Abstract
The paper analyzes the basic principles of stabilizer codes, focusing on how to construct stabilizer codes for achieving the continuous-variable quantum error correction. Stabilizer codes can be used in the reconciliation of continuous-variable quantum key distribution system. The construction method of stabilizer codes is very important and it can be turned into finding the check matrix for stabilizer codes. In this paper, a new algorithm called region elimination algorithm for finding the check matrix of stabilizer codes was presented which can seek the voluntary check matrix for continuous-variable stabilizer codes within 8 bit code length quickly and effectively, and it was simulated by Visual C++. The algorithm is mainly realized by initializing search region, reducing the search region and then keeping searching till finding all the commuting generators. The finding of check matrix of stabilizer codes lays important foundations for the further development of stabilizer codes in the continuous-variable quantum key distribution.
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Supported by the Science and Technology Foundation of the Education Department of Fujian Province (No. JA08001).
Communication author: Huang Chunhui, born in 1959, male, Ph.D., Professor.
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Lin, L., Huang, C. The construction method of stabilizer codes for continuous variables. J. Electron.(China) 28, 370–374 (2011). https://doi.org/10.1007/s11767-011-0580-2
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DOI: https://doi.org/10.1007/s11767-011-0580-2