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Boolean Functions, Projection Operators, and Quantum Error Correcting Codes

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2 Author(s)
Aggarwal, V. ; Princeton Univ., Princeton ; Calderbank, A.R.

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.

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Information Theory, IEEE Transactions on  (Volume:54 ,  Issue: 4 )