Tripartite entanglement decompositions for tensor networks

The candidate will consider the problem of efficiently decomposing a tripartite tensor into a small tensor network (3-6), with three tensors and six total links (three external, three internal). In the information perspective, an efficient decomposition is such that each correlation between the three parties takes the shortest route along the (3-6) network. The candidate will develop numerical algorithms to acquire such efficient tripartite decomposition, which in turn will play the role of a key component when designing and running algorithms for loopy tensor networks. Finding the most efficient decomposition translates into an optimization problem, which can be tackled by the candidate both with direct search strategies as well as machine learning strategies.