Entanglement Holonomies
arXiv:1807.04276
Abstract
We introduce a quantum notion of parallel transport between subsystems of a quantum state whose holonomies characterize the structure of entanglement. In AdS/CFT, entanglement holonomies are reflected in the bulk spacetime connection. When the subsystems are a pair of holographic CFTs in an entangled state, our quantum transport measures Wilson lines threading the dual wormhole. For subregions of a single CFT it is generated by the modular Berry connection and computes the effect of the AdS curvature on the transport of minimal surfaces. Our observation reveals a new aspect of the spacetime-entanglement duality and yet another concept shared between gravity and quantum mechanics.
15 pages, 4 figures
References in corpus (3)
Cited by in corpus (4)
- Holographic Order from Modular Chaos
- Geometric phases distinguish entangled states in wormhole quantum mechanics
- Entanglement wedge reconstruction and correlation measures in mixed states: modular flows versus quantum recovery channels
- Perspective-neutral approach to quantum frame covariance for general symmetry groups