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Quantum Information Approaches to Quantum Gravity
High Energy Physics - Theory · Submitted 29 Sep 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This thesis presents refinements of a duality between operator product expansion (OPE) blocks in the CFT, giving the contribution of a conformal family to the OPE, and geodesic integrated fields in AdS which are diffeomorphism invariant quantities.
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The abstract, sentence by sentence
In this thesis we apply techniques from quantum information theory to study quantum gravity within the framework of the anti-de Sitter / conformal field theory correspondence (AdS/CFT). Through AdS/CFT, progress has been made in understanding the structure of entanglement in quantum field theories, and in how gravitational physics can emerge from these structures. However, this understanding is far from complete and will require the development of new tools to quantify correlations in CFT. This thesis presents refinements of a duality between operator product expansion (OPE) blocks in the CFT, giving the contribution of a conformal family to the OPE, and geodesic integrated fields in AdS which are diffeomorphism invariant quantities. This duality was originally discovered in the maximally symmetric setting of pure AdS dual to the CFT ground state. In less symmetric states the duality must be modified. Working with excited states within AdS$_3$/CFT$_2$, this thesis shows how the OPE block decomposes into more fine-grained CFT observables that are dual to AdS fields integrated over non-minimal geodesics. Additionally, this thesis contains results on the dynamics of entanglement measures for general quantum systems. Results are presented for the family of quantum R\'enyi entropies and entanglement negativity. R\'enyi entropies are studied for general dynamics by imposing special initial conditions. Around pure, separable initial states, all R\'enyi entropies grow with the same timescale at leading, and next-to-leading order. Mathematical tools are developed for the differentiation of non-analytic matrix functions with respect to constrained arguments and are used to construct analytic expressions for derivatives of negativity. We establish bounds on the rate of change of state distinguishability and the rate of entanglement growth for closed systems. Note: Abstract shortened.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this thesis we apply techniques from quantum information theory to study quantum gravity within the framework of the anti-de Sitter / conformal field theory correspondence (AdS/CFT). | contribution 0.90 | 0.88 | 0.06 | asserted 0.96 |
| s1 | Through AdS/CFT, progress has been made in understanding the structure of entanglement in quantum field theories, and in how gravitational physics can emerge from these structures. | background 1.00 | 0.07 | 0.07 | asserted 0.98 |
| s2 | However, this understanding is far from complete and will require the development of new tools to quantify correlations in CFT. | gap 0.98 | 0.07 | 0.04 | asserted 0.92 |
| s3 | This thesis presents refinements of a duality between operator product expansion (OPE) blocks in the CFT, giving the contribution of a conformal family to the OPE, and geodesic integrated fields in AdS which are diffeomorphism invariant quantities. | contribution 0.97 | 0.86 | 0.25 | asserted 1.00 |
| s4 | This duality was originally discovered in the maximally symmetric setting of pure AdS dual to the CFT ground state. | background 0.99 | 0.06 | 0.03 | asserted 1.00 |
| s5 | In less symmetric states the duality must be modified. | background 0.57 | 0.09 | 0.03 | asserted 0.96 |
| s6 | Working with excited states within AdS$_3$/CFT$_2$, this thesis shows how the OPE block decomposes into more fine-grained CFT observables that are dual to AdS fields integrated over non-minimal geodesics. | result 0.60 | 0.95 | 0.21 | asserted 1.00 |
| s7 | Additionally, this thesis contains results on the dynamics of entanglement measures for general quantum systems. | contribution 1.00 | 0.88 | 0.07 | asserted 0.99 |
| s8 | Results are presented for the family of quantum R\'enyi entropies and entanglement negativity. | contribution 0.88 | 0.83 | 0.07 | asserted 0.96 |
| s9 | R\'enyi entropies are studied for general dynamics by imposing special initial conditions. | method 0.70 | 0.82 | 0.05 | asserted 0.95 |
| s10 | Around pure, separable initial states, all R\'enyi entropies grow with the same timescale at leading, and next-to-leading order. | result 1.00 | 0.88 | 0.08 | asserted 1.00 |
| s11 | Mathematical tools are developed for the differentiation of non-analytic matrix functions with respect to constrained arguments and are used to construct analytic expressions for derivatives of negativity. | method 0.88 | 0.93 | 0.04 | asserted 1.00 |
| s12 | We establish bounds on the rate of change of state distinguishability and the rate of entanglement growth for closed systems. | result 0.94 | 0.94 | 0.12 | asserted 1.00 |
| s13 | Note: Abstract shortened. | limitation 1.00 | 0.11 | 0.01 | asserted 0.73 |
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Original abstract
In this thesis we apply techniques from quantum information theory to study quantum gravity within the framework of the anti-de Sitter / conformal field theory correspondence (AdS/CFT). Through AdS/CFT, progress has been made in understanding the structure of entanglement in quantum field theories, and in how gravitational physics can emerge from these structures. However, this understanding is far from complete and will require the development of new tools to quantify correlations in CFT. This thesis presents refinements of a duality between operator product expansion (OPE) blocks in the CFT, giving the contribution of a conformal family to the OPE, and geodesic integrated fields in AdS which are diffeomorphism invariant quantities. This duality was originally discovered in the maximally symmetric setting of pure AdS dual to the CFT ground state. In less symmetric states the duality must be modified. Working with excited states within AdS$_3$/CFT$_2$, this thesis shows how the OPE block decomposes into more fine-grained CFT observables that are dual to AdS fields integrated over non-minimal geodesics. Additionally, this thesis contains results on the dynamics of entanglement measures for general quantum systems. Results are presented for the family of quantum R\'enyi entropies and entanglement negativity. R\'enyi entropies are studied for general dynamics by imposing special initial conditions. Around pure, separable initial states, all R\'enyi entropies grow with the same timescale at leading, and next-to-leading order. Mathematical tools are developed for the differentiation of non-analytic matrix functions with respect to constrained arguments and are used to construct analytic expressions for derivatives of negativity. We establish bounds on the rate of change of state distinguishability and the rate of entanglement growth for closed systems. Note: Abstract shortened.
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What it cites · 279 sentences without a confident label
Builds on 1 paper
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To confirm this suspicion we now consider the holographic dictionary entry relating OPE blocks and bulk fields integrated over geodesics that was established in [ref] , and find that partial OPE blocks are dual to bulk fields integrated over individual minimal or non-minimal geodesics.
A Stereoscopic Look into the Bulk · Discussion · 0.87
Uses the method or tool of 4 papers
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In turn, the asymptotic map $f(z)$ can be extended into the bulk using [ref] [equation] which gives the full map between [ref] and [ref].
Time evolution of entanglement entropy from a pulse · Euclidean AdS · 0.88
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Instead, in Chapter [ref] the excited CFT states were lifted to vacuum states of a covering space CFT on an $N$-times longer circle parametrized by $ϕ$ [ref] .
Entwinement and the emergence of spacetime · OPE blocks and kinematic space · 0.86
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We will be making use of powerful maps that relate pure AdS$_3$ to other locally AdS$_3$ geometries [ref] .
Three-dimensional quantum geometry and black holes · Euclidean AdS · 0.92
Compares with 8 papers
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We show that the differential entropy approach [ref] , and the quotient approach [ref] produce different fundamental regions of the same kinematic space, but are entirely equivalent.
Integral Geometry and Holography · Kinematic space from the bulk · 0.84
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We show that the differential entropy approach [ref] , and the quotient approach [ref] produce different fundamental regions of the same kinematic space, but are entirely equivalent.
Kinematic Space and Wormholes · Kinematic space from the bulk · 0.84
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Indeed, [ref] exactly matches the main result of [ref] when we account for the difference in the definitions of the purity and Rényi entropy.
The Entanglement Timescale · The entanglement timescale for Rényi entropies · 0.99
Cites as support 6 papers
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This motivates the interpretation of an OPE block as a negative mass scalar field propagating freely on kinematic space [ref] ,
A Stereoscopic Look into the Bulk · OPE blocks · 0.98
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The new quantities $ℬ^ij_k,m$ are each defined as a sum over vacuum OPE blocks which are known to be convergent inside correlation functions [ref] , but any required normalization has been neglected above.
Remarks on the Convergence Properties of the Conformal Block Expansion · Euclidean analysis · 0.96
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The new quantities $ℬ^ij_k,m$ are each defined as a sum over vacuum OPE blocks which are known to be convergent inside correlation functions [ref] , but any required normalization has been neglected above.
OPE Convergence in Conformal Field Theory · Euclidean analysis · 0.96
Cites as background 94 papers
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Full details can be found in [ref] .
A Stereoscopic Look into the Bulk · Duality between OPE blocks and geodesic integrals of bulk fields · 0.91
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Kinematic space has been defined as the space of pairs of CFT points, or equivalently as the space of boundary anchored geodesics in pure AdS [ref] .
Entanglement, Holography and Causal Diamonds · OPE blocks and kinematic space · 0.90
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A useful auxiliary space termed kinematic space has been introduced describing the structure of geodesics while also geometrizing entanglement entropy [ref] .
Integral Geometry and Holography · Introduction · 0.93
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