Related papers: Space from Hilbert Space: Recovering Geometry from…
In this paper we investigate the possibility of constructing a complete quantization procedure consisting of geometric and deformation quantization. The latter assigns a noncommutative algebra to a symplectic manifold, by deforming the…
We compute the entanglement entropy for some quantum field theories on de Sitter space. We consider a superhorizon size spherical surface that divides the spatial slice into two regions, with the field theory in the standard vacuum state.…
We argue that the requirement of a finite entanglement entropy of quantum degrees of freedom across a boundary surface is closely related to the phenomenon of running spectral dimension, universal in approaches to quantum gravity. If…
Classical surfaces in phase space correspond to quantum states in Hilbert space. Subsystems specify factor spaces of the Hilbert space. An entangled state corresponds semiclassically to a surface that cannot be decomposed into a product of…
We reconstruct entanglement thermodynamics by means of Hessian geometry, since this method exactly generalizes thermodynamics into much wider exponential family cases including quantum entanglement. Starting with the correct first law of…
Spacetime emergence from entanglement proposes an alternative to quantizing gravity and typically derives a notion of distance based on the amount of mutual information shared across sub-systems. Albeit promising, this program still faces…
We put forward a general classification for a structural description of the entanglement present in compound entities experimentally violating Bell's inequalities, making use of a new entanglement scheme that we developed recently. Our…
Optimal universal entanglement processes are discussed which entangle two quantum systems in an optimal way for all possible initial states. It is demonstrated that the linear character of quantum theory which enforces the peaceful…
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…
This article is an expository account aimed at viewing entanglement in finite-dimensional quantum many-body systems as a phenomenon of global geometry. While the mathematics of general quantum states has been studied extensively, this…
Recently the $\text{SU}(2)$ spin-network states in loop quantum gravity is generalized to those of the corresponding affine Lie algebra. We show that if one literally starts from the full $\text{SL}(2,\mathbb{C})$ group, this procedure…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
Entanglement asymmetry is an observable in quantum systems, constructed using quantum-information methods, suited to detecting symmetry breaking in states -- possibly out of equilibrium -- relative to a subsystem. In this paper we define…
We study holographic entanglement entropy in four-dimensional quantum gravity with negative cosmological constant. By using the replica trick and evaluating path integrals in the minisuperspace approximation, in conjunction with the…
Let $H_k$, $k\in {\mathbb{N}}$, be the Hilbert spaces of geometric quantization on a K\"ahler manifold $M$. With two points in $M$ we associate a Bell-type state $b_k \in H_k\otimes H_k$. When $M$ is compact or when $M$ is ${\mathbb{C}}^n$,…
The aim of this thesis is to investigate quantum entanglement and quantum nonlocality of bipartite finite-dimensional systems (bipartite qudits). Entanglement is one of the most fascinating non-classical features of quantum theory, and…
The aim of this dissertation is to clarify the structure of entanglement, a type of quantum correlations, in various quantum systems with a large number of degrees of freedom for holography between generic quantum systems and spacetimes…
We calculate the entanglement of formation and the entanglement of distillation for arbitrary mixtures of the zero spin states on an arbitrary-dimensional bipartite Hilbert space. Such states are relevant to quantum black holes and to…
In this work, we explore physical systems which support not only multipartite interparticle entanglement, but also intraparticle entanglement between different degrees of freedom of the constituent particles and entanglement between…
Entanglement is a Hilbert-space based measure of nonseparability of states that leads to unique quantum possibilities such as teleportation. It has been at the center of intense activity in the area of quantum information theory and…