Extracting the entanglement dimension of cold atom system

The entanglement dimension is an interesting property of condensed matter system, which could contain information about quantum phase transitions. However, it is difficult to observe the entanglement dimension in a real system. Therefore, quantum simulators are used to understand real condensed matter systems. They are simplified systems, which contain the essential physical properties, but are highly tunable and can be read out directly. One such system is a cold atom quantum simulator containing cold atoms in an optical lattice. In this simulator only local observables are directly accessible, but interesting properties, like the entanglement dimension, are non-local.
Therefore, this project focuses on finding lower bounds on non-local observables, like the entanglement dimension, in planned cooperation with an experimental group in Munich. The lower bounds are based on information from a new measurement method for local observables.