标题： 贝肯斯滕边界对于近似局域带电态的限制 显示英文标题

标题： Bekenstein Bound for Approximately Local Charged States

摘要： 我们将其中一人在量子场论（QFT）中建立的能量-熵比不等式从局域化态推广到更大一类态。本文所考虑的态可以处于QFT的带电（非真空）表示中，也可能只是近似局域于所考虑的区域。 我们的不等式是$S(\Psi |\!| \Omega) \le 2\pi R \, ( \Psi, H_\rho \Psi ) + \log d(\rho) + \varepsilon$，其中$S$是相对熵，$R$是一个“半径”（宽度），用于表征区域的大小， $d(\rho)$是给定带电扇区的统计（量子）维数， $\rho$所处的量子态为$\Psi$，$\Omega$是真空态，$H_\rho$是带电扇区中的哈密顿量，而$\varepsilon$是一个容差，用于根据区域因果补集中的观察者测量$\Psi$偏离真空的程度。 显示英文摘要

摘要： 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 $S(\Psi |\!| \Omega) \le 2\pi R \, ( \Psi, H_\rho \Psi ) + \log d(\rho) + \varepsilon$, where $S$ is the relative entropy, where $R$ is a "radius" (width) characterizing the size of the region, $d(\rho)$ is the statistical (quantum) dimension of the given charged sector $\rho$ hosting the quantum state $\Psi$, $\Omega$ is the vacuum state, $H_\rho$ is the Hamiltonian in the charged sector, and $\varepsilon$ is a tolerance measuring the deviation of $\Psi$ from the vacuum according to observers in the causal complement of the region.