# IQIM Postdoctoral and Graduate Student Seminar

*,*Postdoctoral Scholar

*,*University of Innsbruck and IQOQI

*,*

**Abstract:** Entanglement is the distinguishing feature of quantum many-body systems, and ``learning'' the entanglement structure of the many-particle wavefunction is a fundamental challenge in quantum information science.

In this talk, I will discuss protocols that achieve this task in quantum simulation experiments via efficient learning of the Entanglement Hamiltonian (EH). This approach is enabled by a quasi-local operator structure of the EH, as suggested by the Bisognano-Wichmann (BW) theorem. I will report recent experiments with a trapped ion quantum simulator, where the EH of a variationally prepared ground state has been measured, providing the first experimental demonstration of the BW theorem. From the learned EH we extract the entanglement entropy and observe a cross-over to ``thermal'' volume-law behaviour when adding excitations to the ground state.

As another application of our protocols, I will discuss how to identify topological states by inspecting the eigenvalues of the EH, i.e. the entanglement spectrum (ES). This identification is based on the one-to-one correspondence between low-lying levels of the ES and the structure of physical edge excitations according to the Li-Haldane (LH) conjecture. For the example of an integer quantum Hall state, I will illustrate explicitly how the LH conjecture can be probed in cold-atom quantum simulation experiments.

**Lunch** will be provided, following the talk, on the lawn outside the Bridge arcade.

Attendees joining in person must demonstrate that they comply with Caltech's vaccination requirements (present Caltech ID or AWS ID or vaccination and booster confirmation).

Amid the recent increase in COVID-19 cases on campus due to the arrival of the highly infectious BA.2 subvariant in Los Angeles County and a return to routine social activities, the Institute has reinstated its requirement that high-quality masks (surgical, N95s, KN95s, or KF95s) must be worn in all indoor locations on campus.