Physics 4999E Study Guide - Final Guide: Erhard Schmidt, Schmidt Decomposition, Schmidt Number
22 Feb 2020
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Cs 766/qic 820 theory of quantum information (fall 2011) Lecture 15: separable mappings and the locc paradigm. In the previous lecture we discussed separable operators. The focus of this lecture will be on analogous concepts for mappings between operator spaces. In particular, we will discuss separable channels, as well as the important subclass of locc channels. The acronym locc is short for local operations and classical communication, and plays a central role in the study of entanglement. Before discussing separable and locc channels, it will be helpful to brie y discuss a general- ization of the concept of separability for operators. Suppose two complex euclidean spaces x and y are xed, and for a given choice of a non- negative integer k let us consider the collection of operators. Rk (x : y ) = conv {vec(a) vec(a) : a l (y, x ) , rank(a) k} .
