scholarly journals Correlation functions and quantum measures of descendant states

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Enrico M. Brehm ◽  
Matteo Broccoli
Keyword(s):  
Differential Operator ◽  
Correlation Functions ◽  
Recursive Formula ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Two Dimensional ◽  
Computer Implementation ◽  
Point Function ◽  
Rényi Divergence ◽  
Holographic Description

Abstract We discuss a computer implementation of a recursive formula to calculate correlation functions of descendant states in two-dimensional CFT. This allows us to obtain any N-point function of vacuum descendants, or to express the correlator as a differential operator acting on the respective primary correlator in case of non-vacuum descendants. With this tool at hand, we then study some entanglement and distinguishability measures between descendant states, namely the Rényi entropy, trace square distance and sandwiched Rényi divergence. Our results provide a test of the conjectured Rényi QNEC and new tools to analyse the holographic description of descendant states at large c.

scholarly journals Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part I. Single-particle states

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Jiaju Zhang ◽  
M.A. Rajabpour
Keyword(s):  
Excited States ◽  
Single Particle ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Large Momentum ◽  
Particle State ◽  
Two Dimensional ◽  
Universal Form ◽  
Conformal Field ◽  
Harmonic Chain

Abstract We investigate the Rényi entropy of the excited states produced by the current and its derivatives in the two-dimensional free massless non-compact bosonic theory, which is a two-dimensional conformal field theory. We also study the subsystem Schatten distance between these states. The two-dimensional free massless non-compact bosonic theory is the continuum limit of the finite periodic gapless harmonic chains with the local interactions. We identify the excited states produced by current and its derivatives in the massless bosonic theory as the single-particle excited states in the gapless harmonic chain. We calculate analytically the second Rényi entropy and the second Schatten distance in the massless bosonic theory. We then use the wave functions of the excited states and calculate the second Rényi entropy and the second Schatten distance in the gapless limit of the harmonic chain, which match perfectly with the analytical results in the massless bosonic theory. We verify that in the large momentum limit the single-particle state Rényi entropy takes a universal form. We also show that in the limit of large momenta and large momentum difference the subsystem Schatten distance takes a universal form but it is replaced by a new corrected form when the momentum difference is small. Finally we also comment on the mutual Rényi entropy of two disjoint intervals in the excited states of the two-dimensional free non-compact bosonic theory.

Rényi Entropy and Rényi Divergence in Sequential Effect Algebra

2020 ◽  
Vol 27 (02) ◽  
pp. 2050008
Author(s):  
Zahra Eslami Giski
Keyword(s):  
Shannon Entropy ◽  
Effect Algebra ◽  
Sequential Effect ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Numerical Examples ◽  
Basic Properties ◽  
Rényi Divergence ◽  
Leibler Divergence ◽  
Entropy Measures

The aim of this study is to extend the results concerning the Shannon entropy and Kullback–Leibler divergence in sequential effect algebra to the case of Rényi entropy and Rényi divergence. For this purpose, the Rényi entropy of finite partitions in sequential effect algebra and its conditional version are proposed and the basic properties of these entropy measures are derived. In addition, the notion of Rényi divergence of a partition in sequential effect algebra is introduced and the basic properties of this quantity are studied. In particular, it is proved that the Kullback–Leibler divergence and Shannon’s entropy of partitions in a given sequential effect algebra can be obtained as limits of their Rényi divergence and Rényi entropy respectively. Finally, to illustrate the results, some numerical examples are presented.

scholarly journals Infrared Electric Image Thresholding Using Two-Dimensional Fuzzy Renyi Entropy

2011 ◽  
Vol 12 ◽  
pp. 411-419 ◽  
Author(s):  
Songhai Fan ◽  
Shuhong Yang ◽  
Pu He ◽  
Hongyu Nie
Keyword(s):  
Renyi Entropy ◽  
Rényi Entropy ◽  
Two Dimensional ◽  
Image Thresholding ◽  
Electric Image

scholarly journals Rényi Entropy and Rényi Divergence in the Intuitionistic Fuzzy Case

2018 ◽  
Vol 72 (1) ◽  
pp. 77-105
Author(s):  
Beloslav Riečan ◽  
Dagmar Markechová
Keyword(s):  
Shannon Entropy ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Numerical Examples ◽  
Rényi Divergence ◽  
Intuitionistic Fuzzy ◽  
Leibler Divergence

Abstract Our objective in this paper is to define and study the Rényi entropy and the Rényi divergence in the intuitionistic fuzzy case. We define the Rényi entropy of order of intuitionistic fuzzy experiments (which are modeled by IF-partitions) and its conditional version and we examine their properties. It is shown that the suggested concepts are consistent, in the case of the limit of q going to 1, with the Shannon entropy of IF-partitions. In addition, we introduce and study the concept of Rényi divergence in the intuitionistic fuzzy case. Specifically, relationships between the Rényi divergence and Kullback-Leibler divergence and between the Rényi divergence and the Rényi entropy in the intuitionistic fuzzy case are studied. The results are illustrated with several numerical examples.

scholarly journals Entanglement entropy from TFD entropy operator

2021 ◽  
Vol 36 (13) ◽  
pp. 2150092
Author(s):  
M. Dias ◽  
Daniel L. Nedel ◽  
C. R. Senise
Keyword(s):  
Analytic Continuation ◽  
Moduli Space ◽  
Degrees Of Freedom ◽  
Entanglement Entropy ◽  
Expected Value ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Two Dimensional ◽  
Von Neumann

In this work, a canonical method to compute entanglement entropy is proposed. We show that for two-dimensional conformal theories defined in a torus, a choice of moduli space allows the typical entropy operator of the TFD to provide the entanglement entropy of the degrees of freedom defined in a segment and their complement. In this procedure, it is not necessary to make an analytic continuation from the Rényi entropy and the von Neumann entanglement entropy is calculated directly from the expected value of an entanglement entropy operator. We also propose a model for the evolution of the entanglement entropy and show that it grows linearly with time.

scholarly journals Rényi entropy of a line in two-dimensional Ising models

2010 ◽  
Vol 82 (12) ◽  
Author(s):  
J.-M. Stéphan ◽  
G. Misguich ◽  
V. Pasquier
Keyword(s):  
Ising Models ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Two Dimensional
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