Location of quantum information in additive graph codes
arXiv:0912.2017 · doi:10.1103/PhysRevA.81.032326
Abstract
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.
Comments are welcome. 17 pages with 4 figures
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- On the equivalence between sharing quantum and classical secrets, and error correction
- A linearized stabilizer formalism for systems of finite dimension
- Tripartite Entanglement in Qudit Stabilizer States and Application in Quantum Error Correction
- Generalized Graph States Based on Hadamard Matrices
- Parafermion stabilizer codes
- Construction of Equientangled Bases in Arbitrary Dimensions via Quadratic Gauss Sums and Graph States
- Entanglement Sharing Protocol via Quantum Error Correcting Codes
- Access structure in graphs in high dimension and application to secret sharing
- Separable Operations, Graph Codes and the Location of Quantum Information