Quantum Dimension as Entanglement Entropy in 2D CFTs
  We study entanglement entropy of excited states in two dimensional conformal field theories (CFTs). Especially we consider excited states obtained by acting primary operators on a vacuum. We show that under its time evolution, entanglement entropy increases by a finite constant when the causality condition is satisfied. Moreover, in rational CFTs, we prove that this increased amount of (both Renyi and von-Neumann) entanglement entropy always coincides with the log of quantum dimension of the primary operator. 
Song He, Tokiro Numasawa, Tadashi Takayanagi and Kento Watanabe
hep-th cond-mat.str-el quant-ph