Related papers: A Free Entropy Dimension Lemma

We carry out a systematic study of entanglement entropy in relativistic quantum field theory. This is defined as the von Neumann entropy S_A=-Tr rho_A log rho_A corresponding to the reduced density matrix rho_A of a subsystem A. For the…

We consider entanglement across a planar boundary in flat space. Entanglement entropy is usually thought of as the von Neumann entropy of a reduced density matrix, but it can also be thought of as half the von Neumann entropy of a product…

We give an analytical approach to the definition of additive and multiplicative free convolutions which is based on the theory of Nevanlinna and of Schur functions. We consider the set of probability distributions as a semigroup $\bold M$…

Let $\M$ be a finite von Neumann algebra acting on a Hilbert space $\H$ and $\AA$ be a transitive algebra containing $\M'$. In this paper we prove that if $\AA$ is 2-fold transitive, then $\AA$ is strongly dense in $\B(\H)$. This implies…

A reduction formula for compressions of von Neumann algebras arising as free products is proved. This shows that the fundamental group is all of the positive reals for some such algebras. Additionally, by taking a sort of free product with…

We show that the entanglement entropy and alpha entropies corresponding to spatial polygonal sets in $(2+1)$ dimensions contain a term which scales logarithmically with the cutoff. Its coefficient is a universal quantity consisting in a sum…

The entanglement entropy of an arbitrary spacetime region $A$ in a three-dimensional conformal field theory (CFT) contains a constant universal coefficient, $F(A)$. For general theories, the value of $F(A)$ is minimized when $A$ is a round…

The notion of a $*$-law or $*$-distribution in free probability is also known as the quantifier-free type in Farah, Hart, and Sherman's model theoretic framework for tracial von Neumann algebras. However, the full type can also be…

For a quantum state undergoing unitary Schr\"odinger time evolution, the von Neumann entropy is constant. Yet the second law of thermodynamics, and our experience, show that entropy increases with time. Ingarden introduced the quantum…

We introduce the notion of tubular dimension, and give a formula for it. As an application we show that every invariant measure of a $C^{1+\gamma}$ diffeomorphism of a closed Riemannian manifold admits an asymptotic local product structure…

In this paper we study conditions under which, for an inclusion of finite von Neumann algebras $N \subseteq M$, we have the reduced amalgamated free product $\ast_N M$ is embeddable into $(R \bar{\otimes} N_1)^\omega$ for some other finite…

In a remarkable paper [Phys. Rev. Lett. 96, 100503 (2006)], Dimitri Gioev and Israel Klich conjectured an explicit formula for the leading asymptotic growth of the spatially bi-partite von-Neumann entanglement entropy of non-interacting…

A new series of central elements is found in the free alternative algebra. More exactly, let $Alt[X]$ and $SMalc[X]\subset Alt[X]$ be the free alternative algebra and the free special Malcev algebra over a field of characteristic 0 on a set…

We consider the entanglement entropy of a free massive scalar field in the one parameter family of $\alpha$-vacua in de Sitter space by using a method developed by Maldacena and Pimentel. An $\alpha$-vacuum can be thought of as a state…

The statistical mechanics characterization of a finite subsystem embedded in an infinite system is a fundamental question of quantum physics. Nevertheless, a full closed form { for all required entropic measures} does not exist in the…

In this letter we define a natural generalization of the von Neumann entropy to multiple parties that is symmetric with respect to all the parties. We call this measure multi-entropy. We show that for conformal field theories with…

We present an alternative approach to the theory of free Gibbs states with convex potentials. Instead of solving SDE's, we combine PDE techniques with a notion of asymptotic approximability by trace polynomials for a sequence of functions…

In this paper we study three aspects of (P(M)/~), the set of Murray-von Neumann equivalence classes of projections in a von Neumann algebra M. First we determine the topological structure that (P(M)/~) inherits from the operator topologies…

We develop a variational approximation to the entanglement entropy for scalar $\phi^4$ theory in 1+1, 2+1, and 3+1 dimensions, and then examine the entanglement entropy as a function of the coupling. We find that in 1+1 and 2+1 dimensions,…

Let G be an amenable group and V be a finite dimensional vector space. Gromov pointed out that the von Neumann dimension of linear subspaces of l^2(G;V) (with respect to G) can be obtained by looking at a growth factor for a dynamical…