文档介绍：1
Classical and Quantum Information∗
Dan C. Marinescu and Gabriela M. Marinescu
November 18, 2010
∗Copyright 2006, 2007, 2008, 2009, 2010 by Dan C. Marinescu and Gabriela M. Marinescu
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To Vera Rae
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Contents
1 Preliminaries 14
Elements of Linear Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Hilbert Spaces and Dirac Notations . . . . . . . . . . . . . . . . . . . . . . . . 23
Hermitian and Unitary Operators; Projectors. . . . . . . . . . . . . . . . . . . 27
Postulates of Quantum Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . 34
Quantum State Postulate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Dynamics Postulate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Measurement Postulate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Linear Algebra and Systems Dynamics . . . . . . . . . . . . . . . . . . . . . . 50
Symmetry and Dynamic Evolution . . . . . . . . . . . . . . . . . . . . . . . . 52
Uncertainty Principle; Minimum Uncertainty States . . . . . . . . . . . . . . . 54
Pure and Mixed Quantum States . . . . . . . . . . . . . . . . . . . . . . . . . 55
Entanglement; Bell States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Quantum Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Physical Realization of Quantum Information Processing Systems . . . . . . . 65
puters; The Circuit Model putation . . . . . . . . . . . . 68
Quantum Gates, Circuits, and puters . . . . . . . . . . . . . . . 74
Universality of Quantum Gates; Solovay-Kitaev Theorem . . . . . . . . . . . . 79
putational Models and Quantum Algorithms . . . . . . . . . . . 82
Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, and Simon Oracles . . . . . . . . 89
Quantum Phase Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96