arXiv:2205.05582 · Journal of High Energy Physics

Reflected entropy in AdS3/WCFT

Bin Chen, Yuefeng Liu, Boyang Yu

Published Dec 1, 2022• 16 citations

Abstract

A bstract Reflected entropy is a newly proposed notion in quantum information. It has important implications in holography. In this work, we study the reflected entropy in the framework of the AdS 3 /WCFT correspondence. We determine the scaling dimensions and charges of various twist operators in non-Abelian orbifold WCFT by generalizing the uniformization map and taking into account of the charge conservation. This allows us to compute the reflected entropy, logarithmic negativity and odd entropy for two disjoint intervals in holographic WCFT. We find that the reflected entropy can be related holographically to the pre-entanglement wedge cross-section, which is given by the minimal distance between the benches in two swing surfaces.

DOI: 10.1007/jhep12(2022)008

Related papers

Reflected entropy, symmetries and free fermions

Pablo Bueno, Horacio Casini

A bstract Exploiting the split property of quantum field theories (QFTs), a notion of von Neumann entropy associated to pairs of spatial subregions has been recently proposed both in the holographic context — where it has been argued to be related to the entanglement wedge cross section — and for general QFTs. We argue that the definition of this “reflected entropy” can be canonically generalized in a way which is particularly suitable for orbifold theories — those obtained by restricting the full algebra of operators to those which are neutral under a global symmetry group. This turns out to be given by the full-theory reflected entropy minus an entropy associated to the expectation value of the “twist” operator implementing the symmetry operation. Then we show that the reflected entropy for Gaussian fermion systems can be simply written in terms of correlation functions and we evaluate it numerically for two intervals in the case of a two-dimensional Dirac field as a function of the conformal cross-ratio. Finally, we explain how the aforementioned twist operators can be constructed and we compute the corresponding expectation value and reflected entropy numerically in the case of the ℤ 2 bosonic subalgebra of the Dirac field.

arXiv:2003.09546Journal of High Energy PhysicsMay 22, 202043 citations

Covariant holographic reflected entropy in AdS3/CFT2

Mir Afrasiar, Himanshu Chourasiya, Vinayak Raj +1 more

We substantiate a covariant proposal for the holographic reflected entropy in CFTs dual to non-static AdS geometries from the bulk extremal entanglement wedge cross section in the literature with explicit computations in the AdS3/CFT2 scenario. In this context we obtain the reflected entropy for zero and finite temperature time dependent bipartite mixed states in CFT1+1s with a conserved charge dual to bulk rotating extremal and non-extremal BTZ black holes through a replica technique. Our results match exactly with the corresponding extremal entanglement wedge cross section for these bulk geometries in the literature. This constitutes a significant consistency check for the proposal and its possible extension to the corresponding higher dimensional AdS/CFT scenario.

arXiv:2209.02654Physics Letters BNov 23, 20223 citations

Reflected entropy in double holography

Yi Ling, Peng Liu, Yuxuan Liu +3 more

Abstract Recently, the reflected entropy is proposed in holographic approach to describe the entanglement of a bipartite quantum system in a mixed state, which is identified as the area of the reflected minimal surface inside the entanglement wedge. In this paper, we study the reflected entropy in the doubly holographic setup, which contains the degrees of freedom of quantum matter in the bulk. In this context, we propose a notion of quantum entanglement wedge cross-section, which may describe the reflected entropy with higher-order quantum corrections. We numerically compute the reflected entropy in pure AdS background and black hole background in four dimensions, respectively. In general, the reflected entropy contains the contribution from the geometry on the brane and the contribution from the CFT. We compute their proportion for different Newton constants and find that their behaviors are in agreement with the results based on the semi-classical gravity and the correlation of CFT coupled to the bath CFT.

arXiv:2109.09243Journal of High Energy PhysicsFeb 1, 202237 citations

Reflected entropy for communicating black holes. Part I. Karch-Randall braneworlds

Mir Afrasiar, Jaydeep Kumar Basak, Ashish Chandra +1 more

A bstract We obtain the reflected entropy for bipartite mixed state configurations of two adjacent and disjoint intervals at a finite temperature in BCFT 2 s with two distinct boundaries through a replica technique in the large central charge limit. Subsequently these field theory results are reproduced from bulk computations involving the entanglement wedge cross section in the dual BTZ black hole geometry truncated by two Karch-Randall branes. Our result confirms the holographic duality between the reflected entropy and the bulk entanglement wedge cross section in the context of the AdS 3 / BCFT 2 scenario. We further investigate the critical issue of the holographic Markov gap between the reflected entropy and the mutual information for these configurations from the bulk braneworld geometry and study its variation with subsystem sizes and time.

arXiv:2211.13246Journal of High Energy PhysicsFeb 20, 202315 citations

Holographic reflected entropy and islands in interface CFTs

Jaydeep Kumar Basak, Debarshi Basu, Vinay Malvimat +2 more

A bstract We investigate the reflected entropy for various mixed state configurations in the two dimensional holographic conformal field theories sharing a common interface (ICFTs). In the AdS 3 /ICFT 2 framework, we compute the holographic reflected entropy for the required configurations in the vacuum state of the ICFT 2 which is given by twice the entanglement wedge cross section (EWCS) in a spacetime involving two AdS 3 geometries glued along a thin interface brane. Subsequently, we evaluate the EWCS in the bulk geometry involving eternal BTZ black strings with an AdS 2 interface brane, which is dual to an ICFT 2 in the thermofield double (TFD) state. We explore the system from a doubly holographic perspective and determine the island contributions to the reflected entropy in the two dimensional semi-classical description involving two CFT 2 s coupled to an AdS 2 brane. We demonstrate that the results from the island formula match precisely with the bulk AdS 3 results in the large tension limit of the interface brane. We illustrate that the phase structure of the reflected entropy is quite rich involving many novel induced island phases and demonstrate that it obeys the expected Page curve for the reflected entropy in a radiation bath coupled to the AdS 2 black hole.

arXiv:2312.12512Journal of High Energy PhysicsMay 13, 20248 citations

Aspects of the reflected entropy

Souvik Dutta

The aim of this thesis is to compile our study of a quantum information quantity, called the reflected entropy, which is a measure of quantum correlations in mixed states. Our work is motivated by, and generalizes, an earlier work on the thermo-field double purification of thermal states, in the purview of the AdS/CFT correspondence. Our main result is that in so-called holographic CFT states, the reflected entropy is given by the area of a class of bulk geometric quantities inside the entanglement wedge, called reflected minimal surfaces. From the bulk point of view, we show that half the area of the reflected minimal surface, in Planck units, gives a reinterpretation of the notion of the entanglement wedge cross-section. In doing so, we address the connection with a recent conjecture on the entanglement of purification. We prove some general properties of the reflected entropy and introduce a novel replica trick in CFTs for studying it. The duality is established using a recently introduced approach to holographic modular flow. We also consider an Engelhardt-Wall holographic construction of the canonical purification − the reflected minimal surfaces are simply Ryu-Takayanagi surfaces in this new spacetime. When we move to the continuum limit, we find a relation to the split property − the reflected entropy computes the von Neumann entropy of a canonical splitting type-I factor. In this limit, we show that the reflected entropy serves as a regulator for the UV divergent entanglement entropy. Finally, we consider the reflected entropy for free fermions in two dimensions. Working directly in the continuum theory, we extract the reflected entropy from the spectrum of a singular integral equation whose kernel is determined by the modular flowed free fermion correlation function. We find the spectrum numerically and analytically in certain limits, in one of which, the reflected entanglement spectrum rapidly approaches the spectrum of the thermal density matrix. This suggests that the reflected entanglement spectrum is well suited to the task of extracting physical data of the theory directly from the vacuum/ground state wave function.

Mar 8, 20210 citations