Symplectically entangled states and their applications to coding
Apostol Vourdas · Journal of Physics A Mathematical and General · 2004
An angular momentum (2 j + 1)-dimensional Hilbert space H is considered. Symplectic transformations S on the tensor product of N of these spaces H ⊗ ⋅⋅⋅ ⊗ H are studied for the case when the 2 j + 1 is a power of a prime (Galois case). The corresponding operators are calculated numerically. The formalism is applied to quantum coding. A simple repetition code based on the space H A spanned by the direct products of N angular momentum states with the same m , has distance 1. It is shown that a code based on the symplectically transformed space SH A has (in general) larger distance. An example with three qutrits is discussed in detail.