Entanglement in tripartitions of topological orders: a diagrammatic approach

Abstract

Recent studies have demonstrated that measures of tripartite entanglement can probe data characterizing topologically ordered phases to which bipartite entanglement is insensitive. Motivated by these observations, we compute the reflected entropy and logarithmic negativity, a mixed state entanglement measure, in tripartitions of bosonic topological orders using the anyon diagrammatic formalism. We consider tripartitions in which three subregions meet at trijunctions and tetrajunctions. In the former case, we find a contribution to the negativity which distinguishes between Abelian and non-Abelian order while in the latter, we find a distinct universal contribution to the reflected entropy. Finally, we demonstrate that the negativity and reflected entropy are sensitive to the $F$-symbols for configurations in which we insert an anyon trimer, for which the Markov gap, defined as the difference between the reflected entropy and mutual information, is also found to be non-vanishing.

v2: updated references; v3: updated references, corrected typos and notation

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Cited by in corpus (8)

• A Noisy Approach to Intrinsically Mixed-State Topological Order
• Multipartite entanglement in two-dimensional chiral topological liquids
• Multi wavefunction overlap and multi entropy for topological ground states in (2+1) dimensions
• Mixed-State Entanglement Measures in Topological Order
• Anyon Quantum Dimensions from an Arbitrary Ground State Wave Function
• Finite-Entanglement Scaling of 2D Metals
• Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
• Topological entanglement entropy for torus knot bipartitions and the Verlinde-like formulas