Holographic Mutual Information is Monogamous


Hayden, P. (2012). Holographic Mutual Information is Monogamous. Perimeter Institute. https://pirsa.org/12060070


Hayden, Patrick. Holographic Mutual Information is Monogamous. Perimeter Institute, Jun. 28, 2012, https://pirsa.org/12060070


          @misc{ pirsa_PIRSA:12060070,
            doi = {10.48660/12060070},
            url = {https://pirsa.org/12060070},
            author = {Hayden, Patrick},
            keywords = {Quantum Information},
            language = {en},
            title = {Holographic Mutual Information is Monogamous},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {jun},
            note = {PIRSA:12060070 see, \url{https://pirsa.org}}

Patrick Hayden Stanford University


I'll describe a special information-theoretic property of quantum field theories with holographic duals: the mutual informations among arbitrary disjoint spatial regions A,B,C obey the inequality I(A:BC) >= I(A:B)+I(A:C), provided entanglement entropies are given by the Ryu-Takayanagi formula. Inequalities of this type are known as monogamy relations and are characteristic of measures of quantum entanglement. This suggests that correlations in holographic theories arise primarily from entanglement rather than classical correlations. Moreover, monogamy property implies that the Ryu-Takayanagi formula is consistent with all known general inequalities obeyed by the entanglement entropy, including an infinite set recently discovered by Cadney, Linden, and Winter; this constitutes significant evidence in favour of its validity.