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Using the concept of non-degenerate Bell inequality, we show that quantumentanglement, the critical resource for various quantum information processingtasks, can be quantified for any unknown quantum states in asemi-device-independent manner, where the quantification is based on theexperimentally obtained probability distribution and beforehand knowledge onquantum dimension only. Specifically, as an application of our approach onmulti-level systems, we experimentally quantify the entanglement of formationand the entanglement of distillation for qutrit-qutrit quantum systems. Inaddition, to demonstrate our approach for multi-partite systems, we furtherquantify the geometry measure of entanglement of three-qubit quantum systems.Our results supply a general way to reliably quantify entanglement inmulti-level and multi-partite systems, thus paving the way to characterizemany-body quantum systems by quantifying involved entanglement.

Experimental Entanglement Quantification for Unknown Quantum States in a Semi-Device-Independent Manner