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

Abstract

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. In case of a successful detection of the desired property, the method outputs a linear witness which admits an exact tensor network representation, composed of connectors. We demonstrate the power of our method by certifying using a normal desktop computer entanglement, Bell nonlocality and supra-quantum Bell nonlocality in systems with hundreds of sites.