The parts and the whole: how the tensor product affects Quantum Theory

Abstract

The aim of the present work is to use arguments from Graph Theory, Topology and Geometry, and Multi-Linear Algebra in order to show how the tensor product structure affects Quantum Theory. Saying with other words, we will take seriously the idea of parts at the CSW approach; we will also study the Finite Time Disentanglement for certain classes of quantum dynamics; and by the end we will analyse the behaviour of Quantum Information Protocols (in the LOCC paradigm) when an extra entangled is allowed, all of that to show how the structure of tensorproduct, albeit inherent, brings striking features to Quantum Theory.