Physics 4999E Study Guide - Final Guide: Density Matrix, Convex Cone, Euclidean Space
22 Feb 2020
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Cs 766/qic 820 theory of quantum information (fall 2011) For the next several lectures we will be discussing various aspects and properties of entanglement. Mathematically speaking, we de ne entanglement in terms of what it is not, rather than what it is: we de ne the notion of a separable operator, and de ne that any density operator that is not separable represents an entangled state. 14. 1 de nition and basic properties of separable operators. Let x and y be complex euclidean spaces. A positive semide nite operator p pos (x y ) is separable if and only if there exists a positive integer m and positive semide nite operators. , rm pos (y ) such that. We will write sep (x : y ) to denote the collection of all such operators. 1. Operators p pos (x y ) that are not contained in sep (x : y ) are said to be entangled.
