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Topological correlation: anyonic states cannot be determined by local operations and classical communication. (arXiv:2306.03596v2 [quant-ph] UPDATED)

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Anyonic system not only has potential applications in the construction of
topological quantum computer, but also presents a unique property known as
topological entanglement entropy in quantum many-body systems. How to
understand topological entanglement entropy is one of the most concerned
problems for physicists. For an anyonic bipartite system, we define an
operational measure of topological correlation based on the principle of
maximal entropy, where the topological correlation is the information that
cannot be accessed by local operations constrained by anyonic superselection
rules and classical communication. This measure can be extended to measure
non-local resources of other compound quantum systems in the presence of
superselection rules. For a given anyonic bipartite state with maximal rank, we
prove that its topological correlation is equal to its entropy of anyonic
charge entanglement that has been shown in the literature to be able to derive
topological entanglement entropy. This measure provides a more refined
classification of correlations in a multipartite system with superselection
rules and an illuminating approach to topological phase classification.

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