Journal. Quantum nonlocality is sometimes understood as being equivalent to entanglement. The emphasis is on trying to show the ideas behind the calculations. 1 (2005), 47{79], we call a quantum … A characteristic feature of these systems is the local nature of their interactions. 1 I'll call one type “topological non-locality", and the other type “quantum entanglement non-locality". Several bounds on the time evolution of correlations have been derived for these systems. Two different models describing, respectively, lattice bosons, and spins are considered. Non-locality and quantum systems. Selected Contributions of the XVth International Congress on Mathematical Physics, edited by Sidovaricius, V. (Springer Verlag, 2009), pp. 45 Downloads; 2 Citations; Abstract . However, an analysis based on such models is only a preliminary to an analysis based on a complete dynamical model. Models of the EPR-Bohm experiment usually consider just two times, an initial time, and the time of measurement. Nachtergaele, B. and Sims, R., “ Locality estimates for quantum spin systems,” in New Trends in Mathematical Physics. Models of the EPR-Bohm experiment usually consider just two times, an initial time, and the time of measurement. The Lieb-Robinson theorem states that locality is approximately preserved in the dynamics of quantum lattice systems. Another of the remarkable features of the microscopic world prescribed by quantum theory is the idea of nonlocality, what Albert Einstein rather dismissively called “spooky actions at a distance”. Whenever one has finite-dimensional constituents, observables evolving in time under a local Hamiltonian will essentially grow linearly in their support, up to exponentially suppressed corrections. This was first described in the “EPR papers” of Einstein, Boris Podolsky and Nathan Rosen in 1935, and it is sometimes referred to as the EPR (Einstein-Podolsky-Rosen) paradox. Dalton1 ,2 a 1 Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122, Australia 2 School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, UK Received 12 April 2018 / Received in nal form 18 July 2018 Published online 13 February 2019 Abstract. Moreover, today’s large-scale distributed systems must accommodate heterogeneity in both the offered load and in the makeup of the available storage and compute capacity. The ideal resource assignment must balance the utilization of the underlying system against the loss of locality incurred when individual tasks or data objects are fragmented among several servers. These lecture notes focus on the application of ideas of locality, in particular Lieb-Robinson bounds, to quantum many-body systems. These lecture notes focus on the application of ideas of locality, in particular Lieb-Robinson bounds, to quantum many-body systems. Bell non-locality in macroscopic systems B.J. For such systems, Lieb and Robinson proved in a seminal work in 1972 that there is an emergent speed limit slower than the speed of light, which limits the maximal information transport in quantum many-body systems. The dynamics of local observables in these systems cannot be described with the standard methods used in equilibrium statistical physics and completely new methods have to be developed. We finally provide a microscopic justification of the different regimes observed and of the origin of the protected locality in bosonic models. We consider applications including correlation decay, topological order, a higher dimensional Lieb-Schultz-Mattis theorem, and a nonrelativistic Goldstone theorem. 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