Temporal Entanglement from Holographic Entanglement Entropy

TL;DR

This paper introduces a systematic method to characterize temporal entanglement in relativistic quantum field theories, extending entanglement entropy concepts into the time domain using holographic duality, and demonstrates its consistency in thermal states.

Contribution

It provides a novel prescription for defining and computing temporal entanglement in quantum field theories, especially within holographic frameworks, by extending spatial entanglement entropy to the time dimension.

Findings

The prescription yields physically consistent measures of temporal entanglement.

Application to holographic CFTs in thermal states confirms the method's validity.

Results are obtained for theories on a 2D Lorentzian cylinder and 3D Minkowski space.

Abstract

Recently, several notions of entanglement in time have emerged as a novel frontier in quantum many-body physics, quantum field theory and gravity. We propose a systematic prescription to characterize temporal entanglement in relativistic quantum field theory in a general state for an arbitrary subregion on a flat, constant-time slice in a flat spacetime. Our prescriptions starts with the standard entanglement entropy of a spatial subregion and amounts to transporting the unchanged subregion to boosted time slices all the way across the light cone when it becomes in general a complex characterization of the corresponding temporal subregion. For holographic quantum field theories, our prescription amounts to an analytic continuation of all codimension-two bulk extremal surfaces satisfying the homology constraint and picking the one with the smallest real value of the area as the leading saddle point. We implement this prescription for holographic conformal field theories in thermal states on both a two-dimensional Lorentzian cylinder and three-dimensional Minkowski space, and show that it leads to results with self-consistent physical properties of temporal entanglement.