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arXiv · 1807.04276

Entanglement Holonomies

Bartlomiej Czech·Lampros Lamprou·Leonard Susskind
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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.

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Bartlomiej Czech, Lampros Lamprou, Leonard Susskind. 2018-07-11. Entanglement Holonomies. https://arxiv.org/abs/1807.04276

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