Random tensor networks with nontrivial links

Abstract

Random tensor networks are a powerful toy model for understanding the entanglement structure of holographic quantum gravity. However, unlike holographic quantum gravity, their entanglement spectra are flat. It has therefore been argued that a better model consists of random tensor networks with link states that are not maximally entangled, i.e., have nontrivial spectra. In this work, we initiate a systematic study of the entanglement properties of these networks. We employ tools from free probability, random matrix theory, and one-shot quantum information theory to study random tensor networks with bounded and unbounded variation in link spectra, and in cases where a subsystem has one or multiple minimal cuts. If the link states have bounded spectral variation, the limiting entanglement spectrum of a subsystem with two minimal cuts can be expressed as a free product of the entanglement spectra of each cut, along with a Marchenko-Pastur distribution. For a class of states with unbounded spectral variation, analogous to semiclassical states in quantum gravity, we relate the limiting entanglement spectrum of a subsystem with two minimal cuts to the distribution of the minimal entanglement across the two cuts. In doing so, we draw connections to previous work on split transfer protocols, entanglement negativity in random tensor networks, and Euclidean path integrals in quantum gravity.

85 pages, 7 figures

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Cited by in corpus (11)

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• Free Independence and the Noncrossing Partition Lattice in Dual-Unitary Quantum Circuits
• Entanglement Negativity and Replica Symmetry Breaking in General Holographic States
• Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
• The resource theory of tensor networks
• On Infinite Tensor Networks, Complementary Recovery and Type II Factors
• Holographic Tensor Networks as Tessellations of Geometry
• Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity