Elements Of Quantum Information Theory, Decoherence And Error Correcting Codes - Harold Ollivier.pdf

文档介绍：Elements of quantum information theory,
decoherence and error correcting codes
Harold Ollivier
INRIA - Codes
BP 105, Domaine de Voluceau
F-78153, Le Chesnay,
France
Presented at École Polytechnique
in partial fulllment of the
requirements for the degree of
Docteur en mathématiques.
Committee:
President : J.-M. Steyaert
Thesis director : P. Charpin
Referees : R. Jozsa & R. Laamme
Jury : P. Grangier & J.-P. Tillich (invited)
Contents
Preface ix
Acknowledgments xi
I The quantum-classical transition: an information
theoretical point of view 3
1 Introduction to quantum mechanics 5
Prologue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
General considerations about physical theories . . . . . . . . . . 6
Axioms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Collapse of the wave-function . . . . . . . . . . . . . . . . . . . . 9
Open quantum systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Superposition and entanglement . . . . . . . . . . . . . . . . . . . . . . . 14
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Introduction to decoherence and einselection 17
The need for an interpretation . . . . . . . . . . . . . . . . . . . . . . . . 17
The measurement problem . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Copenhagen interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Many world interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Existential interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . 20
A transition to the classical reality . . . . . . . . . . . . . . . . . 20
Decoherence and einselection . . . . . . . . . . . . . . . . . . . . 20
Several criteria, pros and cons . . . . . . . . . .