Classical and Quantum Information Theory: An Introduction by Emmanuel Desurvire

By Emmanuel Desurvire

Info thought lies on the center of contemporary expertise, underpinning all communications, networking, and knowledge garage platforms. This booklet units out, for the 1st time, a whole evaluate of either classical and quantum info conception. all through, the reader is brought to key effects with out changing into misplaced in mathematical info. beginning chapters current the elemental ideas and diverse functions of Shannon's entropy, relocating directly to the center good points of quantum details and quantum computing. themes comparable to coding, compression, error-correction, cryptography and channel ability are lined from classical and quantum viewpoints. using a casual but scientifically exact technique, Desurvire presents the reader with the data to appreciate quantum gates and circuits. hugely illustrated, with a variety of useful examples and end-of-chapter routines, this article is perfect for graduate scholars and researchers in electric engineering and laptop technological know-how, and practitioners within the telecommunications undefined. extra assets and instructor-only suggestions can be found at www.cambridge.org/9780521881715.

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Example text

In this case, we have the property n(a ∪ b) = n(a) + n(b). As a third definition, the complementary event of x is the event that occurs if x does not occur. It is noted x¯ or sometimes ¬x. In Fig. 4, the complementary event of a ∪ b, which is noted a ∪ b, is represented by the shaded surface spreading inside the space S and outside the surface of a ∪ b. 3 Combined, joint, and conditional probabilities where p(a ∪ b) ≡ p(a + b) is the combined probability of the two events a, b and p(a ∩ b) ≡ p(a, b) is the corresponding joint probability (one must be careful to read the + sign in p(a + b) as meaning “or” and not “and”).

The mean and variance of the binomial distribution is N = nq and σ 2 = N (1 − q), respectively. 4 shows plots of the binomial PDF for n = 10 and different values of q. 5, in which case the peak value is exactly centered about N . A physical illustration of the Bernoulli distribution is the passing, one at a time, of a stream of individual particles (like light quanta or photons) through a piece of absorbing material. These particles may either successfully pass through the material (success, probability q), or absorbed by it (failure, probability 1 − q).

It can also be shown that, for large mean numbers N , the Poisson (or binomial) PDF asymptotically converges towards the Gaussian or normal distribution, which is described in the next section. 3 Continuous distributions At the beginning of this chapter, I discussed the possibility that the events form a continuous and infinite suite of real numbers, which, in the physical world, represent the unbounded set of measurements of a physical quantity. The likelihood of the measurement then corresponds mathematically to a continuous probability distribution.

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