Quantum Information Measures for Mixed States and Holographic Principle

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  • 混合状態に対する量子情報量とホログラフィー原理
  • コンゴウ ジョウタイ ニ タイスル リョウシ ジョウホウリョウ ト ホログラフィー ゲンリ

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Abstract

<p>We propose dualities between quantum information measures for mixed states and geometrical objects in the light of holography, especially the AdS/CFT correspondence in the string theory. First, we review the Ryu–Takayanagi formula which relates the entanglement entropy in CFT and the area of minimal surfaces in AdS. This formula suggests that the structure of entanglement should be directly related to one of spacetime via holography. We also stress that this formula should be generalized when we consider mixed states on the CFT side. Next, we define entanglement wedge cross-sections as a generalization of minimal surfaces that appeared in the Ryu–Takayanagi formula. Finally, we introduce entanglement of purification and odd entropy, which are measures of quantum correlations for mixed states. In particular, we argue that these quantities are dual to the entanglement wedge cross-sections. We discuss the validity of our proposals from both qualitative and quantitative viewpoints.</p>

Journal

  • Butsuri

    Butsuri 75 (6), 335-339, 2020-06-05

    The Physical Society of Japan

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