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Introduction to Quantum Information Science$
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Vlatko Vedral

Print publication date: 2006

Print ISBN-13: 9780199215706

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780199215706.001.0001

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Quantum mechanics

Quantum mechanics

Chapter:
(p.14) 2 Quantum mechanics
Source:
Introduction to Quantum Information Science
Author(s):

Vlatko Vedral

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199215706.003.0002

This chapter reviews all the rules of quantum mechanics and their mathematical notation. It also considers quantum entanglement, a fundamental resource in quantum information. There are four basic postulates of quantum mechanics, that indicate how to represent physical systems, how to represent observations, how to carry out measurements, and how systems evolve when “not measured”. Before describing the laws of quantum mechanics, their mathematical background is first described, along with a Mach Zehnder interferometer experiment in which the (strange) readings on the detectors can be explained by quantum mechanics. This chapter also discusses the Dirac notation, qubits, Hilbert spaces, projective measurements and operations, unitary operations, eigenvectors and eigenvalues, spectral decomposition, applications of the spectral theorem, Dirac notation shorthands, and mixed states.

Keywords:   quantum mechanics, mathematical notation, Dirac notation, quantum entanglement, Mach Zehnder interferometer, Hilbert spaces, qubits, mixed states, spectral decomposition

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