Related papers: Space from Hilbert Space: Recovering Geometry from…
We propose entanglement entropy as a probe of the architecture of spacetime in quantum gravity. We argue that the leading contribution to this entropy satisfies an area law for any sufficiently large region in a smooth spacetime, which, in…
We show that, in discrete models of quantum gravity, emergent geometric space can be viewed as the entanglement pattern in a mixed quantum state of the "universe", characterized by a universal topological network entanglement. As a concrete…
Recently it has been proposed that the Bekenstein-Hawking formula for the entropy of spacetime horizons has a larger significance as the leading contribution to the entanglement entropy of general spacetime regions, in the underlying…
The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an…
Various problems concerning the geometry of the space $u^*(\cH)$ of Hermitian operators on a Hilbert space $\cH$ are addressed. In particular, we study the canonical Poisson and Riemann-Jordan tensors and the corresponding foliations into…
A scalar field in the ground state, when partially hidden from observation by a spherical boundary, acquires entanglement entropy $S$ proportional to the area of the surface. This area law is well established in flat space, where it follows…
The area law conjecture states that the entanglement entropy of a region of space in the ground state of a gapped, local Hamiltonian only grows like the surface area of the region. We show that, for any quantum state that fulfills an area…
Quantum kinetically constrained models have recently attracted significant attention due to their anomalous dynamics and thermalization. In this work, we introduce a hitherto unexplored family of kinetically constrained models featuring a…
Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle…
The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a…
Field theories place one or more degrees of freedom at every point in space. Hilbert spaces describing quantum field theories, or their finite-dimensional discretizations on lattices, therefore have large amounts of structure: they are…
A definition for the entanglement entropy in a gauge theory was given recently in arXiv:1501.02593. Working on a spatial lattice, it involves embedding the physical state in an extended Hilbert space obtained by taking the tensor product of…
We introduce a general approach to realize quantum states with holographic entanglement structure via monitored dynamics. Starting from random unitary circuits in $1+1$ dimensions, we introduce measurements with a spatiotemporally-modulated…
Entanglement entropy for a spatial partition of a quantum system is studied in theories which admit a dual description in terms of the anti-de Sitter (AdS) gravity one dimension higher. A general proof of the holographic formula which…
Entanglement is the powerful and enigmatic resource central to quantum information processing, which promises capabilities in computing, simulation, secure communication, and metrology beyond what is possible for classical devices. Exactly…
We elaborate on our earlier proposal connecting entanglement renormalization and holographic duality in which we argued that a tensor network can be reinterpreted as a kind of skeleton for an emergent holographic space. Here we address the…
We investigate the reconstruction of asymptotically anti-de Sitter (AdS) bulk geometries from boundary entanglement entropy data for ball-shaped entangling regions. By deriving an explicit inversion formula, we relate variations in…
We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…
Quantum entanglement entropy has a geometric character. This is illustrated by the interpretation of Rindler space or black hole entropy as entanglement entropy. In general, one can define a "geometric entropy", associated with an event…
Black hole entropy is one of the few windows toward the quantum aspects of gravitation and its study over the years have highlighted the holographic nature of gravity. At the non-perturbative level in quantum gravity, promising explanations…