量子场论中任意定域代数间的通有Bell关联
Generic Bell correlation between arbitrary local algebras in quantum field theory
摘要：
证明了对任意两个可交换的无穷型冯诺依曼代数，这两个代数的Bell关联态的开集是范数稠密的。然后，我们将这一结果应用到代数量子场论-其中所有的本地代数是无限型-为了表明，对于任何两个类空分离的区域，有一个开放的密集的一组场状态，决定区域之间的贝尔相关。我们还证明了一对交换非交换冯诺依曼代数之一的任何向量状态循环是纠缠的（即，不可分）的代数-由此得出，每一个有界能量的场态都是纠缠在任何两个类空分离区域。
英文摘要：
We prove that for any two commuting von Neumann algebras of infinite type, the open set of Bell correlated states for the two algebras is norm dense. We then apply this result to algebraic quantum field theory -- where all local algebras are of infinite type -- in order to show that for any two spacelike separated regions, there is an open dense set of field states that dictate Bell correlations between the regions. We also show that any vector state cyclic for one of a pair of commuting nonabelian von Neumann algebras is entangled (i.e., nonseparable) across the algebras -- from which it follows that every field state with bounded energy is entangled across any two spacelike separated regions.
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