Boolean Functions, Projection Operators and Quantum Error Correcting Codes

Details Boolean Functions, Projection Operators and Quantum Error Correcting Codes Boolean Functions, Projection Operators and Quantum Error Correcting Codes

2006-10-27

arxiv.org/abs/cs/0610159v3

IEEE Trans. Inf. Theory, vol. 54, no. 4, pp.1700-1707, Apr. 2008.

Computer Science

Information Theory

Submitted to IEEE Transactions on Information Theory, October 2006, to appear in IEEE Transactions on Information Theory, 2008

Scientific paper

10.1109/TIT.2008.917720

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 non-additive 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 [21]. It also extends to operator quantum error correcting codes.

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