Partial Trace of Hypergraph States

Hypergraph states are generalizations of graph states, which are known resources for models of quantum computation and error correction. We have shown that partial tracing over single qubit subsystems of hypergraph states results in the equal mixture of smaller hypergraph states, that is, of their density matrices. We have also described all possible hypergraphs that could share the same reduced density matrices that are smaller by one qubit. Comparing reduced density matrices of different quantum systems can show if they share entanglement properties.