  Multipartite entanglement is an essential resource for quantum information
theory and technologies, but its quantification has been a persistent
challenge. Recently, Concentratable Entanglement (CE) has been introduced as a
promising candidate for a multipartite entanglement measure, which can be
efficiently estimated across two state copies. In this work, we introduce
Generalized Concentratable Entanglement (GCE) measures, highlight a natural
correspondence to quantum Tsallis entropies, and conjecture a new entropic
inequality that may be of independent interest. We show how to efficiently
measure the GCE in a quantum computer, using parallelized permutation tests
across a prime number of state copies. We exemplify the practicality of such
computation for probabilistic entanglement concentration into W states with
three state copies. Moreover, we show that an increased number of state copies
provides an improved error bound on this family of multipartite entanglement
measures in the presence of imperfections. Finally, we prove that GCE is still
a well-defined entanglement monotone as its value, on average, does not
increase under local operations and classical communication (LOCC).
