Quantum decoherence. A work on the quantum measurement problem

Abstract

The objectives of this project are several and their achievement has been organized in three different chapters. In the first one, It has been tried to explain what the measurement problem is and how decoherence partially solves it, explaining why we are only able to measure non-superposed states. In the second chapter it is shown how, indeed, decoherence emerges naturally when considering the interaction between a system and its environment, thus giving a justification to Von Neumann’s irreversible reduction process. With these first two chapters, moreover, a mathematical framework based on master equations and CPT maps is established, which is used in the last chapter to achieve the ultimate goal of being able to describe the evolution of the accessible states of a quantum system on which a measurement is performed without having to resort to the measurement postulates.

Los objetivos de este proyecto son varios y su consecuci´on se ha organizado en tres cap´ıtulos distintos. En el primero se ha tratado de explicar en qu´e consiste el problema de la medida y c´omo la decoherencia lo resuelve parcialmente, explicando por qu´e tan solo somos capaces de medir estados no superpuestos. En el segundo cap´ıtulo se demuestra c´omo, en efecto, la decoherencia emerge de forma natural cuando se considera la interacci´on entre un sistema y su entorno, dando una justificaci´on as´ı al proceso de reducci´on irreversible de Von Neumann. Con estos dos primeros cap´ıtulos, adem´as, se consigue establecer un marco matem´atico basado en las ecuaciones maestras y los mapas CPT que, en el tercer cap´ıtulo, se emplea para lograr el objetivo final de poder describir la evoluci´on de los estados accesibles de un sistema cu´antico sobre el que se realiza una medici´on sin tener que recurrir a los postulados de la medida.