Timelike Entanglement Entropy

Motivated by the geometrical understanding of quantum information measures in AdS/CFT, I will introduce a two-state generalization of von Neumann entropy known as pseudo-entanglement entropy as well as a novel quantity corresponding to timelike regions on the CFT side which we call “timelike entanglement entropy” (TEE). It turns out that TEE is a special case of pseudo-entanglement entropy. Concrete definitions on the CFT side together with a prescription to calculate TEE in $2d$ free quantum field theories will be introduced, which contains some clues about how to understand TEE in quantum information theory. I will also introduce our first version of a holographic prescription to calculate TEE in AdS$_3$/CFT$_2$ and address how TEE in AdS$_3$/CFT$_2$ is related to EE in dS$_3$/CFT$_2$.