Holographic Entropy Cone Measures

Bao, Ning; Blitz, Samuel; Stoica, Bogdan

doi:10.48550/arxiv.1701.03498

Cited by 2 publications

(4 citation statements)

References 7 publications

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“…Throughout our discussion, we are not interested in individual threads, but only in a coarse-grained description of macroscopic numbers of threads on length scales much larger than the Planck scale (which we've set to 1 by setting 4G N = 1). 9 If the threads are locally parallel-i.e. parallel in every small neighborhood-then the only natural definition of density is the transverse density, which we call ν t ; this is the number per unit area intersecting a small disk orthogonal to the threads.…”

Section: Threads and Density Boundsmentioning

confidence: 99%

“…We do not impose any restrictions on the dimension or topology of the bulk or on the topology of the boundary regions. Formal definitions will be given in subsection 2.1.3 For further recent work on higher entropy inequalities, see[6][7][8][9][10][11][12][13][14][15][16].…”

mentioning

confidence: 99%

“…Restoring units, the density is required to be less than or equal to 1/4GN. Since the threads are 1dimensional, the density has units of length 1−d 9. As discussed in[18], we can define a thread configuration mathematically as a set of unoriented curves equipped with a measure, allowing us to "count" the number passing through a surface or connecting one boundary region to another.…”

mentioning

confidence: 99%

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Crossing versus locking: Bit threads and continuum multiflows

Headrick¹,

Held²,

Herman³

2020

Preprint

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Bit threads are curves in holographic spacetimes that manifest boundary entanglement, and are represented mathematically by continuum analogues of network flows or multiflows. Subject to a density bound, the maximum number of threads connecting a boundary region to its complement computes the Ryu-Takayanagi entropy. When considering several regions at the same time, for example in proving entropy inequalities, there are various inequivalent density bounds that can be imposed. We investigate for which choices of bound a given set of boundary regions can be "locked", in other words can have their entropies computed by a single thread configuration. We show that under the most stringent bound, which requires the threads to be locally parallel, non-crossing regions can in general be locked, but crossing regions cannot, where two regions are said to cross if they partially overlap and do not cover the entire boundary. We also show that, under a certain less stringent density bound, a crossing pair can be locked, and conjecture that any set of regions not containing a pairwise crossing triple can be locked, analogously to the situation for networks.

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Section: Threads and Density Boundsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Crossing versus locking: Bit threads and continuum multiflows

Headrick¹,

Held²,

Herman³

2020

Preprint

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“…One particular area of impact is the study of entanglement entropy in the context of holography pioneered by [1]. In this context, it was discovered that entanglement entropies for states in holographic theories dual to a classical bulk geometry obeyed additional inequalities beyond those obeyed by all quantum states [2,3] and that such states are a small fraction of the set of all quantum states in the entropy space measure [4]. These inequalities, though not true for all quantum systems, therefore serve as a useful discriminator for which quantum states, even in theories known to possess a holographic duality, can be dual to (semi)-classical spacetimes.…”

Section: Introductionmentioning

confidence: 99%

Conditional and multipartite entanglements of purification and holography

Bao

Halpern

2019

Phys. Rev. D

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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 duals of each other. Further, we find inequalities that are true only for the bulk objects, and thus could provide additional consistency checks for states dual to (semi)-classical bulk geometries.

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Holographic Entropy Cone Measures

Cited by 2 publications

References 7 publications

Crossing versus locking: Bit threads and continuum multiflows

Crossing versus locking: Bit threads and continuum multiflows

Conditional and multipartite entanglements of purification and holography

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