Tight and Self-Testing Multipartite Quantum Bell Inequalities from the Renormalization Group

Attempts to understand multipartite quantum nonlocality are thwarted by the difficulty of devising quantum Bell inequalities (QBI) for systems composed of more than a few separate parties. In this Letter, we introduce the notion of tight connectors, a class of tensors which, if contracted according to some simple rules, result in tight QBIs. The new inequalities are saturated by tensor network states whose structure mimics the corresponding network of connectors. We further formulate the connector property of "full self-testing," which singles out a subset of tight connectors whose associated QBIs can only be saturated (modulo local isometries) by probing the corresponding tensor network state with specific measurement operators. We provide large analytic families of tight, full self-testing connectors that allow for the generation, via contraction, of N-partite QBIs with a ratio between the maximum quantum and classical values that grows exponentially with N. In turn, our method provides a modular recipe for the generation of extremal quantum behaviors and associated tight bounds in arbitrarily large systems.