An m-fold superposition of typical sub-maximally entangled states gains a universal ln(m) entanglement enhancement, while maximally entangled states relax to the Haar limit via N-independent scaling laws.
Introduction to representation theory
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abstract
These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students, and its extended version given by the first author to MIT undergraduate math students in the Fall of 2008. The notes cover a number of standard topics in representation theory of groups, Lie algebras, and quivers, and contain many problems and exercises. They should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra, and may be used for an undergraduate or introductory graduate course in representation theory.
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Typical Entanglement of Superpositions
An m-fold superposition of typical sub-maximally entangled states gains a universal ln(m) entanglement enhancement, while maximally entangled states relax to the Haar limit via N-independent scaling laws.