Timelike entanglement entropy

A bstract We define a new complex-valued measure of information called the timelike entanglement entropy (EE) which in boundary theory can be viewed as Wick rotation that changes spacelike subregion to one. An explicit definition EE 2d field theories is provided followed by numerical computations agree with analytic continuation replica method for CFTs. argue should correctly interpreted another previously considered, pseudo entropy, von Neumann reduced transition matrix. Our results strongly imply imaginary part describes an emergent time generalizes notion space from quantum entanglement. For holographic systems we total complex valued area particular stationary combination both and extremal surfaces are homologous region. examples considered find matching our optimization procedure careful implementation CFT. also make progress on higher dimensional generalizations relations de Sitter space.