Related papers: Quantum complexity and generalized area law in ful…
A study of the artificial neural network representation of quantum many-body states is presented. The locality and entanglement properties of states for shallow and deep quantum neural networks are investigated in detail. By introducing the…
We explore the constraints following from requiring the Area Law in the entanglement entropy in the context of loop quantum gravity. We find a unique solution to the single link wave-function in the large j limit, believed to be appropriate…
We prove an area law for the entanglement entropy in gapped one dimensional quantum systems. The bound on the entropy grows surprisingly rapidly with the correlation length; we discuss this in terms of properties of quantum expanders and…
Recent results on the stability of the spectral gap under general perturbations for frustration-free Hamiltonians, have motivated the following question: Does the entanglement entropy of quantum states that are connected to states…
Most states in the Hilbert space are maximally entangled. This fact has proven useful to investigate - among other things - the foundations of statistical mechanics. Unfortunately, most states in the Hilbert space of a quantum many body…
Real-space renormalization-group techniques for quantum systems can be divided into two basic categories - those capable of representing correlations following a simple boundary (or area) law, and those which are not. I discuss the scaling…
Area laws for entanglement in quantum many-body systems give useful information about their low-temperature behaviour and are tightly connected to the possibility of good numerical simulations. An intuition from quantum many-body physics…
We review a number of ideas related to area law scaling of the geometric entropy from the point of view of condensed matter, quantum field theory and quantum information. An explicit computation in arbitrary dimensions of the geometric…
Quantum phase transitions occur at zero temperature and involve the appearance of long-range correlations. These correlations are not due to thermal fluctuations but to the intricate structure of a strongly entangled ground state of the…
Entanglement entropy obeys area law scaling for typical physical quantum systems. This may naively be argued to follow from locality of interactions. We show that this is not the case by constructing an explicit simple spin chain…
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 establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy of a distinguished block saturates, and hence follows an…
Entanglement entropy for nonlocal field theories displays a universal ``volume law" scaling \cite{Barbon:2008ut, Karczmarek:2013xxa, Shiba:2013jja, Pang:2014tpa} as opposed to the ``area law" scaling for local field theories. The aim of…
We explore the connection between the area law for entanglement and geometry by representing the entanglement entropies corresponding to all $2^N$ bipartitions of an $N$-party pure quantum system by means of a (generalized) adjacency…
The entanglement entropy of the integer Quantum Hall states satisfies the area law for smooth domains with a vanishing topological term. In this paper we consider polygonal domains for which the area law acquires a constant term that only…
Entanglement entropy is now widely accepted as having deep connections with quantum gravity. It is therefore desirable to understand it in the context of causal sets, especially since they provide in a natural manner the UV cutoff needed to…
We prove that a finite correlation length, i.e. exponential decay of correlations, implies an area law for the entanglement entropy of quantum states defined on a line. The entropy bound is exponential in the correlation length of the…
We demonstrate an area law bound on the ground state entanglement entropy of a wide class of gapless quantum states of matter using a strategy called local entanglement thermodynamics. The bound depends only on thermodynamic data, actually…
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
Machine learning, one of today's most rapidly growing interdisciplinary fields, promises an unprecedented perspective for solving intricate quantum many-body problems. Understanding the physical aspects of the representative artificial…