Download Classical and quantum information by Dan C. Marinescu PDF

By Dan C. Marinescu

A new self-discipline, Quantum info technological know-how, has emerged within the final 20 years of the 20 th century on the intersection of Physics, arithmetic, and computing device technological know-how. Quantum info Processing is an software of Quantum info technological know-how which covers the transformation, garage, and transmission of quantum details; it represents a innovative method of info processing.

This booklet covers issues in quantum computing, quantum details conception, and quantum blunders correction, 3 vital parts of quantum info processing.

Quantum info concept and quantum mistakes correction construct at the scope, recommendations, method, and methods constructed within the context in their shut kinfolk, classical info conception and classical errors correcting codes.

Presents fresh leads to quantum computing, quantum info conception, and quantum mistakes correcting codes.

Covers either classical and quantum info thought and blunder correcting codes.

The final bankruptcy of the e-book covers actual implementation of quantum details processing devices.

Covers the mathematical formalism and the strategies in Quantum Mechanics severe for figuring out the homes and the differences of quantum information.

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As we shall see in Chapter 6, the physical processes for the storage, transformation, and transport of information for photons, ion traps, quantum dots, nuclear magnetic resonance (NMR), and other quantum systems are very different and could distract us from the goal of discovering the common properties of quantum information independent of its physical support. To study the properties of quantum information, we have to resort to an abstract model that captures the essence of quantum behavior; this model, quantum mechanics, describes the properties of physical systems as objects in a finite-dimensional Hilbert space.

N If the eigenvalues, λj , are degenerate (not distinct), then there are many bases of eigenvectors that diagonalize matrix A. If λ is an eigenvalue of multiplicity K > 1, the set of corresponding eigenvectors generates a subspace of dimension K, the eigenspace corresponding to that λ; the eigenspaces corresponding to different eigenvalues are orthogonal. Assume that λ is a degenerate eigenvalue, and the corresponding eigenvectors are | ψλ1 and | ψλ2 : A | ψλ1 = λ | ψλ1 and A | ψλ2 = λ | ψλ2 .

The superposition of a state with itself results in the original state: α1 | ϕ + α2 | ϕ = (α1 + α2 ) | ϕ . If α1 + α2 = 0, there is no superposition and the two components cancel each other by an interference effect. If a1 + a2 = a3 , we assume that the result of the superposition is the original state itself, and we can conclude that if the ket (bra) vector corresponding to a state is multiplied by any nonzero complex number, the resulting ket (bra) vector will correspond to the same state. There is a fundamental difference between a quantum and a classical superposition.

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