Download e-book for iPad: An Introduction to Information Theory: Symbols, Signals and by John R. Pierce

By John R. Pierce

ISBN-10: 0486134970

ISBN-13: 9780486134970

Covers encoding and binary digits, entropy, language and which means, effective encoding and the noisy channel, and explores ways that info idea pertains to physics, cybernetics, psychology, and paintings. "Uncommonly good...the so much enjoyable dialogue to be found." - medical American. 1980 variation.

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7 Measurement Postulate The numerical outcome of a measurement of observable A of a quantum system in state | ϕ ∈ Hn is an eigenvalue λi of the operator A used to measure observable A; immediately after the measurement, the quantum state of the system is an eigenvector | ai of A corresponding to the eigenvalue λi . This postulate is sometimes called the postulate of collapse because as we shall see later a measurement projects, or collapses, the state of the quantum system being measured. Another formulation of this postulate is that mutually exclusive measurement outcomes correspond to orthogonal projection operators (projectors) {P0 , P1 , .

Eigenvectors of a Hermitian operator corresponding to different eigenvalues are mutually orthogonal. 4. If two Hermitian operators commute, they have a common basis of orthonormal eigenvectors (an eigenbasis). If they do not commute, then no common eigenbasis exists. 5. A complete set of commuting observables is the minimal set of Hermitian operators with a unique common eigenbasis. 6. The eigenvalues of a unitary operator are complex numbers of modulus 1. 7. Eigenvectors of a unitary operator corresponding to different eigenvalues are mutually orthogonal.

In this expression S(ω) = F (s(t)) is the Fourier transform of the function s(t) and ω = (2π)/f , with f = 1/T the frequency and T the period of the signal. Peres observes [325] that in the case of acoustic signals we can have approximate values for the time and the frequency; musical scores indicate both time and frequency and allow musicians to produce sounds that capture the information generated by the composer. It seems quite reasonable to consider also approximate values for the observables of a quantum system.

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An Introduction to Information Theory: Symbols, Signals and Noise by John R. Pierce


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