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Does the Lieb-Robinson bound actually proved the speed of light from the assumptions of quantum theory. If it did, would that be a derivation of Special relativity? Thanks.
The Lieb-Robinson bound is a mathematical theorem that describes the maximum speed at which information can be transmitted between two distant points in a quantum system. It is used to understand the dynamics of quantum systems and has applications in quantum information theory, condensed matter physics, and quantum field theory.
The Lieb-Robinson bound was first introduced by mathematicians Elliott H. Lieb and Daniel W. Robinson in their 1972 paper "The Finite Group Velocity of Quantum Spin Systems".
The Lieb-Robinson bound is used to understand the propagation of information and correlations in quantum systems. In particular, it can be used to study the dynamics of quantum many-body systems and to determine the speed at which quantum entanglement can spread through a system.
The Lieb-Robinson bound has applications in various areas of physics, including quantum information theory, condensed matter physics, and quantum field theory. Some specific applications include studying the dynamics of quantum spin systems, understanding the behavior of quantum phase transitions, and analyzing the spread of quantum entanglement in different types of systems.
The Lieb-Robinson bound is not considered a fundamental limit in quantum systems, but rather a useful tool for understanding the behavior of these systems. It is a mathematical bound and does not take into account all possible physical effects, so it may not accurately describe all aspects of a quantum system. However, it has been shown to be a good approximation in many cases and has been used to make important predictions about the behavior of quantum systems.