Generalized concentratable entanglement via parallelized permutation tests

Multipartite entanglement is an essential resource for quantum information theory and technologies, but its quantification has been a persistent challenge. Concentratable entanglement (CE), introduced recently, can be estimated from just two copies of a quantum state. Here, we propose generalized concentratable entanglement (GCE), a broader class of multipartite entanglement measures naturally tied to quantum Tsallis entropies, and present a parallelized protocol for estimating GCE across multiple state copies. Increasing the number of copies yields an improved error bound in the presence of imperfections. We prove that GCE is a well-defined entanglement monotone and conjecture some new entropic inequalities. Moreover, we demonstrate the concentration of entanglement into <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>W</a:mi></a:math> states using three-state copies. Our results contribute to more robust and versatile characterizations of multipartite entanglement.