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arXiv:quant-ph/0512078 · Birkhäuser Basel eBooks

Roots and Fruits of Decoherence

H. D. Zeh

Published Jan 1, 2006• 81 citations
arXivHTMLPDF

Abstract

The concept of decoherence is defined, and discussed in a historical context. This is illustrated by some of its essential consequences which may be relevant for the interpretation of quantum theory. Various aspects of the formalism are also reviewed for this purpose. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/978-3-7643-7808-0_5

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The concept of decoherence is defined, and discussed in a historical context. This is illustrated by some of its essential consequences which may be relevant for the interpretation of quantum theory. Various aspects of the formalism are also reviewed for this purpose. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
In recent years decoherence has been widely discussed and accepted as a mechanism responsible for the emergence of classicality in quantum measurements and the absence in the real world of Schrödinger-cat-like states [ 2 , 6 , 7 , 11 , 12 ]. Let me start with recalling the Schrödinger cat paradox. It was a hypothetical experiment proposed by Schrödinger in 1935 which can be briefly described as follows. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This chapter reviews the quantum theoretical formalism and sketches its foundational problems. The main function of this chapter is to establish common ground for the interpretive discussions which follow, not to provide a comprehensive introduction to quantum theory. 6 Its first section recapitulates the essential aspects of the Hilbert space formalism of quantum mechanics, the second section covers the textbook account of measurement and measurement collapse, and the third and final section outlines the quantum theoretical treatment of many-component systems and explains the concept of quantum entanglement. Further introductory material is provided in the Appendices A, B, and C, all of which cover important no-go theorems for the interpretation of the theory. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The authors briefly review quantum game theory and its application in economics. This review is addressed at newcomers and some basic ideas of quantum theory are necessary to follow the text—the short introduction in chapter “A Brief Introduction to Quantum Formalism” will be sufficient. Due to the lack of space only the flagship issues will be discussed. Quantum game theory, whatever opinions may be held due to its abstract physical formalism, have already found various applications even outside the orthodox physics domain. We are aware that the implementation of genuine quantum models is not an easy task. Nevertheless, such models are already an interesting although sophisticated theoretical tool. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
A general quantum machine is characterized to capture all the possible physical structures that may be employed for effective or efficient computation. As an illustration, a specific machine is described for the permanent evaluation problem. The contrast between quantum and classical parallelism is also discussed, as is the effect of quantum error correction against decoherence and loss. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.