Rényi Generalizations of the Operational Entanglement Entropy

Entanglement in bipartite systems of indistinguishable particles could be reduced due to restrictions on the allowed local operations such as particle number conservation. In order to quantify such effects, Wiseman and Vaccaro [Phys. Rev. Lett. 91, 097902 (2003)] introduced an operational measure of the von Neumann entanglement entropy. Motivated by the difficulty of computing von Neumann entropies in quantum many-body systems, we introduce a Rényi generalization of the operational entanglement that is computationally and, potentially, experimentally accessible. Using the Widom conjecture, we investigate its scaling for free fermions in any dimension with the partition size and find that it has a logarithmically violated area law scaling, similar to the corresponding spatial entanglement, with at most, a double-log leading-order correction. By employing the correlation matrix method, we illustrate our theoretical findings in systems of up to 10⁵ particles.