Related papers: Information Geometry of Entanglement Renormalizati…
Starting from recent results on the geometric formulation of quantum mechanics, we propose a new information geometric characterization of entanglement for spin network states in the context of quantum gravity. For the simple case of a…
In recent years, the import of quantum information techniques in quantum gravity opened new perspectives in the study of the microscopic structure of spacetime. We contribute to such a program by establishing a precise correspondence…
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…
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…
Random fields are useful mathematical objects in the characterization of non-deterministic complex systems. A fundamental issue in the evolution of dynamical systems is how intrinsic properties of such structures change in time. In this…
The fields of entanglement theory and tensor networks have recently emerged as central tools for characterising quantum phases of matter. In this article, we determine the entanglement structure of ground states of gapped symmetric quantum…
We propose a fundamental duality between the geometric properties of spacetime and the informational content of quantum fields. Specifically, we establish that the curvature of spacetime is directly related to the entanglement entropy of…
We examine geometry and dynamics of classical spacetime derived from entanglement spectrum. The spacetime is a kind of canonical parameter space defined by the Fisher information metric. As a concrete example, we focus on the spectrum for…
In this paper, we revisit the notion of quantum entanglement induced by the deformation of phase-space through noncommutative space (NC) parameters. The geometric structure of the state space for Gaussian states in NC-space is illustrated…
We introduce a new approach to evaluating entangled quantum networks using information geometry. Quantum computing is powerful because of the enhanced correlations from quantum entanglement. For example, larger entangled networks can…
Entanglement entropy plays a variety of roles in quantum field theory, including the connections between quantum states and gravitation through the holographic principle. This article provides a review of entanglement entropy from a mixed…
We investigate the global-symmetry projections applied to the tensor network states from the view point of the entanglement entropy and the mutual information. The projections to the translational invariant space and to the total-$S^z$-zero…
Motivated by the idea that, in the background-independent framework of a Quantum Theory of Gravity, entanglement is expected to play a key role in the reconstruction of spacetime geometry, we investigate the possibility of using the…
Entanglement is defined between subsystems of a quantum system, and at fixed time two regions of space can be viewed as two subsystems of a relativistic quantum field. The entropy of entanglement between such subsystems is ill-defined…
The renormalization of entanglement entropy of quantum field theories is investigated in the simplest setting with a $\lambda \phi^4$ scalar field theory. The 3+1 dimensional spacetime is separated into two regions by an infinitely flat…
The degrees of freedom of any interacting quantum field theory are entangled in momentum space. Thus, in the vacuum state, the infrared degrees of freedom are described by a density matrix with an entanglement entropy. We derive a relation…
In this article we present analytical results on the exact tensor network representations and correlation functions of the first examples of 2D ground states with quantum phase transitions between area law and extensive entanglement…
The entanglement entropy in a quantum field theory between two regions of space has been shown in simple cases to be proportional to the volume of the hypersurface separating the regions. We prove that this is true for a free scalar field…
Recent developments on holography and quantum information physics suggest that quantum information theory come to play a fundamental role in understanding quantum gravity. Cosmology, on the other hand, plays a significant role in testing…
We introduce a new method permitting the analytical determination of entanglement entropy (and related quantities) between configurations of a quantum field, which is either free or in interaction with a classical source, at two distinct…