By Giuliano;Casati, Giulio;Strini, Giuliano Benenti
ISBN-10: 9812563458
ISBN-13: 9789812563453
ISBN-10: 9812565280
ISBN-13: 9789812565280
Quantum computation and data is a brand new, quickly constructing interdisciplinary box. Its basic innovations and vital effects will not be simply understood with no dealing with various technical info. construction at the simple techniques brought in Vol I, this moment quantity offers with quite a few vital features, either theoretical and experimental, of quantum computation and knowledge intensive. The components contain quantum facts compression, obtainable details, entanglement focus, limits to quantum computation because of decoherence, quantum error-correction, and the 1st experimental implementations of quantum info protocols. This quantity additionally incorporates a collection of designated themes: chaos and quantum to classical transition, quantum trajectories, quantum computation and quantum chaos, and the Zeno impression
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Additional info for Principles of quantum computation and information. Vol. 2: Basic tools and special topics
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35) for i, j = x, y, z. For a generic density matrix, the qubit polarization along the direction ˆ is given by singled out by the unit vector n σnˆ = Tr(ρ σnˆ ) = Tr 1 2 ˆ ·σ . 36) ˆ · σ, σ = (σx , σy , σz ) and the density matrix ρ has been Here, σnˆ ≡ n expressed as in Eq. 32). 2, we have ˆ · r. 37) Thus, the vector r parametrizes the polarization of the qubit. As we shall see in Sec. 5, if many identically prepared systems are available; that is, the same density matrix ρ describes each system, then we can determine ˆ · σ along three r (and therefore the density matrix ρ) by measuring n independent axes.
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 , . . , xn ) − H(p1 , . . 157) then, for any δ > 0, the probability that a given sequence is -typical is larger than 1 − δ, for sufficiently large n. Therefore, most of the sequences are -typical in the limit of large n. Since there are 2nH typical sequences (asymptotically in n), each occurring with probability 2−nH , we can identify which one of these sequences actually occurred using nH bits.
There are 24 = 16 such strings (0 ≡ 0000, 1 ≡ 0001, . . , 15 ≡ 1111). Let Pi denote the probability that the string i occurs, with i = 0, . . , 15. We have P0 = p40 , P1 = p30 p1 , . . , P15 = p41 . 27 bits, which is very close to the optimal value. This shows the power of data compression codes. The enormous practical importance of data compression in fields such as telecommunication is self-evident. Data compression allows us to increase the transmission rate or the storage capacity of a computer.
Principles of quantum computation and information. Vol. 2: Basic tools and special topics by Giuliano;Casati, Giulio;Strini, Giuliano Benenti
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