Holographic entanglement in spin network states: a focused review

Abstract

In the longstanding quest to reconcile gravity with quantum mechanics, profound connections have been unveiled between concepts traditionally pertaining to quantum information theory, such as entanglement, and constitutive features of gravity, like holography. Developing and promoting these connections from the conceptual to the operational level unlocks access to a powerful set of tools, which can be pivotal towards the formulation of a consistent theory of quantum gravity. Here, we review recent progress on the role and applications of quantum informational methods, in particular tensor networks, for quantum gravity models. We focus on spin network states dual to finite regions of space, represented as entanglement graphs in the group field theory approach to quantum gravity, and illustrate how techniques from random tensor networks can be exploited to investigate their holographic properties. In particular, spin network states can be interpreted as maps from bulk to boundary, whose holographic behaviour increases with the inhomogeneity of their geometric data (up to becoming proper quantum channels). The entanglement entropy of boundary states, which are obtained by feeding such maps with suitable bulk states, is then proved to follow a bulk area law, with corrections due to the entanglement of the bulk state. We further review how exceeding a certain threshold of bulk entanglement leads to the emergence of a black hole-like region, revealing intriguing perspectives for quantum cosmology.

Intertwiner entanglement excitation and holonomy operator

“…We refer the interested reader to [47], and to the recent work [40,42,48], for more details on wave-functions for bounded regions and interesting work on typical bulk states.…”

“…In the context of LQG, the work investigating the entanglement carried by spin networks states have slowly built since the birth of the theory [25][26][27][28][29][30][31][32][33][34][35][36][37], but has definitely sped up in the past few years with the burst of interest in the bulk-to-boundary propagator and bulk-fromboundary reconstruction in the light of holography, see for instance [38][39][40][41][42]. In this paper, we focus on intertwiner entanglement 2 , i.e.…”