Note on quantum entanglement and quantum geometry

Abstract

In this note we present preliminary study on the relation between the quantum entanglement of boundary states and the quantum geometry in the bulk in the framework of spin networks. We conjecture that the emergence of space with non-zero volume reflects the non-perfectness of the $SU(2)$-invariant tensors. Specifically, we consider four-valent vertex with identical spins in spin networks. It turns out that when $j=1/2$ and $j=1$, the maximally entangled $SU(2)$-invariant tensors on the boundary correspond to the eigenstates of the volume square operator in the bulk, which indicates that the quantum geometry of tetrahedron has a definite orientation.

arXiv comment19 pages, 3 figures

References in corpus (24)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Discreteness of area and volume in quantum gravity
• Entanglement renormalization
• Building up spacetime with quantum entanglement
• Quantum Geometry and Black Hole Entropy
• Entanglement Renormalization and Holography
• Spin Networks and Quantum Gravity
• The Ryu-Takayanagi Formula from Quantum Error Correction
• Geometry Eigenvalues and Scalar Product from Recoupling Theory in Loop Quantum Gravity
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Closed formula for the matrix elements of the volume operator in canonical quantum gravity
• THE VOLUME OPERATOR IN DISCRETIZED QUANTUM GRAVITY
• Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity II
• Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity I
• Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy
• Gluing polyhedra with entanglement in loop quantum gravity
• Intertwiner Entanglement on Spin Networks
• Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity
• Fisher Metric, Geometric Entanglement and Spin Networks
• Invariant Perfect Tensors
• Quantum error correction and entanglement spectrum in tensor networks
• Graphical method in loop quantum gravity: I. Derivation of the closed formula for the matrix element of the volume operator
• Random Invariant Tensors
• Entanglement in simple spin networks with a boundary

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