Oral: Detecting Entanglement with Transport Measurement in Weak-interacting Multi-terminal Island Systems

Entanglement plays a fundamental role in understanding quantum correlations in many-body systems. In this work, we explore how multipartite entanglement in weakly interacting multiterminal island systems can be detected through measurable quantities such as nonlocal conductance. By relating von Neumann entropy and mutual information to transport properties, we provide a practical approach to studying entanglement in complex systems. Using the topological Kondo effect as a case study, we show that the mutual information production is closely tied to the system's isolation from external environments, providing insights into the quantum nature of multiterminal devices. Our results offer a novel method for probing entanglement in condensed matter systems using conventional transport measurements.