Institute for Quantum Studies, Chapman University, Orange, CA 92866;
Schmid College of Science and Technology, Chapman University, Orange, CA 92866.
Proc Natl Acad Sci U S A. 2018 Nov 13;115(46):11730-11735. doi: 10.1073/pnas.1807554115. Epub 2018 Oct 22.
Can a large system be fully characterized using its subsystems via inductive reasoning? Is it possible to completely reduce the behavior of a complex system to the behavior of its simplest "atoms"? In this paper we answer these questions in the negative for a specific class of systems and measurements. After a general introduction of the topic, we present the main idea with a simple two-particle example, where strong correlations arise between two apparently empty boxes. This leads to surprising effects within atomic and electromagnetic systems. A general construction based on pre- and postselected ensembles is then suggested, wherein the N-body correlation can be genuinely perceived as a global property, as long as one is limited to performing measurements which we term "strictly local." We conclude that under certain boundary conditions, higher-order correlations within quantum mechanical systems can determine lower-order ones, but not vice versa. Surprisingly, the lower-order correlations provide no information whatsoever regarding the higher-order correlations. This supports a top-down structure in many-body quantum mechanics.
能否通过归纳推理，仅用子系统来充分描述一个大系统？能否将一个复杂系统的行为完全简化为其最简单的“原子”行为？在本文中，我们针对特定类别的系统和测量，对这些问题给出否定的答案。在一般性介绍主题之后，我们用一个简单的双粒子例子展示了主要思想，其中两个看似空的盒子之间会出现强烈的相关性。这会在原子和电磁系统中产生令人惊讶的效应。然后，我们提出了一种基于预选择和后选择集合的一般构造，其中只要限于进行我们称之为“严格局部”的测量，N 体相关性就可以真正被视为全局属性。我们的结论是，在某些边界条件下，量子力学系统中的高阶相关性可以决定低阶相关性，但反之则不然。令人惊讶的是，低阶相关性对于高阶相关性没有提供任何信息。这支持了多体量子力学中的自上而下的结构。
