Holographic mutual information is monogamous

By Patrick M. Hayden, M. Headrick, A. Maloney. 2011

367 citations recorded by the source corpus.

We identify 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. We also show 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 strong evidence in favour of its validity.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/8d94e866e9ea64ae46de3561414624a91a8b0008

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Citations in the corpus

A canonical purification for the entanglement wedge cross-section (2019, background): “It is well known that the tripartite information in holographic states is non-positive [44].”
Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence (2015, methodology): “In this section we explore to what extent holographic states reproduce key properties of the AdS/CFT correspondence, such as the Ryu-Takayanagi formula for entropy of a boundary region [3] and the negativity of tripartite information [9].”
Entanglement of purification: from spin chains to holography (2017, background): “[40] Patrick Hayden, Matthew Headrick, and Alexander Maloney, “Holographic Mutual Information is Monogamous,” Phys.”
Multiboundary wormholes and holographic entanglement (2014, background): “8), whose sign is opposite to that of the GHZ4 state as is always the case for holographic I3 [23].”
The holographic entropy cone (2015, methodology): “2) for any three disjoint regions A, B, C [21].”
Strong subadditivity and the covariant holographic entanglement entropy formula (2012, methodology): “y to bulk quantum corrections, whose eect on the entanglement entropy is not simply to correct the functional being minimized in (2.1), as can be argued for example by looking 6It was recently shown [17] using a similar method that the RT formula also implies the inequality S(AB) + S(BC) + S(AC) S(A”
Holographic evolution of the mutual information (2011, background): “Recently it has been shown [12] that for quantum systems with a holographic dual the tripartite information is always monogamous.”
Entanglement of purification through holographic duality (2017, background): “The main purpose of this paper is to explore its properties and interpretation in conformal ﬁeld theories (CFTs) by employing quantum information theoretic considerations.”
Entanglement entropy from a holographic viewpoint (2012, background): “Moreover, it was recently found that another inequality called monogamy can be derived in an analogous way [47].”
The Ryu–Takayanagi Formula from Quantum Error Correction (2016, background): “Since we know that the thread prescription is equivalent to the area term of the RT formula, once we consider four regions the entropies will obey inequalities such as the monogamy of mutual information that are not actually true for general quantum states [79,80], so at that point we will start see”
Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy (2012, background): “ three disjoint regions A, B, and C, Area[m(AB)] +Area[m(BC)] +Area[m(AC)] ≥ Area[m(A)] +Area[m(B)] +Area[m(C)] +Area[m(ABC)]. (4) This result was shown for the static Ryu-Takayanagi surfaces by Ref. [11]. Evidence for its validity in the covariant case was presented by Refs. [10,12]. This relation ”
Bit Threads and Holographic Entanglement (2016, background): “Our main interest here is in the fact that, in holographic theories, the tripartite information is always non-positive, I3(A : B : C) ≤ 0 (2.22) a property called16 “monogamy of mutual information” (MMI) [8,20].”
Chaos in quantum channels (2015, background): “4 However, for holographic systems the tripartite information must always be negative [19].”