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Boolean Functions, Projection Operators and Quantum Error Correcting Codes

Vaneet Aggarwal·A. Robert Calderbank
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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 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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BibTeXRIS

Vaneet Aggarwal, A. Robert Calderbank. 2007-09-24. Boolean Functions, Projection Operators and Quantum Error Correcting Codes. https://doi.org/10.1109/tit.2008.917720

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