The resource theory of tensor networks

Understand

Tensor networks provide succinct representations of quantum many-body states and are an important computational tool for strongly correlated quantum systems.

• Their expressive and computational power is characterized by an underlying entanglement structure, on a lattice or more generally a (hyper)graph, with virtual entangled pairs or multipartite entangled states associated to (hyper)edges.
• Changing this underlying entanglement structure into another can lead to both theoretical and computational benefits.
• We study a natural resource theory which generalizes the notion of bond dimension to entanglement structures using multipartite entanglement.