We discuss quantum two-block codes, a large class of CSS codes constructed from two commuting square matrices. Interesting families of such codes are generalized-bicycle (GB) codes and two-block group-algebra (2BGA) codes, where a cyclic group is replaced with an arbitrary finite group, generally non-abelian. We present code construction and give several expressions for code dimension, applicable depending on whether the constituent group is cyclic, abelian, or non-abelian. This gives a simple criterion for an essentially non-abelian 2BGA code guaranteed not to be permutation-equivalent to such a code based on an abelian group. We also give a lower bound on the distance which, in particular, applies to the case when a 2BGA code reduces to a hypergraph-product code constructed from a pair of classical group codes.We discuss quantum two-block codes, a large class of CSS codes constructed from two commuting square matrices. Interesting families of such codes are generalized-bicycle (GB) codes and two-block group-algebra (2BGA) codes, where a cyclic group is replaced with an arbitrary finite group, generally non-abelian. We present code construction and give several expressions for code dimension, applicable depending on whether the constituent group is cyclic, abelian, or non-abelian. This gives a simple criterion for an essentially non-abelian 2BGA code guaranteed not to be permutation-equivalent to such a code based on an abelian group. We also give a lower bound on the distance which, in particular, applies to the case when a 2BGA code reduces to a hypergraph-product code constructed from a pair of classical group codes.

arXiv:2305.06890International Symposium on Turbo Codes and Iterative Information ProcessingSep 4, 20236 citations

On the Wehrl entropy lower bound for a locally compact abelian group

Evgenii Igorevich Zelenov

A Wehrl entropy construction is proposed for an arbitrary locally compact abelian group $G$ . It is proved that the Wehrl entropy is not less than a non-negative integer, which is an invariant of the group $G$ . The minimum of the Wehrl entropy is achieved on coherent states.A Wehrl entropy construction is proposed for an arbitrary locally compact abelian group $G$. It is proved that the Wehrl entropy is not less than a non-negative integer, which is an invariant of the group $G$. The minimum of the Wehrl entropy is achieved on coherent states.

arXiv:2306.15357Jun 27, 20231 citation

A Wehrl entropy construction is proposed for an arbitrary locally compact abelian group

G

. It is proved that the Wehrl entropy is not less than a non-negative integer, which is an invariant of the group

G

. The minimum of the Wehrl entropy is achieved on coherent states.