Location of quantum information in additive graph codes

Understand

The location of quantum information in various subsets of the qudit carriers of an additive graph code is discussed using a collection of operators on the coding space which form what we call the information group.

• It represents the input information through an encoding operation constructed as an explicit quantum circuit.
• Partial traces of these operators down to a particular subset of carriers provide an isomorphism of a subgroup of the information group, and this gives a precise characterization of what kinds of information they contain.
• All carriers are assumed to have the same dimension D, an arbitrary integer greater than 1.