Boolean Functions, Projection Operators, and Quantum Error Correcting Codes

Authors:
V. Aggarwal;A. R. Calderbank
Affiliations:
Princeton Univ., Princeton;-
Venue:
IEEE Transactions on Information Theory
Year:
2008

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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.