Modular energy inequalities from relative entropy

Abstract

We obtain new constraints for the modular energy of general states by using the monotonicity property of relative entropy. In some cases, modular energy can be related to the energy density of states and these constraints lead to interesting relations between energy and entropy. In particular, we derive new quantum energy inequalities that improve some previous bounds for the energy density of states in a conformal field theory. Additionally, the inequalities derived in this manner also lead us to conclude that the entropy of the state further restricts the possible amount of negative energy allowed by the theory.

23 pages, 9 figures

References in corpus (8)

• Towards a derivation of holographic entanglement entropy
• Relative entropy and the Bekenstein bound
• Entanglement hamiltonians in two-dimensional conformal field theory
• Proof of a Quantum Bousso Bound
• Entropy on a null surface for interacting quantum field theories and the Bousso bound
• Local temperatures and local terms in modular Hamiltonians
• Lectures on quantum energy inequalities
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Cited by in corpus (18)

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• Modular Hamiltonians in flat holography and (W)AdS/WCFT
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• Surface Theory: the Classical, the Quantum, and the Holographic
• The Return of the Singularities: Applications of the Smeared Null Energy Condition
• Resolving modular flow: a toolkit for free fermions
• Entanglement of a chiral fermion on the torus
• Properties of Modular Hamiltonians on Entanglement Plateaux
• Explicit reconstruction of the entanglement wedge via the Petz map
• Modular conjugation for multicomponent regions
• Rényi entropies of the massless Dirac field on the torus
• Holography of negative energy states
• Localized thermal states and negative energy
• Virasoro algebras, kinematic space and the spectrum of modular Hamiltonians in CFT${}_2$
• Petz-Rényi relative entropy in QFT from modular theory
• Rényi entropy of single-character CFTs on the torus
• Bekenstein bound in the bulk and AdS/CFT