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arXiv:1603.00184 · Physical review. D/Physical review. D.

On the monogamy of holographic n -partite information

Sepideh Mirabi, Mohammad Reza Tanhayi, R. Vazirian

Published May 25, 2016• 19 citations
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Abstract

We investigate the monogamy of holographic $n$-partite information for a system consisting of $n$ disjoint parallel strips with the same width and separation in AdS and AdS black brane geometries. More precisely, we study the sign of this quantity, e.g., for $n=4$, 5, in various dimensions and for different parameters. Our results show that for quantum field theories with holographic duals, the holographic 4-partite information is always positive, and the sign of holographic 5-partite information is found to be negative in the dual strongly coupled $1+1$ dimensional conformal field theory. This latter result indicates that the holographic 4-partite information is monogamous. We also find the critical points corresponding to the possible phase transitions of these quantities.

DOI
10.1103/physrevd.93.104049

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We investigate the monogamy of holographic nnn-partite information for a system consisting of nnn disjoint parallel strips with the same width and separation in AdS and AdS black brane geometries. More precisely, we study the sign of this quantity, e.g., for n=4n=4n=4, 5, in various dimensions and for different parameters. Our results show that for quantum field theories with holographic duals, the holographic 4-partite information is always positive, and the sign of holographic 5-partite information is found to be negative in the dual strongly coupled 1+11+11+1 dimensional conformal field theory. This latter result indicates that the holographic 4-partite information is monogamous. We also find the critical points corresponding to the possible phase transitions of these quantities.
We study various scaling behaviors of n-partite information during a process of thermalization for n disjoint system consisting of n parallel strips whose widths are much larger than the separation between them. By making use of the holographic description for entanglement entropy we explore holographic description of the n-partite information by which we show that it has a definite sign: it is positive for even n and negative for odd n. This might thought of as an intrinsic property of a field theory which has gravity dual.
Holographic entanglement negativity for disjoint subsystems in AdSd+1/CFTd\mathrm{AdS_{d+1}/CFT_d}AdSd+1​/CFTd​
We propose a construction to compute the holographic entanglement negativity for bipartite mixed state configurations of two disjoint subsystems in higher dimensional conformal field theories (CFTd_dd​s) dual to bulk AdSd+1_{d+1}d+1​ geometries. Our proposal follows from the corresponding AdS3_33​/CFT2_22​ scenario and involves an algebraic sum of the areas of bulk RT surfaces for certain combinations of subsystems. Utilizing our construction we compute the holographic entanglement negativity at the leading order through a perturbative expansion, for such bipartite mixed states of two disjoint subsystems with long rectangular strip geometries in CFTd_dd​s dual to bulk pure AdSd+1_{d+1}d+1​ geometries and AdSd+1_{d+1}d+1​-Schwarzschild black holes.
In this paper, we propose a construction to compute the holographic entanglement negativity (HEN) for bipartite mixed state configurations of two disjoint subsystems in higher-dimensional conformal field theories (CFTds) dual to bulk AdS[Formula: see text] geometries. Our proposal follows from the corresponding AdS3/CFT2 scenario and involves an algebraic sum of the areas of bulk RT surfaces for certain combinations of subsystems. By utilizing our construction, we compute the HEN at the leading order through a perturbative expansion, for such bipartite mixed states of two disjoint subsystems with long rectangular strip geometries in CFTds dual to bulk pure AdS[Formula: see text] geometries and AdS[Formula: see text]-Schwarzschild black holes.
A bstract The n -partite information (nI) is formulated as a measure of multi-partite entanglement. Field theory computation revealed that the sign of nI is indefinite for n ≥ 3, while holographic studies conjectured a sign property that holographic nI is non-negative/non-positive for even/odd n , with tripartite information (TI, n = 3) proved. We investigate the aspects of nI with holographic duality in hyperscaling violating geometry. We confirm the conjectured sign property for strips of equal length with equal separation distance, and disprove this conjecture for n > 3 with general configurations. Therefore, nI in field theories and holography exhibits compatibility except for n = 3. We also discuss other properties of holographic nI with analytic computation: the monotonicity, linearity, relation to hyperscaling violating parameters, temperature and UV cutoff effects, and the physical implications. It is doubtful that nI is an effective measure of entanglement considering the indefinite sign, non-monotonicity, and quasi-linearity of its holographic dual. In this respect, we propose constraints on the multi-partite entanglement measures.
In this paper, we extend a holographic construction for the entanglement negativity of two disjoint subsystems in the literature to [Formula: see text]s with a conserved charge dual to bulk [Formula: see text] geometries. This involves an algebraic sum of the areas of bulk RT surfaces for certain appropriate combinations of subsystems. In this context, we compute the holographic entanglement negativity for two disjoint subsystems with long rectangular strip geometries in [Formula: see text]s dual to bulk RN-[Formula: see text] black holes in a perturbative framework. Our results at the leading order reproduce significant features observed earlier in the literature and conform to quantum information theory, which constitute strong substantiation of our construction.
We construct an extensive model of bulk mutual information (MI) in anti-de Sitter spacetime and use it to describe the leading quantum corrections to the MI of certain holographic theories. The equivalence between bulk and boundary MI follows from the Faulkner--Lewkowycz--Maldacena prescription. We show that the extensivity of the bulk MI is sufficient for the quantum-corrected boundary entropy vector to satisfy monogamy of MI and all other holographic entropy cone inequalities. Our model is built from a covariantly conserved current-current kernel in AdS and is realized explicitly by a free massive Dirac fermion, whose boundary MI at long distances is that of a fermionic generalized free field (GFF). The construction also reproduces the expected short-distance divergence structure of a GFF, and the current-current correlator defines a positive and monotonically decreasing function along the renormalization-group flow. We illustrate this explicitly for disjoint half-disks at the conformal fixed point of the model in AdS3_33​, where we present the exact result.