Connector tensor networks: a renormalization-type approach to quantum certification

Understand

As quantum technologies develop, we acquire control of an ever-growing number of quantum systems.

• Unfortunately, current tools to detect relevant quantum properties of quantum states, such as entanglement and Bell nonlocality, suffer from severe scalability issues and can only be computed for systems of a very modest size, of around $6$ sites.
• In order to address large many-body systems, we propose a renormalisation-type approach based on a class of local linear transformations, called connectors, which can be used to coarse-grain the system in a way that preserves the property under investigation.
• Repeated coarse-graining produces a system of manageable size, whose properties can then be explored by means of usual techniques for small systems.