Topological Pseudo Entropy

Recently, a new quantum information measure called pseudo entropy was introduced as a generalization of entanglement entropy to quantify quantum correlation between initial and final states in a time-dependent system. In this talk, I will examine some aspects of pseudo entropy in topological field theory and conformal field theory (CFT). In three-dimensional Chern-Simons theory, pseudo entropy can be given by a partition function on a three-sphere with Wilson loops in a similar manner to topological entanglement entropy. I will also show that the pseudo entropy in a certain setup is equivalent to the interface entropy in two-dimensional CFTs, and leverage the equivalence to calculate the pseudo entropies in particular examples. Furthermore, I will define a pseudo entropy extension of the left-right entanglement entropy in two-dimensional boundary CFTs and derive a universal formula for a pair of arbitrary boundary states.



Yukawa Institute for Theoretical Physics, Kyoto University