Minimal-Entanglement Entanglement-Assisted Quantum Error Correction Codes from Modified Circulant Matrices

Duc Manh Nguyen, Sunghwan Kim
2017 Symmetry  
In this paper, new construction methods of entanglement-assisted quantum error correction code (EAQECC) from circulant matrices are proposed. We first construct the matrices from two vectors of constraint size, and determine the isotropic subgroup. Then, we also propose a method for calculation of the entanglement subgroup based on standard forms of binary matrices to satisfy the constraint conditions of EAQECC. With isotropic and entanglement subgroups, we determine all the parameters and the
more » ... inimum distance of the EAQECC. The proposed EAQECC with small lengths are presented to explain the practicality of this construction of EAQECC. Comparison with some earlier constructions of EAQECC shows that the proposed EAQECC is better.
doi:10.3390/sym9070122 fatcat:augbjgcms5ekngrngmdtu4pvgi