Coding with finite quantum systems.

Abstract

Coding using quantum states in an angular-momentum (2j+1)-dimensional Hilbert space H is considered in this paper. A concatenated code is studied in two steps. In the first step the space HN is considered and the code is its subspace HA spanned by the direct products of N angular-momentum states with the same m. In the second step the space HAM is considered and the code is its subspace HB spanned by the direct products of M angle states with the same m. It is shown that the code introduces redundancy with respect to any transformation.