Boolean Functions, Projection Operators, and Quantum Error Correcting Codes

Author

Aggarwal, Vaneet ; Calderbank, A. Robert

Author_Institution

Princeton Univ., Princeton

Volume

54

Issue

4

fYear

2008

fDate

4/1/2008 12:00:00 AM

Firstpage

1700

Lastpage

1707

Abstract

This paper describes a fundamental correspondence between Boolean functions and projection operators in Hilbert space. The correspondence is widely applicable, and it is used in this paper to provide a common mathematical framework for the design of both additive and nonadditive quantum error correcting codes. The new framework leads to the construction of a variety of codes including an infinite class of codes that extend the original ((5, 6, 2)) code found by Rains It also extends to operator quantum error correcting codes.

Keywords

Boolean functions; Hilbert spaces; error correction codes; Boolean functions; Hilbert space; additive quantum error correcting codes; common mathematical framework; nonadditive quantum error correcting codes; projection operators; Additives; Binary codes; Boolean functions; Error correction; Error correction codes; Helium; Hilbert space; Information theory; Rain; Sufficient conditions; Additive and nonadditive quantum codes; Boolean functions; operator quantum error correction; projection operators in Hilbert space; quantum error correction;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2008.917720

Filename

4475353