The paper by Michael Levin and Xiao-Gang Wen introduces a method to detect topological order in a ground state wave function using the concept of "topological entropy." The authors focus on $(2+1)$-dimensional systems and show that the quantum dimension $D$ of the wave function can be determined by computing the entanglement entropy of specific regions in the plane. They define the topological entropy as $(S_1 - S_2) - (S_3 - S_4)$, where $S_1, S_2, S_3, S_4$ are the entropies of four chosen regions. This quantity is shown to be equal to $-\log(D^2)$, providing a universal measure of topological order. The method is demonstrated through an example of the $Z_2$ model and generalized to string-net models, which describe a wide class of topological orders. The paper highlights the importance of nonlocal correlations in topological states and suggests that this approach can be used to classify and test topological phases in various wave functions.The paper by Michael Levin and Xiao-Gang Wen introduces a method to detect topological order in a ground state wave function using the concept of "topological entropy." The authors focus on $(2+1)$-dimensional systems and show that the quantum dimension $D$ of the wave function can be determined by computing the entanglement entropy of specific regions in the plane. They define the topological entropy as $(S_1 - S_2) - (S_3 - S_4)$, where $S_1, S_2, S_3, S_4$ are the entropies of four chosen regions. This quantity is shown to be equal to $-\log(D^2)$, providing a universal measure of topological order. The method is demonstrated through an example of the $Z_2$ model and generalized to string-net models, which describe a wide class of topological orders. The paper highlights the importance of nonlocal correlations in topological states and suggests that this approach can be used to classify and test topological phases in various wave functions.