Quantum birthday problems: geometrical aspects of quantum random coding

Author

Fujiwara, Akio

Author_Institution

Dept. of Math., Osaka Univ., Japan

Volume

47

Issue

6

fYear

2001

fDate

9/1/2001 12:00:00 AM

Firstpage

2644

Lastpage

2649

Abstract

This article explores the asymptotics of randomly generated vectors on extended Hilbert spaces. In particular, we are interested to know how “orthogonal” these vectors are. We investigate two types of asymptotic orthogonality, the weak orthogonality and the strong orthogonality, that are regarded as quantum analogs of the classical birthday problem and its variant. As regards the weak orthogonality, a new characterization of the von Neumann entropy is derived, and a mechanism behind the noiseless quantum channel coding theorem is clarified. As regards the strong orthogonality, on the other hand, a characterization of the quantum Renyl (1965) entropy of degree 2 is derived

Keywords

channel coding; entropy; quantum communication; random codes; asymptotic orthogonality; asymptotics; extended Hilbert spaces; geometrical aspects; noiseless quantum channel coding theorem; orthogonal vectors; quantum Renyl entropy; quantum analogs; quantum birthday problems; quantum random coding; randomly generated vectors; strong orthogonality; von Neumann entropy; weak orthogonality; Channel coding; Density measurement; Entropy; Extraterrestrial measurements; Hilbert space; Information theory; Mathematics; Quantum mechanics; Random variables;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.945283

Filename

945283