13609 2004.04163 10.1007/JHEP08(2020)078 78 78 A field theory study of entanglement wedge cross section: odd entropy Regular Article - Theoretical Physics 1 24 2020 8 18 2020 4 23 2020 6 22 2020 7 14 2020 8 18 The Author(s) 2020 Open Access. 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. 13130 2020 2020 8 8 Ali Mollabashi alim@mppmu.mpg.de Kotaro Tamaoka kotaro.tamaoka@yukawa.kyoto-u.ac.jp grid.4372.2 0000 0001 2105 1091 Max-Planck-Institut for Physics, Werner-Heisenberg-Institut 80805 Munich Germany grid.258799.8 0000 0004 0372 2033 Center for Gravitational Physics, Yukawa Institute for Theoretical Physics (YITP) Kyoto University Kitashirakawa Oiwakecho, Sakyo-ku Kyoto 606-8502 Japan Abstract We study odd entanglement entropy (odd entropy in short), a candidate of measure for mixed states holographically dual to the entanglement wedge cross section, in two-dimensional free scalar field theories. Our study is restricted to Gaussian states of scale-invariant theories as well as their finite temperature generalizations, for which we show that odd entropy is a well-defined measure for mixed states. Motivated from holographic results, the difference between odd and von Neumann entropy is also studied. In particular, we show that large amounts of quantum correlations ensure the odd entropy to be larger than von Neumann entropy, which is qualitatively consistent with the holographic CFT. In general cases, we also find that this difference is not even a monotonic function with respect to size of (and distance between) subsystems. Keywords AdS-CFT Correspondence Conformal Field Theory Field Theories in Lower Dimensions ArXiv ePrint: 2004.04163