Gapped two-dimensional topological phases can feature ungappable edge states which are robust even in the absence of protecting symmetries. In this Letter we argue that a multipartite entanglement measure recently proposed in the context of holography, the Markov gap, provides a universal diagnostic of ungappable edge states. Defined as a difference of the reflected entropy and mutual information $h\left(A\text{:}B\right)=S_R\left(A\text{:}B\right)-I\left(A\text{:}B\right)$ between two parties, we argue that for $A,B$ being adjacent subregions in the bulk $h=\frac{c_{+}}{3}ln2$, where $c_{+}$ is the minimal total central charge of the boundary theory. As evidence, we prove that $h=0$ for string-net models and numerically verify that $h=\frac{\left|C\right|}{3}ln2$ for a Chern-$C$ insulator. Our Letter establishes a unique bulk entanglement criteria for the presence of a conformal field theory on the boundary.

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• Entanglement measures
• Quantum entanglement
• Topological phase transition
• Topological phases of matter
• Conformal field theory