Topological correlation in anyonic states constrained by anyonic superselection rules

An anyonic system not only has potential applications in the construction of topological quantum computers but also presents a unique property known as topological entanglement entropy (TEE) in quantum many-body systems. Recently, Bonderson et al. [Ann. Phys. (NY) 385, 399 (2017)] have formally defined the entropy of anyonic charge entanglement (ACE) in anyonic states that has been shown to be able to derive TEE. We give it operational meaning from the perspective of quantum information theory. Specifically, for an anyonic bipartite system, we define an operational measure of topological correlation based on the principle of maximum entropy, where the topological correlation is the information that cannot be accessed by local operations constrained by anyonic superselection rules (SSRs) and classical communication. For a given anyonic bipartite state with maximal rank, we prove that its topological correlation is equal to its entropy of ACE. This measure can be extended to measure nonlocal resources of other compound quantum systems in the presence of SSRs and can provide a more refined classification of correlations in a multipartite system with SSRs.