Boolean Functions, Projection Operators and Quantum Error Correcting Codes
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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2006
- DOI:
- 10.48550/arXiv.cs/0610159
- arXiv:
- arXiv:cs/0610159
- Bibcode:
- 2006cs.......10159A
- Keywords:
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- Computer Science - Information Theory;
- Quantum Physics
- E-Print:
- Submitted to IEEE Transactions on Information Theory, October 2006, to appear in IEEE Transactions on Information Theory, 2008