The experimental characterization and quantification of entanglement properties, and the entanglement spectrum in particular, play a major role in our understanding of modern quantum many body physics in the lab. In this talk, I will present recent results in which we determine the entanglement Hamiltonian for sub-systems of quantum-many body states, which we prepared on an ion-trap quantum simulator with up to 51 ions using variational quantum algorithms. In these experiments, we verify for the first time the prediction of Bisognano and Wichmann that the reduced density matrix is described by a local Hamiltonian density with a local inverse temperature as a signature of entanglement. As I will demonstrate, the geometrically local structure of the Entanglement Hamiltonian allows for learning it’s structure efficiently, with a number of samples that scales only polynomially in the system size. As an outlook, I will describe quantum protocols that can be used to investigate important properties of the Entanglement Hamiltonian directly on the quantum device, without the need of computationally expensive classical post-processing steps.
Host: Walter Goldberger (walter.goldberger@yale.edu)