  Using the concept of non-degenerate Bell inequality, we show that quantum
entanglement, the critical resource for various quantum information processing
tasks, can be quantified for any unknown quantum states in a
semi-device-independent manner, where the quantification is based on the
experimentally obtained probability distribution and beforehand knowledge on
quantum dimension only. Specifically, as an application of our approach on
multi-level systems, we experimentally quantify the entanglement of formation
and the entanglement of distillation for qutrit-qutrit quantum systems. In
addition, to demonstrate our approach for multi-partite systems, we further
quantify the geometry measure of entanglement of three-qubit quantum systems.
Our results supply a general way to reliably quantify entanglement in
multi-level and multi-partite systems, thus paving the way to characterize
many-body quantum systems by quantifying involved entanglement.
