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Quantum Communications pp 639–663Cite as

Applications of Quantum Information

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Part of the book series: Signals and Communication Technology ((SCT))

Abstract

This chapter presents some applications of Quantum Information Theory that deviate from the problem of reliably transmitting classical information. In fact, the inherent randomness in quantum measurements lends itself to devising methods for the fast automatic generation of true random numbers with quantum devices. Similarly, the possibility of detecting the presence of a measurement operation on a single quantum system, from another, nonorthogonal measurement on the same system, has opened the way to quantum cryptography. This constitutes an unconditionally secure replacement for the schemes that currently lie at the core of many protocols for securing the transmission and storing of information from a rational attacker. Eventually, we devote a paragraph to the topic of quantum teleportation, that is, the transfer of an unknown quantum state between two different locations that is achieved by making use of entanglement and only transmitting classical information.

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Notes

  1. 1.

    Citing the paper of Marsaglia [2] the mathematician that was the first to discover this weird behavior.

  2. 2.

    Historically, the first formulation of a QKD protocol [15] preceded that of general information theoretic key agreement schemes [16].

  3. 3.

    A somewhat subtle point should be made here. The security of the protocol does not guarantee that eavesdropping is unlikely, given that no errors have been detected in the minority basis. Rather, it states that if eavesdropping takes place, it will be detected with high probability. In symbols, let \(E\) denote the event that eavesdropping has taken place and \(D\) the event that no errors have been detected, we can only upper bound \(P_\mathrm{{md}} = \mathrm{P}[D|E]\), but nothing can be said about \(\mathrm{P}[E|D]\), since assumption can be made on the probability of event \(E\) which is totally under the control of the attacker.

  4. 4.

    That is, the number of positions at which they differ.

  5. 5.

    A class \(\mathcal{F}\) of functions mapping the same domain \(X\) to the same range \(Y\) is called universal hashing if it maps inputs to outputs “uniformly”, that is,

    $$ {\left\{ \begin{array}{ll}|\{f\,|\,f(x) = y\}| = |\mathcal{F}|/|Y| &{} {\text {for all}}\,\, x\in X, y \in Y\\ |\{f\,|\,f(x_1) = f(x_2)\}| = |\mathcal{F}|/|Y| &{} {\text {for all}}\, \,x_1, x_2 \in X. \end{array}\right. } $$
  6. 6.

    A complex-valued random variable \(X\) is called circular symmetric Gaussian if \(\mathfrak {R}X\) and \(\mathfrak {I}X\) are independent Gaussian variables with zero mean and the same variance \(\sigma ^2_X\).

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  1. Department of Information Engineering, University of Padova, Padova, Italy

    Gianfranco Cariolaro

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Cariolaro, G. (2015). Applications of Quantum Information. In: Quantum Communications. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-15600-2_13

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  • DOI: https://doi.org/10.1007/978-3-319-15600-2_13

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