R\'enyi generalization of the operational entanglement entropy

TL;DR

This paper generalizes the operational entanglement entropy using Rényi entropies, providing a computationally feasible way to measure entanglement in many-body systems with conservation laws, and studies its scaling behavior.

Contribution

It introduces a Rényi-based generalization of operational entanglement entropy that is accessible experimentally and computationally, extending previous measures to more practical scenarios.

Findings

Rényi operational entanglement entropy exhibits logarithmic violation of the area law.

Scaling analysis confirms double-logarithmic correction in free fermion systems.

Modified correlation matrix method supports findings up to 10^5 particles.

Abstract

Operationally accessible entanglement in bipartite systems of indistinguishable particles could be reduced due to restrictions on the allowed local operations as a result of particle number conservation. In order to quantify this effect, Wiseman and Vaccaro [Phys. Rev. Lett. 91, 097902 (2003)] introduced an operational measure of the von Neumann entanglement entropy. Motivated by advances in measuring R\'enyi entropies in quantum many-body systems subject to conservation laws, we derive a generalization of the operational entanglement that is both computationally and experimentally accessible. Using the Widom theorem, we investigate its scaling with the size of a spatial subregion for free fermions and find a logarithmically violated area law scaling, similar to the spatial entanglement entropy, with at most, a double-log leading-order correction. A modification of the correlation matrix method confirms our findings in systems of up to $10^5$ particles.