Download Classical and Quantum Information by Dan C. Marinescu PDF

By Dan C. Marinescu

ISBN-10: 0123838746

ISBN-13: 9780123838742

A brand new self-discipline, Quantum info technology, has emerged within the final twenty years of the 20 th century on the intersection of Physics, arithmetic, and laptop technology. Quantum info Processing is an program of Quantum info technology which covers the transformation, garage, and transmission of quantum info; it represents a innovative method of info processing. This e-book covers subject matters in quantum computing, quantum info concept, and quantum mistakes correction, 3 vital parts of quantum info processing. Quantum details conception and quantum errors correction construct at the scope, suggestions, technique, and strategies built within the context in their shut family members, classical info conception and classical errors correcting codes. provides fresh ends up in quantum computing, quantum details conception, and quantum blunders correcting codes. Covers either classical and quantum details thought and blunder correcting codes. The final bankruptcy of the ebook covers actual implementation of quantum info processing units. Covers the mathematical formalism and the techniques in Quantum Mechanics severe for figuring out the homes and the variations of quantum details.

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We define two possible state vectors of a system in this space | ϕA = αx | x + αy | y and | ϕB = βx | x + βy | y The initial state of the system could be | ψA with probability p or | ψB with probability 1 − p; we say that the system is in a mixed ensemble of quantum states. Pn } Pi = |e i>∈ New state: P1 n Outcome of the measurement: 1 Probability of the outcome: |P1 λ | φ >|2 | φ >∈ New state: Pi n Outcome of the measurement: Probability of the outcome: Pi λi | φ >|2 | φ >∈ New state: Pn n Outcome of the measurement: Probability of the outcome: Pn λn | φ >|2 Figure 6: The measurement of observable A of a quantum system in state | ϕ ∈ Hn .

En } of eigenvectors simultaneously for (A+A† )/2 and (A − A† )/2i. Hence they are also eigenvectors for A − A† A + A† +i 2 2i A= . Let λ1 , λ2 , . . λn be the eigenvalues corresponding to the eigenvectors {e1 , e2 , . . , en }. A= λi P i with Pi =| ei ei | . i Indeed, both A and {e1 , e2 , . . , en }. i λi Pi have the same matrix representation with respect to the base Example. Choose an orthonormal basis in H2 . Let A be a 2 × 2 matrix in this basis is A= a11 a12 a21 a22 . Calculate its eigenvalues λ1 and λ2 , possibly equal.

An impressive number of experiments have produced results consistent with the prediction of Quantum Mechanics and so far there is no experimental evidence to disprove it thus, we shall used this model to study the properties of quantum information. The correspondence and transformation rules are captured by the postulates of Quantum Mechanics, Figure 4. We find it useful to expand the traditional three postulates of Quantum Mechanics, the state postulate, the dynamics postulate, and the measurement postulate, to emphasize some aspects important for quantum information processing: 1.

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