Abstract
The theory of Quantum Information deals with the information processing with quantum states. What is interesting is that in several cases the quantum information processing can have a great advantage with respect to classical information processing and its features often find no correspondence in the classical counterparts. The main examples of quantum information processing are the quantum computer, quantum communications, quantum key distribution (QKD), and quantum teleportation. Quantum Information exhibits two forms, discrete, as the qubit, and continuous, as coherent and more generally Gaussian states. An important remark is that most of the operations in quantum information processing can be carried out both with discrete and with continuous variables (this last possibility is a quite recent discovery). The comparison of these two possibilities should be made upon practical considerations. This chapter gives an introduction to Quantum Information, which will be developed in the last three chapters. Some advanced fundamentals, not sufficiently developed before, as entanglement, partial trace, purification, will be introduced in this chapter.
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Notes
- 1.
The quantum entropy of a state \(\rho \) will be introduced in Sect. 12.4 and defined as \(S(\rho )=-\mathop {\mathrm{{Tr}}}\nolimits [\rho \log _2\rho ]\). It can be calculated from the eigenvalues \(\lambda _k\) of \(\rho \) as \(S(\rho )= -\sum _k\lambda _k\log _2 \lambda _k\) and it is constrained as \(0\le S(\rho )\le \log _2K\). Note that in (10.9) \(d^2_k\) are the eigenvalues of both \(\rho _A\) and \(\rho _B\).
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Cariolaro, G. (2015). Introduction to Quantum Information. In: Quantum Communications. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-15600-2_10
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DOI: https://doi.org/10.1007/978-3-319-15600-2_10
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