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.
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