Measuring Entanglement by Exploiting its Anti-symmetric Nature

Despite notable advancements in experimental quantum science, measuring entanglement entropy continues to pose challenges. By adopting a new geometric perspective, we uncover the intrinsic anti-symmetric nature of entanglement. We show that various entanglement measures, such as von Neumann and Rényi entropies, can be uniquely expressed through exterior products and, thus, fundamentally anti-symmetric products. Furthermore, we show that this anti-symmetric characterization of entanglement can be directly linked to bosonic and fermionic particle symmetries. This relationship enables the experimental measurement of anti-symmetries via many-body interference. Focusing solely on these identified anti-symmetries, we introduce a resource-efficient approach for measuring bipartite entanglement across diverse quantum simulation platforms.