Bit Threads and Holographic Monogamy

Cui, Shawn X.; Hayden, Patrick; He, Temple; Headrick, Matthew; Stoica, Bogdan; Walter, Michael

doi:10.1007/s00220-019-03510-8

Cited by 93 publications

(164 citation statements)

References 36 publications

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“…To this end having a framework that allows for efficient exploration of this object is a necessary first step. We will already see a few glimpses of patterns towards the end of our discussion (see also earlier comments in [] and more recent work []), but we hope to make clear that there is more information to be mined here.…”

Section: Introductionmentioning

confidence: 91%

“…See [] which generalize the RT‐based proof of SSA . Two further (distinct) proofs of MMI based on the ‘bit thread’ reformulation of holographic entanglement entropy recently appeared in [].…”

mentioning

confidence: 99%

“…On the other hand, using intuition from bit threads and multi‐commodity flows, one might suspect that these multi‐color junctions do implement new entanglement structures. We thank Matt Headrick for sharing this perspective.…”

mentioning

confidence: 99%

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Holographic Entropy Relations

Hubeny

Rangamani

Rota

2018

Fortschritte der Physik

127

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We develop a framework for the derivation of new information theoretic quantities which are natural from a holographic perspective. We demonstrate the utility of our techniques by deriving the tripartite information (the quantity associated to monogamy of mutual information) using a set of abstract arguments involving bulk extremal surfaces. Our arguments rely on formal manipulations of surfaces and not on local surgery or explicit computation of entropies through the holographic entanglement entropy prescriptions. As an application, we show how to derive a family of similar information quantities for an arbitrary number of parties. The present work establishes the foundation of a broader program that aims at the understanding of the entanglement structures of geometric states for an arbitrary number of parties. We stress that our method is completely democratic with respect to bulk geometries and is equally valid in static and dynamical situations. While rooted in holography, we expect that our construction will provide a useful characterization of multipartite correlations in quantum field theories.

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Section: Introductionmentioning

confidence: 91%

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confidence: 99%

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Holographic Entropy Relations

Hubeny

Rangamani

Rota

2018

Fortschritte der Physik

127

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“…These new inequalities were the result of a search algorithm which unfortunately does not provide a systematic way to derive new ones, nor does it suggest an interpretation for their significance in the holographic context. An interesting suggestion in this direction was recently put forth in [], which used arguments based on the bit‐thread interpretation of the RT formula to conjecture a particular decomposition of geometric states.…”

Section: Introductionmentioning

confidence: 99%

“…However, argues that the techniques of [] cannot be employed for the proof of the five (or more) party inequalities of [] in dynamical situations . A rigorous proof of the inequalities of [], and possibly new inequalities for

N \geq 5

which can emerge from our framework, will therefore require some new technology (perhaps based on bit‐threads, as suggested by the new proofs of MMI given in []). However, the fact that the notion of primitive quantities, and therefore the full holographic entropy arrangement, is insensitive to the distinction between static and dynamical spacetimes, lends support to the intuition that the RT and HRT holographic entropy cones may in fact coincide.…”

Section: Introductionmentioning

confidence: 99%

The Holographic Entropy Arrangement

Hubeny

Rangamani

Rota

2019

Fortschritte der Physik

116

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We develop a convenient framework for characterizing multipartite entanglement in composite systems, based on relations between entropies of various subsystems. This continues the program initiated in [1], of using holography to effectively recast the geometric problem into an algebraic one. We prove that, for an arbitrary number of parties, our procedure identifies a finite set of entropic information quantities that we conveniently represent geometrically in the form of an arrangement of hyperplanes. This leads us to define the holographic entropy arrangement, whose algebraic and combinatorial aspects we explore in detail. Using the framework, we derive three new information quantities for four parties, as well as a new infinite family for any number of parties. A natural construct from the arrangement is the holographic entropy polyhedron which captures holographic entropy inequalities describing the physically allowed region of entropy space. We illustrate how to obtain the polyhedron by winnowing down the arrangement through a sieve to pick out candidate sign‐definite information quantities. Comparing the polyhedron with the holographic entropy cone, we find perfect agreement for 4 parties and corroborating evidence for the conjectured 5‐party entropy cone. We work with explicit configurations in arbitrary (time‐dependent) states leading to both simple derivations and an intuitive picture of the entanglement pattern.

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Bit threads, Einstein’s equations and bulk locality

Agón

Cáceres

Pedraza

2021

J. High Energ. Phys.

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In the context of holography, entanglement entropy can be studied either by i) extremal surfaces or ii) bit threads, i.e., divergenceless vector fields with a norm bound set by the Planck length. In this paper we develop a new method for metric reconstruction based on the latter approach and show the advantages over existing ones. We start by studying general linear perturbations around the vacuum state. Generic thread configurations turn out to encode the information about the metric in a highly nonlocal way, however, we show that for boundary regions with a local modular Hamiltonian there is always a canonical choice for the perturbed thread configurations that exploits bulk locality. To do so, we express the bit thread formalism in terms of differential forms so that it becomes manifestly background independent. We show that the Iyer-Wald formalism provides a natural candidate for a canonical local perturbation, which can be used to recast the problem of metric reconstruction in terms of the inversion of a particular linear differential operator. We examine in detail the inversion problem for the case of spherical regions and give explicit expressions for the inverse operator in this case. Going beyond linear order, we argue that the operator that must be inverted naturally increases in order. However, the inversion can be done recursively at different orders in the perturbation. Finally, we comment on an alternative way of reconstructing the metric non-perturbatively by phrasing the inversion problem as a particular optimization problem.

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Bit Threads and Holographic Monogamy

Cited by 93 publications

References 36 publications

Holographic Entropy Relations

Holographic Entropy Relations

The Holographic Entropy Arrangement

Bit threads, Einstein’s equations and bulk locality

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