相关论文: Microstates free entropy and cost of equivalence r…

We show that, for many choices of finite tuples of generators $X = (x_1, \dots , x_d)$ of a tracial von Neumann algebra $(M, \tau)$ satisfying certain decomposition properties (non-primeness, possessing a Cartan subalgebra, or property…

We derive a functional for the entropy contributed by any microscopic degrees of freedom as arising from their measurable pair correlations. Applicable both in and out of equilibrium, this functional yields the maximum entropy which a…

Entropy and free energy are central concepts in both statistical physics and information theory, with quantum and classical facets. In mathematics these concepts appear quite often in different contexts (dynamical systems, probability…

For a family of unital free *-algebras with a family of states on them, we construct a sequence of noncommutative probability spaces, which are tensor product algebras with tensor product states and which approximate the free product of…

This talk is organized as follows: First we explain some basic concepts in non-commutative probability theory in the frame of operator algebras. In Section 2, we discuss related topics in von Neumann algebras. Sections 3 and 4 contain some…

Consider the real space D_U of directions moving into which from a unitary N x N matrix U we do not disturb its unitarity and the moduli of its entries in the first order. dim( D_U ) is called the defect of U and denoted D(U). We give an…

In various dimensions, we can sometimes compute observables of interacting conformal field theories (CFTs) that are connected to free theories via the renormalization group (RG) flow by computing protected quantities in the free theories.…

This paper is part of a series aiming at proving that the $\limsup$ and $\liminf$ variants of Voiculescu's free entropy coincide. This is based on a Laplace principle (implying a large deviation principle) for hermitian brownian motion on…

We study the relations between the averaged linear entropy production in periodically measured quantum systems and ergodic properties of their classical counterparts. Quantized linear automorphisms of the torus, both classically chaotic and…

We study the properties of pseudo entropy, a new generalization of entanglement entropy, in free Maxwell field theory in $d = 4$ dimension. We prepare excited states by the different components of the field strengths located at different…

Let $\mathcal{A}$ denote the reduced amalgamated free product of a family $\mathsf{A}_1, \mathsf{A}_2, ..., \mathsf{A}_n$ of von Neumann algebras over a von Neumann subalgebra $\Be$ with respect to normal faithful conditional expectations…

Products of truncated unitary matrices, independently and uniformly drawn from the unitary group, can be used to study universal aspects of monitored quantum circuits. The von Neumann entropy of the corresponding density matrix decreases…

We study the analogue in orbit equivalence of free product decomposition and free indecomposability for countable groups. We introduce the (orbit equivalence invariant) notion of freely indecomposable ({\FI}) standard probability measure…

Integrability conditions on local Hamiltonians for one-dimensional quantum systems to be free and interacting fermions are introduced. The definition of free fermion is the simultaneous satisfaction of the Yang-Baxter equation and Shastry's…

We present a bouquet of continuity bounds for quantum entropies, falling broadly into two classes: First, a tight analysis of the Alicki-Fannes continuity bounds for the conditional von Neumann entropy, reaching almost the best possible…

We develop a systematic approach to compute the subsystem trace distances and relative entropies for subsystem reduced density matrices associated to excited states in different symmetry sectors of a 1+1 dimensional conformal field theory…

We define Euler characteristics on classes of residually finite and virtually torsion free groups and we show that they satisfy certain formulas in the case of amalgamated free products and HNN extensions over finite subgroups. These…

Motivated by classification, up to order isomorphism, of some dense subgroups of Euclidean space that are free of minimal rank, we obtain apparently new invariants for an equivalence relation (intermediate between Hermite and Smith) on…

Let $I$ be any nonempty set and $(M_i, \varphi_i)_{i \in I}$ any family of nonamenable factors, endowed with arbitrary faithful normal states, that belong to a large class $\mathcal C_{\rm anti-free}$ of (possibly type III) von Neumann…

We study the microstate free entropy of projections, and establish its basic properties similar to the self-adjoint variable case. Our main contribution is to characterize the pair-block freeness of projections by the additivity of their…