Variational approach to relative entropies with an application to QFT

Hollands, Stefan

doi:10.1007/s11005-021-01474-2

Cited by 6 publications

(7 citation statements)

References 38 publications

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“…Indeed, we avoid talking about the analog of AB \ B at all, because in our applications it is not necessarily associated to an algebra. In line with this, our notation starting in this subsection is to denote the joint algebra as simply A. Additionally, entropic certainty relations closely related to duality (Theorem 2.33) were proven for von Neumann algebras in [32] and an asymptotic equipartition principle (Theorem 2.34) was proven for the max-relative entropy in any von Neumann algebra in [33].…”

Section: One-shot Entropies For Von Neumann Algebrasmentioning

confidence: 99%

One-shot holography

Akers,

Levine,

Penington

et al. 2024

SciPost Phys.

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Following the work of [J. High Energy Phys. 04, 062 (2021)], we define a generally covariant max-entanglement wedge of a boundary region B, which we conjecture to be the bulk region reconstructible from B. We similarly define a covariant min-entanglement wedge, which we conjecture to be the bulk region that can influence the state on B. We prove that the min- and max-entanglement wedges obey various properties necessary for this conjecture, such as nesting, inclusion of the causal wedge, and a reduction to the usual quantum extremal surface prescription in the appropriate special cases. These proofs rely on one-shot versions of the (restricted) quantum focusing conjecture (QFC) that we conjecture to hold. We argue that these QFCs imply a one-shot generalized second law (GSL) and quantum Bousso bound. Moreover, in a particular semiclassical limit we prove this one-shot GSL directly using algebraic techniques. Finally, in order to derive our results, we extend both the frameworks of one-shot quantum Shannon theory and state-specific reconstruction to finite-dimensional von Neumann algebras, allowing nontrivial centers.

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Section: One-shot Entropies For Von Neumann Algebrasmentioning

confidence: 99%

One-shot holography

Akers,

Levine,

Penington

et al. 2024

SciPost Phys.

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“…Such properties of local algebras are not necessarily required by causality and consistency under restriction to smaller regions. Order parameters based on the relative entropy have been developed to probe these superselection sectors [244,245]; see also [246,247]. Generalized global symmetries can also be studied from this perspective [248].…”

Section: Symmetries Charges and Superselection Sectorsmentioning

confidence: 99%

Snowmass white paper: Quantum information in quantum field theory and quantum gravity

Faulkner¹,

Hartman²,

Headrick³

et al. 2022

Preprint

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We present a summary of recent progress and remaining challenges in applying the methods and ideas of quantum information theory to the study of quantum field theory and quantum gravity. Important topics and themes include: entanglement entropy in QFTs and what it reveals about RG flows, symmetries, and phases; scrambling, information spreading, and chaos; state preparation and complexity; classical and quantum simulation of QFTs; and the role of information in holographic dualities. We also highlight the ways in which quantum information science benefits from the synergy between the fields.

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“…The certainty relation was first found in QFT's with global symmetries [1]. It was then proven in generic inclusions of type I algebras in [2], and shortly after extended to type III algebras [22]. The entropic order parameters were used to characterize global symmetries in [1], an approach which we use below.…”

Section: Jhep12(2021)100mentioning

confidence: 99%

“…This is one of the main results in ref. [1], see also [22] for a more rigorous derivation within the context of type III algebras. They constitute yet different equivalent versions of the previous theorem, which is now seen as being controlled by properties of the vacuum alone.…”

Section: Jhep12(2021)100 5 Equipartition Of Entropy In Qft Ee and The Vacuum Sectormentioning

confidence: 99%

Proof of the universal density of charged states in QFT

Magán

2021

J. High Energ. Phys.

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We prove a recent conjecture by Harlow and Ooguri concerning a universal formula for the charged density of states in QFT at high energies for global symmetries associated with finite groups. An equivalent statement, based on the entropic order parameter associated with charged operators in the thermofield double state, was proven in a previous article by Casini, Huerta, Pontello, and the present author. Here we describe how the statement about the entropic order parameter arises, and how it gets transformed into the universal density of states. The use of the certainty principle, relating the entropic order and disorder parameters, is crucial for the proof. We remark that although the immediate application of this result concerns charged states, the origin and physics of such density can be understood by looking at the vacuum sector only. We also describe how these arguments lie at the origin of the so-called entropy equipartition in these type of systems, and how they generalize to QFT’s on non-compact manifolds.

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Variational approach to relative entropies with an application to QFT

Cited by 6 publications

References 38 publications

One-shot holography

One-shot holography

Snowmass white paper: Quantum information in quantum field theory and quantum gravity

Proof of the universal density of charged states in QFT

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