Construction of quantum caps in projective space PG(r, 4) and quantum codes of distance 4

Ruihu Li, Qiang Fu, Luobin Guo +1 more

Qiang Fu, Ruihu Li, Genqi Xu +1 more

The entanglement-assisted (EA) formalism is a generalization of the standard stabilizer formalism, and it can transform classical linear quaternary codes into entanglement-assisted quantum error correcting codes (EAQECCs) by using of shared entangled qubits between the sender and the receiver.In this work, we give elementary recursive constructions of special quaternary codes of length n and dual distance four that constructed from known caps in projective space PG(5,4) and PG(6,4) for all length 6n283.Consequently, good maximal entanglement EAQECCs of minimum distance four for such length n are constructed from the obtained quaternary codes.

Carlos Galindo, Fernando Hernando, Diego Ruano

Qiang Fu, Ruihu Li, Liangdong Lv +1 more

The entanglement-assisted (EA) formalism is a generalization of the standard stabilizer formalism, and it can transform arbitrary quaternary classical linear codes into entanglement-assisted quantum error correcting codes (EAQECCs) by using of shared entanglement between the sender and the receiver. Using a decomposition of the 126-cap in PG(5,4), we firstly constructed LCD n-cap with 6The entanglement-assisted (EA) formalism is a generalization of the standard stabilizer formalism, and it can transform arbitrary quaternary classical linear codes into entanglement-assisted quantum error correcting codes (EAQECCs) by using of shared entanglement between the sender and the receiver. Using a decomposition of the 126-cap in PG(5,4), we firstly constructed LCD n-cap with 6≤n≤120. From these LCD caps, we then derived the related maximal entanglement [[n, n-6,4;6]] EAQECCs. Finally, using LCD LCD subcaps of 126-cap obtained, we constructed maximal entanglement EAQECCs with parameters [[n, n-;k,4;k]] for 6≤k≤11.

Michael Hartley Freedman, DAVID A. MEYER

Jian Yuan, Shixin Zhu, Xiaoshan Kai +1 more