Quantum bit threads and holographic entanglement

Cesar A. Ag\'on; Juan F. Pedraza

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Quantum bit threads and holographic entanglement

Cesar A. Agón, Juan F. Pedraza

High Energy Physics - Theory · Submitted 17 May 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper, we derive a novel dual prescription for the generalized entropy that allows us to interpret the leading quantum corrections in a geometric way with minimal input from the bulk state.

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What the abstract itself states, as probabilities: claims first 0.18 · states limitation 0.39 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.86 · mentions code or data availability 0.02.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

Quantum corrections to holographic entanglement entropy require knowledge of the bulk quantum state. In this paper, we derive a novel dual prescription for the generalized entropy that allows us to interpret the leading quantum corrections in a geometric way with minimal input from the bulk state. The equivalence is proven using tools borrowed from convex optimization. The new prescription does not involve bulk surfaces but instead uses a generalized notion of a flow, which allows for possible sources or sinks in the bulk geometry. In its discrete version, our prescription can alternatively be interpreted in terms of a set of Planck-thickness bit threads, which can be either classical or quantum. This interpretation uncovers an aspect of the generalized entropy that admits a neat information-theoretic description, namely, the fact that the quantum corrections can be cast in terms of entanglement distillation of the bulk state. We also prove some general properties of our prescription, including nesting and a quantum version of the max multiflow theorem. These properties are used to verify that our proposal respects known inequalities that a von Neumann entropy must satisfy, including subadditivity and strong subadditivity, as well as to investigate the fate of the holographic monogamy. Finally, using the Iyer-Wald formalism we show that for cases with a local modular Hamiltonian there is always a canonical solution to the program that exploits the property of bulk locality. Combining with previous results by Swingle and Van Raamsdonk, we show that the consistency of this special solution requires the semi-classical Einstein's equations to hold for any consistent perturbative bulk quantum state.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Quantum corrections to holographic entanglement entropy require knowledge of the bulk quantum state.	background 0.91	0.07	0.03	asserted 1.00
s1	In this paper, we derive a novel dual prescription for the generalized entropy that allows us to interpret the leading quantum corrections in a geometric way with minimal input from the bulk state.	contribution 1.00	0.97	0.69	asserted 1.00
s2	The equivalence is proven using tools borrowed from convex optimization.	method 0.99	0.82	0.04	asserted 1.00
s3	The new prescription does not involve bulk surfaces but instead uses a generalized notion of a flow, which allows for possible sources or sinks in the bulk geometry.	method 0.56	0.91	0.13	asserted 0.93
s4	In its discrete version, our prescription can alternatively be interpreted in terms of a set of Planck-thickness bit threads, which can be either classical or quantum.	interpretation 0.86	0.91	0.08	asserted 0.70
s5	This interpretation uncovers an aspect of the generalized entropy that admits a neat information-theoretic description, namely, the fact that the quantum corrections can be cast in terms of entanglement distillation of the bulk state.	interpretation 1.00	0.91	0.14	asserted 0.97
s6	We also prove some general properties of our prescription, including nesting and a quantum version of the max multiflow theorem.	result 0.55	0.96	0.06	asserted 1.00
s7	These properties are used to verify that our proposal respects known inequalities that a von Neumann entropy must satisfy, including subadditivity and strong subadditivity, as well as to investigate the fate of the holographic monogamy.	result 0.43	0.92	0.06	asserted 1.00
s8	Finally, using the Iyer-Wald formalism we show that for cases with a local modular Hamiltonian there is always a canonical solution to the program that exploits the property of bulk locality.	result 0.58	0.94	0.08	asserted 1.00
s9	Combining with previous results by Swingle and Van Raamsdonk, we show that the consistency of this special solution requires the semi-classical Einstein's equations to hold for any consistent perturbative bulk quantum state.	result 0.86	0.84	0.30	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.74 · evidence from proof or derivation 1.00.

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Original abstract

Quantum corrections to holographic entanglement entropy require knowledge of the bulk quantum state. In this paper, we derive a novel dual prescription for the generalized entropy that allows us to interpret the leading quantum corrections in a geometric way with minimal input from the bulk state. The equivalence is proven using tools borrowed from convex optimization. The new prescription does not involve bulk surfaces but instead uses a generalized notion of a flow, which allows for possible sources or sinks in the bulk geometry. In its discrete version, our prescription can alternatively be interpreted in terms of a set of Planck-thickness bit threads, which can be either classical or quantum. This interpretation uncovers an aspect of the generalized entropy that admits a neat information-theoretic description, namely, the fact that the quantum corrections can be cast in terms of entanglement distillation of the bulk state. We also prove some general properties of our prescription, including nesting and a quantum version of the max multiflow theorem. These properties are used to verify that our proposal respects known inequalities that a von Neumann entropy must satisfy, including subadditivity and strong subadditivity, as well as to investigate the fate of the holographic monogamy. Finally, using the Iyer-Wald formalism we show that for cases with a local modular Hamiltonian there is always a canonical solution to the program that exploits the property of bulk locality. Combining with previous results by Swingle and Van Raamsdonk, we show that the consistency of this special solution requires the semi-classical Einstein's equations to hold for any consistent perturbative bulk quantum state.

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References

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

PEE threads and bit threads in gravitational subregions of AdS
hep-th 2026-08 conditional novelty 7.0 of 10

PEE-thread and bit-thread flows are explicitly constructed for AdS3/BCFT, BTZ, and entanglement-wedge purifications, with the key finding that coarse-grained bit threads are generically non-geodesic.
Monogamous quantum corrections to holographic mutual information
hep-th 2026-09 conditional novelty 6.0 of 10

An extensive bulk mutual-information model in AdS, realized by a free massive Dirac fermion, places the quantum-corrected boundary entropy vector inside the holographic entropy cone and reproduces fermionic generalize...
A Differential Form Description of Partial Entanglement Entropy: Testing a Killing Vector Construction in Covariant Phase Space
hep-th 2026-09 accept novelty 6.0 of 10

The paper proposes a differential form for PEE threads and shows that a Killing-vector covariant-phase-space construction cannot reproduce the known central PEE flow in AdS3/CFT2.
Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
hep-th 2021-06 conditional novelty 6.0 of 10

Recasting complexity=volume as a minimum-flux problem over timelike bulk vector fields, the authors derive conditional-complexity bounds, construct explicit flows in AdS and BTZ, and argue that a first law of complexi...
Quantum Information in Holographic Duality
hep-th 2021-08 accept novelty 3.0 of 10

A self-contained graduate-level review that connects black hole thermodynamics, Ryu-Takayanagi, tensor networks, entropy inequalities, and the island resolution of the information paradox into one narrative.

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27 arXiv papers cite this in 40 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 30 sentences without a confident label

Builds on it 1 paper

Intuitively, in terms of Lorentzian threads, as proposed for the Riemannian case in [ref] , the $1/N$ corrections may allow threads to split such that they connect multiple degrees of freedom on one slice or multiple degrees of freedom on another slice.

Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity · Future directions · 0.87

Uses its method or tool 1 paper

In this section, we use the tools from the convex optimization, i.e. the Lagrangian duality and the strong duality, to prove the equivalence between the entropy formula ([ref]) and the quantum bit thread formulation ([ref]), similar to Refs. [ref] .

Towards bit threads in general gravitational spacetimes · Dual quantum bit thread formulation through the convex optimization · 0.83

Compares with it 1 paper

For example, the paper [ref] gave a flow proposal that captures corrections to first order in $$ (whereas the QES formula and [ref] account for correction to all order in $$).

Quantum Bit Threads and the Entropohedron · Introduction · 0.95

Cites it as background 7 papers

This perspective is inspired by the so-called bit threads [ref] [For the recent developments of bit threads see e.g. [ref] .], which arise from the rephrasing of the RT formula for holographic entanglement entropy.

Holographic coarse-grained states and the necessity of perfect entanglement · Introduction · 0.88
See [ref] for the construction of bit-thread configurations in various situations.

PEE threads and bit threads in gravitational subregions of AdS · PEE threads and bit threads · 0.89
Bit threads have been used to study multipartite entanglement [ref] , holographic monogamy of mutual information [ref] , the hypergraph entropy cone [ref] , metric reconstruction [ref] , etc.

Lorentzian threads and generalized complexities · Introduction · 0.82

What it cites · 107 sentences without a confident label

Builds on 2 papers

In this section we will show that the framework developed in [ref] can, in fact, accommodate for the leading $G_N$ corrections when considering semi-classical states in the bulk.

Bit threads, Einstein's equations and bulk locality · Canonical bit threads from Iyer-Wald · 0.97
It would be very interesting to explicitly check this idea, at least at the first non-linear order, which could be done by extending the work of [ref] to the case of semi-classical bulk states (the ones we considered in this work) and then constructing the non-linear version of our canonical flows.

Nonlinear Gravity from Entanglement in Conformal Field Theories · Discussion · 0.95

Uses the method or tool of 6 papers

Another advantage of ([ref]) is that, written in this way, we can now massage the expression into a max flow program using the same techniques developed in [ref] , which will be our main goal for the rest of this section.

Riemannian and Lorentzian flow-cut theorems · Proof via convex optimization · 0.91
The general idea of our proofs is to first reduce our quantum setup into a classical one via a projective mapping, then apply the theorems of [ref] to the effective classical problem and, finally, map the solution back to the original quantum setup.

Bit Threads and Holographic Monogamy · Properties of quantum bit threads · 0.82
For $Δ>d/2$, the term proportional to $τ_αβ^(1)$ gives the leading normalizable behavior, and the GKPW recipe [ref] leads to the standard result (after appropriate holographic renormalization [ref] ) ⟨T_αβ^CFT⟩=d L^d-1/16πG_Nτ_αβ^(1)(t,x⃗) , so δE_A^grav=d L^d-1/8 G_N∫_A R^2-(x⃗-x⃗_c)^2/2R τ_αβ^(1)(t,x⃗) d^d-1x=δ⟨H_A⟩ .

Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence · ii) Dictionary for $δE_A^grav$ · 0.80

Compares with 3 papers

Even though ([ref]) can be regarded as a linear perturbation of the metric, we emphasize that the perturbative states we are considering here are very different in nature to the states that were studied in [ref] .

Bit threads, Einstein's equations and bulk locality · Perturbative quantum states · 0.98
This is a sufficient condition in our proof, however, it certainly seems stronger than bulk MMI (see, however [ref] ).

Quantum Extremal Surfaces and the Holographic Entropy Cone · Discussion · 0.88
Note added: While we were at the final stages of writing up our paper we became aware of the work of [ref] whose results partially overlap with ours.

Quantum bit threads · Discussion · 0.97

Cites as support 2 papers

However, due to the minimality condition, these corrections do not affect the area [ref] so both formulas give the same result at $𝒪(G_N^0)$, i.e., S[A] = γ̃_A∼Amin[A(γ̃_A)/4 G_N + S_bulk[Σ̃_A]]≈γ_A∼Amin[A(γ_A)/4 G_N] + S_bulk[Σ_A] .

Bulk entanglement entropy in perturbative excited states · Setup and organization of the paper · 0.96
However, due to the minimality condition, these corrections do not affect the area [ref] so both formulas give the same result at $𝒪(G_N^0)$, i.e., S[A] = γ̃_A∼Amin[A(γ̃_A)/4 G_N + S_bulk[Σ̃_A]]≈γ_A∼Amin[A(γ_A)/4 G_N] + S_bulk[Σ_A] .

Local quenches, bulk entanglement entropy and a unitary Page curve · Setup and organization of the paper · 0.96

Cites as background 69 papers

Let us start by reviewing the main results of [ref] , regarding.

Bit threads, Einstein's equations and bulk locality · Classical excited states and vacuum Einstein's equations · 0.91
S[A] = γ_A∼Amin[A(γ_A)/4 G_N] + S_bulk[Σ_A] , which is known as the Faulkner-Lewkowycz-Maldacena (FLM) formula [ref] .

Quantum corrections to holographic entanglement entropy · Setup and organization of the paper · 0.89
A more accurate prescription, valid beyond leading order in $G_N$ is given by the Quantum Extremal Surface (QES) formula, proposed by Engelhardt and Wall [ref] .

Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime · Setup and organization of the paper · 0.89

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