Topical Seminar: Characterizing high-dimensional multipartite entanglement through nonlinear criteria

por Shuheng Liu (IQOQI Vienna)

lunes 17 nov. 2025 11:30 → 12:30 Europe/Madrid

4-4-4426 - Seminari Física Teòrica (Campus Burjassot)

Abstract: High-dimensional multipartite entanglement is both a powerful resource and a barrier to simulation. Therefore, much effort has been devoted to developing practical criteria for certifying the entanglement structure and thus characterizing a system's capability for quantum tasks such as quantum communication and computation. We first introduce a generalized covariance matrix (CM) criterion that determines the Schmidt number, which characterizes entanglement dimensionality in discrete-variable (DV) bipartite systems. >From it we derive simpler, experimentally feasible corollaries that use information comparable to fidelity-based witnesses yet identify a broader set of entangled states. Related results on the quantum Fisher information matrix, which can be viewed as a convex generalized covariance matrix, demonstrate that larger Schmidt numbers enable higher precision limits in multiparameter estimation. When dealing with unknown rotations of the reference frame, we provide a reference-frame–independent inequality that distinguishes Schmidt numbers using moments of randomized correlations. In particular, we give analytic boundary curves using second- and fourth-order moments. We test this method experimentally and certify three-dimensional entanglement in a five-dimensional two-photon state under random phase noise. For systems with more than two parties, our nonlinear generalization shows both how many parties are entangled and their entanglement dimensionality, where genuine multipartite entanglement (GME) is a special case. This criterion outperforms existing ones on many example states. Finally, we adapt our approach to continuous-variable (CV) platforms, enabling Schmidt-number detection without discretization directly from characteristic or Wigner function measurements. These measurements work well with trapped ions and atoms, and circuit quantum electrodynamics/acoustodynamics. Using these measurements, our recent result further shows that the negativity of the Wigner function is closely connected to GME.