AdS/CFT中相邻区间全息纠缠负性的新猜想与应用

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在"AdS / cft中相邻间隔的全息纠缠负猜想"这篇论文中，作者Parul Jaina、Vinay Malvimat、Sayid Mondal和Gautam Sengupta探讨了AdS / CFT对偶关系在(1+1)维双曲保形场论中的一个新颖概念。他们提出的全息纠缠负猜想关注的是AdS空间中相邻区域混合态的量子纠缠性质。这个猜想基于AdS空间中边界上对应区间测地线的特定代数和，这个代数和反映了这些区间之间全息互信息的减少。全息纠缠负性，作为量子信息的一个度量，是通过计算边界上的测地线来定义的，这反映了整个AdS几何结构与边界上的量子系统之间的关系。作者展示了如何利用这个猜想，计算出在零间隔和有限温度的(1+1)维全息共形场理论中，相邻区间的纠缠负性。这两种情况分别对应于AdS3的真空状态和欧几里得BTZ黑洞，它们各自揭示了全息对偶理论的不同特性。该猜想的提出是与大型中心电荷限制下的共形场论复制技术相一致的，这表明了全息纠缠负性可能提供了一种全新的理解量子纠缠在高维引力背景下的行为方式。论文还提到了AdSd+1 / CFTd方案的扩展，暗示了这个猜想可能具有更广泛的适用性和理论价值，尤其是在更高维度的AdS / CFT对称性框架内。这篇工作不仅深化了我们对量子纠缠在弦理论和引力理论中的理解，而且可能对开发新的量子信息处理技术和理论模型有潜在的影响。文章的接收、修订和最终接受过程显示了研究者对这一课题严谨的态度和同行评审的质量，确保了结果的可靠性和可重复性。 AdS / cft中相邻间隔的全息纠缠负猜想是关于量子信息与引力理论之间联系的重要一步，它提供了新的工具来研究高维空间中的量子纠缠现象，并且在理论物理学和量子信息科学的交叉领域中产生了深远的影响。

Physics Letters B 793 (2019) 104–109

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Holographic entanglement negativity conjecture for adjacent intervals

in AdS

/CFT

Parul Jain

a,b

, Vinay Malvimat

, Sayid Mondal

, Gautam Sengupta

c,∗

Dipartimento di Fisica, Università di Cagliari Cittadella Universitaria, 09042 Monserrato, Italy

INFN, Sezione di Cagliari, Italy

Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208016, India

a r t i c l e i n f o a b s t r a c t

Article history:

Received

12 September 2018

Received

in revised form 18 March 2019

Accepted

15 April 2019

Available

online 17 April 2019

Editor:

N. Lambert

We propose a holographic entanglement negativity conjecture involving the bulk geometry, for mixed

states of adjacent intervals in (1 + 1)-dimensional dual conformal ﬁeld theories through the Ad S/CFT

correspondence.

The holographic entanglement negativity is obtained from a speciﬁc algebraic sum of

the geodesics anchored on respective intervals on the boundary which reduces to the holographic mutual

information between them. Utilizing our conjecture we obtain the entanglement negativity of adjacent

intervals in zero and ﬁnite temperature (1 + 1)-dimensional holographic conformal ﬁeld theories dual to

the bulk AdS

vacuum and the Euclidean BTZ black hole respectively. Our holographic conjecture exactly

reproduces the conformal ﬁeld theory results obtained through the replica technique, in the large central

charge limit. We brieﬂy elucidate the corresponding issue for the AdS

d+1

/CFT

scenario.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

Quantum entanglement in recent times has impacted an ex-

pansive

list of theoretical issues from condensed matter physics

to quantum gravity through the holographic AdS /CFT correspon-

dence

[1–5]. This geometric connection has allowed the character-

ization

of quantum entanglement in extended systems like holo-

graphic

conformal ﬁeld theories. For bipartite quantum systems in

a pure state this involves the entanglement entropy which is de-

ﬁned

as the von Neumann entropy of the reduced density matrix.

In a series of interesting communications Calabrese et al. advanced

a comprehensive procedure to compute the entanglement entropy

of (1 + 1)-dimensional conformal ﬁeld theories (CFT

1+1

) [6,7]uti-

lizing

the replica technique.

Following

[6], in a seminal work Ryu and Takayanagi pro-

posed

a holographic characterization of the entanglement entropy

in d-dimensional conformal ﬁeld theories (CFT

), involving bulk

dual Ad S

d+1

geometries through the AdS /CFT correspondence [8,

9](for

an extensive review see [10]). According to the Ryu and

Takayanagi (RT) conjecture the universal part of the entanglement

entropy of a subsystem in a dual CFT

was described by the area

Corresponding author.

E-mail

addresses: parul.jain@ca.infn.it (P. Jain), vinaymm@iitk.ac.in

(V. Malvimat),

sayidphy@iitk.ac.in (S. Mondal), sengupta@iitk.ac.in (G. Sengupta).

of a co-dimension two bulk AdS

d+1

static minimal surface homol-

ogous

to the subsystem. For the Ad S

/CFT

scenario the static

minimal surface reduces to a space like geodesic in the bulk AdS

geometry anchored on the appropriate spatial interval in the dual

CFT

1+1

. The holographic entanglement entropy obtained from the

RT conjecture exactly reproduces the corresponding CFT

1+1

re-

sults

obtained through the replica technique in the large central

charge limit.

is well known however in quantum information theory that

the entanglement entropy ceases to be a valid measure for the

characterization of mixed state entanglement where it receives

contributions from irrelevant correlations. This is a complex issue

in quantum information theory and necessitates the introduction

of suitable entanglement measures for the distillable entanglement.

In a seminal communication Vidal and Werner [11] addressed this

issue and proposed a computable measure termed entanglement

negativity which provides an upper bound on the distillable entan-

glement whose

non convexity was subsequently demonstrated by

Plenio in [12]. In the recent past Calabrese et al. in [13–15]uti-

lized

an alternative replica technique to compute the entanglement

negativity for mixed states in both zero and ﬁnite temperature

CFT

1+1

Naturally

the above developments lead to the signiﬁcant is-

sue

of a holographic description for the entanglement negativ-

ity

involving the bulk geometry for dual conformal ﬁeld theo-

https://doi.org/10.1016/j.physletb.2019.04.037

0370-2693/

SCOAP

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