117831131&ns=0
page length (characters) of wiki page	34400 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Lieb–Robinson_bounds
is Link from a Wikipage to another Wikipage of	Lieb-Robinson bounds Lieb-Robinson bound
is Wikipage redirect of	Lieb-Robinson bounds Lieb-Robinson bound
is foaf:primaryTopic of	wikipedia-en:Lieb–Robinson_bounds

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