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arXiv · 2501.03849

Bekenstein Bound for Approximately Local Charged States

Stefan Hollands·Roberto Longo
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Abstract

We generalize the energy-entropy ratio inequality in quantum field theory (QFT) established by one of us from localized states to a larger class of states. The states considered in this paper can be in a charged (non-vacuum) representation of the QFT or may be only approximately localized in the region under consideration. Our inequality is $S(Ψ|\!| Ω) \le 2πR \, ( Ψ, H_ρΨ) + \log d(ρ) + \varepsilon$, where $S$ is the relative entropy, where $R$ is a "radius" (width) characterizing the size of the region, $d(ρ)$ is the statistical (quantum) dimension of the given charged sector $ρ$ hosting the quantum state $Ψ$, $Ω$ is the vacuum state, $H_ρ$ is the Hamiltonian in the charged sector, and $\varepsilon$ is a tolerance measuring the deviation of $Ψ$ from the vacuum according to observers in the causal complement of the region.

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Stefan Hollands, Roberto Longo. 2025-01-07. Bekenstein Bound for Approximately Local Charged States. https://arxiv.org/abs/2501.03849

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