Abstract
Quantum information science is a future information science. This chapter explains the significance of quantum information science, and the distinction between conventional information science and quantum information science. Then, it describes a future vision of the realization of quantum information processing. This chapter ends with the description of the organization of this book.
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Notes
- 1.
As is mentioned here, even though the formulation in the classical setting is uniquely determined, its quantum extension often has plural formulations. That is, one classical formulation might correspond to plural quantum formulations, in general. When a beginner of quantum information science considers a quantum version of a given problem in the classical information science, he often discuss it with believing that there uniquely exists the quantum extension. Hence, if another person considers a different quantum extension, their argument mismatches each other.
- 2.
In this case, it is required that it is easy only to convert the cipher text from the plain text, and it is not easy to convert the plain text from the cipher text. Furthermore, in order that only the authorized receiver can decrypt the cipher text, it is also required that an additional information kept only by the authorized receiver enables to convert the plain text from the cipher text.
- 3.
A mathematical foundation of statistical mechanics has a similar mathematical formulation. This direction has generated an important area of mathematics “operator algebra” and has contributed many results useful for quantum information science. However, statistical mechanics is different from quantum information science in that statistical mechanics uses a density operator as an ensemble of many particles while quantum information science uses it as a state of one particle.
- 4.
The information spectrum is a unified method in information theory proposed by Han-Verdú in 1993 [3], in which, the asymptotic optimal performance can be characterized by the likelihood ratio. This conjecture has been proposed by Nagaoka [4] in 1999, and is called Nagaoka’s dream. After his proposal, many topics has been characterized in the relation with the hypothesis testing, e.g., quantum channel coding, quantum source coding, entanglement concentration, entanglement dilution, channel resolvability, wire-tap channel coding, and reverse Shannon theorem.
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Hayashi, M., Ishizaka, S., Kawachi, A., Kimura, G., Ogawa, T. (2015). Invitation to Quantum Information Science. In: Introduction to Quantum Information Science. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43502-1_1
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DOI: https://doi.org/10.1007/978-3-662-43502-1_1
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