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タイトル: Towards an entanglement measure for mixed states in CFTs based on relative entropy
著者: Takayanagi, Tadashi  kyouindb  KAKEN_id
Ugajin, Tomonori
Umemoto, Koji
著者名の別形: 髙柳, 匡
梅本, 滉嗣
キーワード: Conformal Field Theory
AdS-CFT Correspondence
Holography and condensed matter physics (AdS/CMT)
発行日: Oct-2018
出版者: Springer Nature America, Inc
誌名: Journal of High Energy Physics
巻: 2018
論文番号: 166
抄録: Relative entropy of entanglement (REE) is an entanglement measure of bipartite mixed states, defined by the minimum of the relative entropy S(ρAB ||σAB ) between a given mixed state ρAB and an arbitrary separable state σAB . The REE is always bounded by the mutual information IAB = S(ρAB ||ρA ⊗ ρB) because the latter measures not only quantum entanglement but also classical correlations. In this paper we address the question of to what extent REE can be small compared to the mutual information in conformal field theories (CFTs). For this purpose, we perturbatively compute the relative entropy between the vacuum reduced density matrix ρ AB 0 on disjoint subsystems A ∪ B and arbitrarily separable state σAB in the limit where two subsystems A and B are well separated, then minimize the relative entropy with respect to the separable states. We argue that the result highly depends on the spectrum of CFT on the subsystems. When we have a few low energy spectrum of operators as in the case where the subsystems consist of finite number of spins in spin chain models, the REE is considerably smaller than the mutual information. However in general our perturbative scheme breaks down, and the REE can be as large as the mutual information.
著作権等: © The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
URI: http://hdl.handle.net/2433/236103
DOI(出版社版): 10.1007/JHEP10(2018)166
出現コレクション:学術雑誌掲載論文等

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