Principles of Quantum Computation and Information: Basic by Giuliano Benenti, Giulio Casati, Giuliano Strini

By Giuliano Benenti, Giulio Casati, Giuliano Strini

Quantum computation and data is a brand new, swiftly constructing interdisciplinary box. Its basic innovations and valuable effects will not be simply understood with out dealing with a number of technical information. construction at the simple ideas brought in Vol I, this moment quantity offers with a variety of vital features, either theoretical and experimental, of quantum computation and knowledge intensive. The components contain quantum information compression, available details, entanglement focus, limits to quantum computation as a result of decoherence, quantum error-correction, and the 1st experimental implementations of quantum info protocols. This quantity additionally contains a choice of detailed themes: chaos and quantum to classical transition, quantum trajectories, quantum computation and quantum chaos, and the Zeno influence.

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This simply means that generalized measurements are equivalent to projective measurements on a larger Hilbert space. , in Peres (1993). In the following, we show that, if we restrict our attention to a subsystem of a given system, a projective measurement performed on the system cannot in general be described as a projective measurement on the subsystem. 129) k where {|k 2 } is an orthonormal basis for subsystem 2. 130) where ρ12 = U |ψ 1 |0 2 1 ψ|2 0|U † and the Kraus operators Ei satisfy the condition i Ei† Ei = I1 and, in general, are not projectors.

Xn is p(x1 , x2 , . . ,pk ) . 155) Indeed, from Eq. 153) we obtain − 1 1 log p(x1 , . . , xn ) = − n n n log p(xi ) ≈ H(p1 , . . 156) i=1 where the last (approximate) equality is guaranteed by the law of large numbers and is obtained as follows: for all j = 1, 2, . . , k, the frequency nj /n of the letter j in the message is substituted by the a priori probability pj (nj is the number of times that j appears in the message). The law of large numbers also tells us that, if we fix > 0 and we say that a sequence is -typical when − 1 log p(x1 , .

This circuit can be decomposed into two parts: (i) the preparation of a specific state of the quantum copier and (ii) the copying process. It can be seen from Fig. 1 that only part (ii) depends on the state |ψ to be copied. Let us first look at the preparation stage. The gates labelled by θi denote the application January 25, 2007 272 11:17 WSPC/Book Trim Size for 9in x 6in qcbook2 Principles of Quantum Computation and Information. 62) where, as discussed in Sec. 1, Ry (−2θi ) corresponds to a counterclockwise rotation through an angle −2θi about the y-axis of the Bloch sphere and the angles θi are chosen as cos 2θ1 = √1 5 √ , cos 2θ2 = 5 3 , cos 2θ3 = √2 5 .

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