Summary
In this chapter, we cover the fundamentals of linear algebra and provide a mathematical formulation of quantum mechanics for use in later chapters. It is necessary to understand these topics since they form the foundation of quantum information processing discussed later. In the first section, we cover the fundamentals of linear algebra and introduce some notation. The next section describes the formulation of quantum mechanics. Further, we examine a quantum two-level system, which is the simplest example of a quantum-mechanical system. Finally, we discuss the tensor product and matrix inequalities. More advanced discussions on linear algebra are available in Appendix A.
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© 2006 Springer-Verlag Berlin Heidelberg
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(2006). Mathematical Formulation of Quantum Systems. In: Quantum Information. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-30266-2_2
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DOI: https://doi.org/10.1007/3-540-30266-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30265-0
Online ISBN: 978-3-540-30266-7
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