Parameterized genuine multipartite entanglement measure based on \(\alpha\)-concurrence

Entanglement is a crucial resource for various applications in quantum information processing. We propose a parameterized genuine multipartite entanglement measure based on \(\alpha\)-concurrence termed \(\alpha\)-\(\text {GME}\), which applies to n-partite quantum systems. Our measure identifies GHZ states as being more entangled than W states, an essential distinction in the study of quantum entanglement. By employing positive partial transposition and realignment criteria, we derive analytical lower bounds for the \(\alpha\)-\(\text {GME}\). Furthermore, the measure is shown to be inequivalent under entanglement ordering comparison, indicating that it captures different aspects of entanglement compared to existing measures. Through detailed examples, we demonstrate that our measure provides a more refined detection of multipartite entanglement, particularly in distinguishing between different entangled states. This makes our proposed measure a valuable tool for characterizing and quantifying entanglement in quantum systems.