Boolean Functions, Projection Operators and Quantum Error Correcting Codes
<|reference_start|>Boolean Functions, Projection Operators and Quantum Error Correcting Codes: 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.<|reference_end|>
@article{aggarwal2006boolean,
    title={Boolean Functions, Projection Operators and Quantum Error Correcting
  Codes},
    author={Vaneet Aggarwal, A. Robert Calderbank},
    journal={IEEE Trans. Inf. Theory, vol. 54, no. 4, pp.1700-1707, Apr. 2008.},
    year={2006},
    doi={10.1109/TIT.2008.917720},
    archivePrefix={arXiv},
    eprint={cs/0610159},
    primaryClass={cs.IT math.IT quant-ph}
}