Preliminaries

Publication year: 2012
Source: Classical and Quantum Information, 2012, Pages 1-131

Dan C., Marinescu , Gabriela M., Marinescu

 Summary: The first chapter of the book reviews basic concepts from mathematics, quantum mechanics, and computer science necessary for understanding the properties of quantum information. First we review linear algebra concepts, Hilbert spaces and Dirac notation used in quantum mechanics, Hermitian and unitary operators, and projectors. The next sections cover the postulates of quantum mechanics, the uncertainity principle, pure and mixed states, and entanglement. Then, we discuss the properties of quantum information and the physical realization of quantum computing and communication systems. The next sections cover the quantum circuit model, quantum gates and circuits and Solovay-Kitaev theorem. Then, we discuss quantum…