Extend the source-transfer characterization beyond tree networks

Extend the source-transfer and mixed-model characterization of quantum correlations from finite source-party trees to general quantum networks containing cycles, including the triangle network, while preserving source independence despite connections between branches through the rest of the network.

Background

The paper proves that the source-transfer model is equivalent to the mixed quantum model for every quantum tree network and uses this equivalence to establish complete semidefinite-programming hierarchies. The reconstruction relies on the fact that branches below distinct child sources are disjoint and therefore carry product source states.

For networks with cycles, such as the quantum triangle, branches below different sources can remain connected through other parties and sources. Consequently, the product-state replacer structure used in the tree reconstruction is unavailable, and a more general method is needed to preserve source independence while accounting for these connections.