Timelike entanglement entropy Revisited

Abstract

We present an operator-algebraic definition for timelike entanglement entropy in QFT under a few mild postulates. This rigorously defined timelike entanglement entropy is real-valued due to the timelike tube theorem. We further demonstrate why the timelike entanglement entropy should be real-valued from both path integral argument and holography perspective.

V4: Match the published version. Substantially improved, especially in Sec III, the arguments about the real-valueness from path integral and holography perspective. 7 pages, 4 figures