Timelike entanglement entropy

Understand

We define a new complex-valued measure of information called the timelike entanglement entropy (EE) which in the boundary theory can be viewed as a Wick rotation that changes a spacelike boundary subregion to a timelike one.

• An explicit definition of the timelike EE in 2d field theories is provided followed by numerical computations which agree with the analytic continuation of the replica method for CFTs.
• We argue that timelike EE should be correctly interpreted as another measure previously considered, the pseudo entropy, which is the von Neumann entropy of a reduced transition matrix.
• Our results strongly imply that the imaginary part of the pseudo entropy describes an emergent time which generalizes the notion of an emergent space from quantum entanglement.