TY - JOUR
T1 - Entanglement-assisted quantum codes from algebraic geometry codes
AU - Fernandes Pereira, Francisco
AU - Pellikaan, Ruud
AU - Gadioli La Guardia, Giuliano
AU - de Assis, Francisco Marcos
PY - 2019
Y1 - 2019
N2 - Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a way for quantum error correcting codes to achieve higher rates than the one obtained via traditional stabilizer formalism. Such codes are called entanglement-assisted quantum (QUENTA) codes. In this paper, we use algebraic geometry codes to construct several families of QUENTA codes via Euclidean and Hermitian construction. Two of the families created has maximal entanglement and have quantum Singleton defect equal to zero or one. Comparing the other families with the codes with the respective quantum Gilbert-Varshamov bound, we show that our codes have a rate that surpasses such bound. In the end, asymptotically good tower of linear complementary dual codes is used to obtain an asymptotically good family of maximal entanglement QUENTA codes with nonzero rate, relative minimal distance, and relative entanglement. Furthermore, a simple comparison with the quantum Gilbert-Varshamov bound demonstrates that from our construction it is possible to create an asymptotically family of QUENTA codes that exceed such this bound.
AB - Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a way for quantum error correcting codes to achieve higher rates than the one obtained via traditional stabilizer formalism. Such codes are called entanglement-assisted quantum (QUENTA) codes. In this paper, we use algebraic geometry codes to construct several families of QUENTA codes via Euclidean and Hermitian construction. Two of the families created has maximal entanglement and have quantum Singleton defect equal to zero or one. Comparing the other families with the codes with the respective quantum Gilbert-Varshamov bound, we show that our codes have a rate that surpasses such bound. In the end, asymptotically good tower of linear complementary dual codes is used to obtain an asymptotically good family of maximal entanglement QUENTA codes with nonzero rate, relative minimal distance, and relative entanglement. Furthermore, a simple comparison with the quantum Gilbert-Varshamov bound demonstrates that from our construction it is possible to create an asymptotically family of QUENTA codes that exceed such this bound.
M3 - Article
SN - 2331-8422
JO - arXiv
JF - arXiv
M1 - 1907.06357v1
ER -