标题： 最大最小是不够的 显示英文标题

标题： Maximin is Not Enough

摘要： 静态时空的RT公式在AdS/CFT对应中满足一些不等式，这些不等式在HRT公式的情况下尚未被证明，HRT公式适用于一般的动态时空。 瓦尔的极大极小构造是将全息纠缠熵的不等式从静态情况扩展到动态情况的唯一已知技术。 我们表明，当处理五个或更少区域的不等式时，这种方法目前没有进一步的用途。 尽管有这个负面结果，我们提出了一个关于五个区域的协变全息纠缠熵的新不等式的有效性。 这个不等式虽然不能通过极大极小方法证明，但比RT公式满足的许多不等式要弱得多，因此应该更容易证明。 如果它有效，那么就有强有力的证据表明，全息纠缠熵在包括宇宙学中出现的时空中起着作用。 我们的新不等式是通过假设HRT公式满足由经典概率分布的香农熵所遵循的每一个已知的平衡不等式而得到的。 这是RT公式已被证明具有的性质，并且之前曾推测该性质在一般量子力学中成立。 显示英文摘要

摘要： The RT formula for static spacetimes arising in the AdS/CFT correspondence satisfies inequalities that are not yet proven in the case of the HRT formula, which applies to general dynamical spacetimes. Wall's maximin construction is the only known technique for extending inequalities of holographic entanglement entropy from the static to dynamical case. We show that this method currently has no further utility when dealing with inequalities for five or fewer regions. Despite this negative result, we propose the validity of one new inequality for covariant holographic entanglement entropy for five regions. This inequality, while not maximin provable, is much weaker than many of the inequalities satisfied by the RT formula and should therefore be easier to prove. If it is valid, then there is strong evidence that holographic entanglement entropy plays a role in general spacetimes including those that arise in cosmology. Our new inequality is obtained by the assumption that the HRT formula satisfies every known balanced inequality obeyed by the Shannon entropies of classical probability distributions. This is a property that the RT formula has been shown to possess and which has been previously conjectured to hold for quantum mechanics in general.