Girolami Davide, Tufarelli Tommaso, Susa Cristian E
Department of Atomic and Laser Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom.
School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
Phys Rev Lett. 2017 Oct 6;119(14):140505. doi: 10.1103/PhysRevLett.119.140505.
We propose an information-theoretic framework to quantify multipartite correlations in classical and quantum systems, answering questions such as what is the amount of seven-partite correlations in a given state of ten particles? We identify measures of genuine multipartite correlations, i.e., statistical dependencies that cannot be ascribed to bipartite correlations, satisfying a set of desirable properties. Inspired by ideas developed in complexity science, we then introduce the concept of weaving to classify states that display different correlation patterns, but cannot be distinguished by correlation measures. The weaving of a state is defined as the weighted sum of correlations of every order. Weaving measures are good descriptors of the complexity of correlation structures in multipartite systems.
我们提出了一个信息论框架来量化经典和量子系统中的多方关联，回答诸如在十个粒子的给定状态下七方关联的量是多少这样的问题。我们确定了真正多方关联的度量，即不能归因于两方关联的统计依赖性，并满足一组理想的性质。受复杂性科学中发展的思想启发，我们接着引入了编织的概念，以对呈现不同关联模式但无法通过关联度量区分的状态进行分类。一个状态的编织被定义为每个阶次关联的加权和。编织度量是多方系统中关联结构复杂性的良好描述符。
