New holographic generalization of entanglement entropy

We introduce a new quantity, called pseudo-entropy, as generalization of entanglement entropy via postselection. expect this quantity to provide class order parameters in quantum many-body systems. In the anti--de Sitter space (AdS)/conformal field theory (CFT) correspondence, is dual areas minimal area surfaces time-dependent Euclidean spaces which are asymptotically AdS. call geometric computation pseudo-entropy $\mathrm{AdS}/\mathrm{CFT}$ holographic pseudo-entropy. study its basic properties and classifications qubit specific examples, we information theoretic meaning an averaged number Bell pairs when post-selection performed. also present for random states. then calculate presence local operator excitations both two dimensional free massless scalar CFT CFTs. find general property CFTs that highly reduced operators get closer boundary subsystem. compute Janus solution, exactly marginal perturbation agreement with perturbative calculation CFT. show linearity holds states, where coincides weak value operator. Finally, propose mixed state give gravity dual.