Multipartite entanglement and topology in holography
Jonathan Harper
备注：
28 pages, 20 figures. Minor overlap with arXiv:1906.05970 due to review of key results in section 2. v2: references added, minor changes to presentation. v3: Published version
Starting from the entanglement wedge of a multipartite mixed state we describe a purification procedure which involves the gluing of several copies. The resulting geometry has non-trivial topology and a single oriented boundary for each original boundary region. In the purified geometry the original multipartite entanglement wedge cross section is mapped to a minimal surface of a particular non-trivial homology class. In contrast each original bipartite entanglement wedge cross section is mapped to the minimal wormhole throat around each boundary. Using the bit thread formalism we show how maximal flows for the bipartite and multipartite entanglement wedge cross section can be glued together to form maximal multiflows in the purified geometry. The defining feature differentiating the flows is given by the existence of threads which cross between different copies of the original entanglement wedge. Together these demonstrate a possible connection between multipartite entanglement and the topology of holographic spacetimes.
In this work we generalize the entanglement of purification and its conjectured holographic dual to conditional and multipartite versions of the same, where the optimization defining the entanglement of purification is now optimized in either a constrained way or over multiple parties. We separately derive new constraints on both the conditional entanglement of purification and its conjectured holographic dual object that match, further reinforcing the likelihood of this conjecture. We also show that the multipartite objects we define, despite obeying several of the same inequalities, are not …
Holographic multipartite entanglement structures in IR modified geometries
School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学理论科学研究所）
We explore ways to quantify multipartite correlations, in quantum information and in holography. We focus on optimized correlation measures, linear combinations of entropies minimized over all possible purifications of a state that satisfy monotonicity conditions. These contain far more information about correlations than entanglement entropy alone. We present a procedure to derive such quantities, and construct a menagerie of symmetric optimized correlation measures on three parties. These include tripartite generalizations of the entanglement of purification, the squashed entanglement, and t…
D-instantons of Type IIB string theory are Ramond-Ramond counterpart of Giddings-Strominger wormholes connecting two asymptotic regions of spacetime. Such wormholes, according to Coleman, might lead to spacetime topology change, third-quantized baby universes and probabilistic determination of fundamental coupling parameters. Utilizing correspondence between AdS5 x M5 Type IIB supergravity and d=4 super Yang-Mills theory, we point out that topology change and sum over topologies not only take place in string theory but also are required for consistency with holography. Nevertheless, the effect…
Quantum correlation beyond entanglement: Holographic discord and multipartite generalizations
Rikkyo University（立教大学）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
Long-range multipartite entanglement in holographic gapless systems
School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Department of Applied Physics, College of Science, China Agricultural University（中国农业大学理学院应用物理系）；Institute for Advanced Study, Tsinghua University（清华大学高等研究院）
We provide a holographic interpretation of a class of three-dimensional wormhole spacetimes. These spacetimes have multiple asymptotic regions which are separated from each other by horizons. Each such region is isometric to the BTZ black hole and there is non-trivial spacetime topology hidden behind the horizons. We show that application of the real-time gauge/gravity duality results in a complete holographic description of these spacetimes with the dual state capturing the non-trivial topology behind the horizons. We also show that these spacetimes are in correspondence with trivalent graphs…
The connection between entanglement and topology manifests itself in the form of the ER-EPR duality. This statement however refers to the maximally entangled states only. In this article I study the multipartite entanglement and the way in which it relates to the topological interpretation of the ER-EPR duality. The $2$ dimensional genus $1$ torus will be generalised to a $n$-dimensional general torus, where the information about the multipartite entanglement will be encoded in the higher inclusion maps of the Mayer-Vietorist sequence.
In this paper,based on the available mathematical works on geometry and topology of hyperbolic manifolds and discrete groups, some results of Freedman et al (hep-th/9804058) are reproduced and broadly generalized. Among many new results the possibility of extension of work of Belavin, Polyakov and Zamolodchikov to higher dimensions is investigated. Known in physical literature objections against such extension are removed and the possibility of an extension is convincingly demonstrated.
We discuss the stability of the topological invariant of the strongly interacting Weyl semi-metal at finite temperature. We find that if the interactions and temperature of the system are controlled by the holography, the topology is stable even in the case the Fermi surface become fuzzy. We give an argument to show that although the self energy changes the spectral function significantly to make the Fermi surface fuzzy, it cannot change the singularity structure of the Berry phase, which leads to the stability of the topology. We also find that depending on the mass term structure of the ferm…
We show that a given conformal boundary can have a rich and intricate space of supersymmetric supergravity solutions filling it, focusing on the case where this conformal boundary is a biaxially squashed Lens space. Generically we find that the biaxially squashed Lens space S^3/Z_p admits Taub-NUT-AdS fillings, with topology R^4/Z_p, as well as smooth Taub-Bolt-AdS fillings with non-trivial topology. We show that the Taub-NUT-AdS solutions always lift to solutions of M-theory, and correspondingly that the gravitational free energy then agrees with the large N limit of the dual field theory fre…
Topological entanglement entropy, a measure of the long-ranged entanglement, is related to the degeneracy of the ground state on a higher genus surface. The exact relation depends on the details of the topological theory. We consider a class of holographic models where such relation might be similar to the one exhibited by Chern-Simons theory in a certain large N limit. Both the non-vanishing topological entanglement entropy and the ground state degeneracy in these holographic models are consequences of the topological Gauss-Bonnet term in the dual gravitational description. A soft wall hologr…
We explore the conjectured duality between a class of large $N$ matrix integrals, known as multicritical matrix integrals (MMI), and the series $(2m-1,2)$ of non-unitary minimal models on a fluctuating background. We match the critical exponents of the leading order planar expansion of MMI, to those of the continuum theory on an $S^2$ topology. From the MMI perspective this is done both through a multi-vertex diagrammatic expansion, thereby revealing novel combinatorial expressions, as well as through a systematic saddle point evaluation of the matrix integral as a function of its parameters. …
A New Genuine Multipartite Entanglement Measure: from Qubits to Multiboundary Wormholes
Gwangju Institute of Science and Technology（光州科学技术院）；College of Science, Kyung Hee University（庆熙大学理学院）；Research Institute for Basic Sciences, Kyung Hee University（庆熙大学基础科学研究院）；International Research Center for Quantum Matter, Kyung Hee University（庆熙大学量子物质国际研究中心）
This thesis is devoted to the study of 3-dimensional quantum gravity as a spin foam model and group field theory. In the first part of this thesis, we review some general physical and mathematical aspects of 3-dimensional gravity, focusing on its topological nature. Afterwards, we review some important aspects of the Ponzano-Regge spin foam model for 3-dimensional Riemannian quantum gravity and explain in some details how it is related to the discretized path integral of general relativity in its first-order formulation. Furthermore, we discuss briefly some related spin foam models and review …
Black hole as a multipartite entangler: multi-entropy in AdS${}_3$/CFT${}_2$
Yonago College, National Institute of Technology Yonago（米子工业高等专门学校）；Department of Physics, College of Humanities and Sciences, Nihon University（日本大学文理学部物理学科）
We study the entanglement entropy in confining theories with gravity duals using the holographic prescription of Ryu and Takayanagi. The entanglement entropy between a region and its complement is proportional to the minimal area of a bulk hypersurface ending on their border. We consider a disk in 2+1 dimensions and a ball in 3+1 dimensions and find in both cases two types of bulk hypersurfaces with different topology, similar to the case of the slab geometry considered by Klebanov, Kutasov and Murugan. Depending on the value of the radius, one or the other type of hypersurfaces dominates the …
Scalar QFT on the boundary $\Im^+$ at null infinity of a general asymptotically flat 4D spacetime is constructed using the algebraic approach based on Weyl algebra associated to a BMS-invariant symplectic form. The constructed theory is invariant under a suitable unitary representation of the BMS group with manifest meaning when the fields are interpreted as suitable extensions to $\Im^+$ of massless minimally coupled fields propagating in the bulk. The analysis of the found unitary BMS representation proves that such a field on $\Im^+$ coincides with the natural wave function constructed out …
Gravity is uniquely situated in between classical topological field theories and standard local field theories. This can be seen in the the quasi-local nature of gravitational observables, but is nowhere more apparent than in gravity's holographic formulation. Holography holds promise for simplifying computations in quantum gravity. While holographic descriptions of three-dimensional spacetimes and of spacetimes with a negative cosmological constant are well-developed, a complete boundary description of zero curvature, four-dimensional spacetime is not currently available. Building on previous…
The reflected entropy $S_R(A:B)$ of a density matrix $ρ_{AB}$ is a bipartite correlation measure lower-bounded by the quantum mutual information $I(A:B)$. In holographic states satisfying the quantum extremal surface formula, where the reflected entropy is related to the area of the entanglement wedge cross-section, there is often an order-$N^2$ gap between $S_R$ and $I$. We provide an information-theoretic interpretation of this gap by observing that $S_R - I$ is related to the fidelity of a particular Markov recovery problem that is impossible in any state whose entanglement wedge cross-sect…
The way in which geometry encodes entanglement is a topic of much recent interest in quantum many-body physics and the AdS/CFT duality. This relation is particularly pronounced in the case of topological quantum field theories, where topology alone determines the quantum states of the theory. In this work, we study the set of quantum states that can be prepared by the Euclidean path integral in three-dimensional Chern-Simons theory. Specifically, we consider arbitrary 3-manifolds with a fixed number of torus boundaries in both abelian U(1) and non-abelian SO(3) Chern-Simons theory. For the abe…
Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models naturally incorporate many features that are analogous to those of the AdS/CFT correspondence. When the bond dimension of the tensors is large, we show th…
