Holographic entanglement, pseudo-entropy and wormholes

The idea of holographic duality in string theory provides a simple geometric computation of entanglement entropy. This generalizes the celebrated Bekenstein–Hawking formula of black hole entropy and strongly suggests that a gravitational space–time consists of many qubits with quantum entanglement. Recently, a new extension of entanglement entropy, called pseudo-entropy, which depends on both an initial and a final state, was introduced. This quantity turned out to have a clear geometric dual via the holography and also plays a role of a new order parameter of quantum phases. In this paper, we would like to point out that pseudo-entropy becomes a useful probe in traversable wormhole geometries, where non-Hermitian density matrices naturally appear in their CFT duals following the paper in Ref. 1 .