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      Entanglement of purification through holographic duality

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      Nature Physics
      Springer Nature

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          Quantum entanglement

          All our former experience with application of quantum theory seems to say: {\it what is predicted by quantum formalism must occur in laboratory}. But the essence of quantum formalism - entanglement, recognized by Einstein, Podolsky, Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, is a potential for many quantum processes, including ``canonical'' ones: quantum cryptography, quantum teleportation and dense coding. However, it appeared that this new resource is very complex and difficult to detect. Being usually fragile to environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation and quantifying. In particular, the authors discuss various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, quantum cryptography and point out some interrelations. They also discuss a basic role of entanglement in quantum communication within distant labs paradigm and stress some peculiarities such as irreversibility of entanglement manipulations including its extremal form - bound entanglement phenomenon. A basic role of entanglement witnesses in detection of entanglement is emphasized.
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            Holographic Derivation of Entanglement Entropy from AdS/CFT

            , (2010)
            A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from AdS/CFT correspondence. We argue that the entanglement entropy in d+1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS_{d+2}, analogous to the Bekenstein-Hawking formula for black hole entropy. We show that our proposal perfectly reproduces the correct entanglement entropy in 2D CFT when applied to AdS_3. We also compare the entropy computed in AdS_5 \times S^5 with that of the free N=4 super Yang-Mills.
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              Building up spacetime with quantum entanglement

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                Author and article information

                Journal
                Nature Physics
                Nature Phys
                Springer Nature
                1745-2473
                1745-2481
                March 26 2018
                Article
                10.1038/s41567-018-0075-2
                188b0d18-a5f3-42b8-a14e-fee4cebea580
                © 2018

                http://www.springer.com/tdm

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