New holographic generalization of entanglement entropy

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

Automated summary

A new quantity called pseudo-entropy is introduced in this paper as a generalization of entanglement entropy via postselection, with potential applications as order parameters in quantum many-body systems. The geometric computation of pseudo-entropy in the AdS/CFT correspondence is explored, along with its properties and classifications in qubit systems. Additionally, the quantum information theoretic meaning of pseudo-entropy in specific examples is discussed, as well as its calculation in various scenarios including the presence of local operator excitations in different CFT models.