Operational Quantum Mereology: an Information Scrambling Approach

将一个物理系统划分为更小的部分的能力是科学还原论方法的一个关键方面。它使人们能够理解复杂系统的基本行为，简单的组件及其相互关系和动态相互作用。对于量子系统，这种划分可以通过多种方式进行，这取决于可用的实验资源、操作约束和追求的目标。该项目的目的是为量子“子系统”的最佳选择开发一个统一的概念和数学框架。这将有助于量子科学的进步，并可能有助于变革性的新型量子技术的部署。该项目还有重要的教育和培训部分，因为研究生将主要参与其中。这将有助于他们未来加入国家、学术和工业的量子劳动力队伍。技术方法将基于“信息加扰”的概念，这是信息最初编码在一组确定的和局部的自由度上的方式，通过其在越来越大的和非局部的自由度上的不可控制的传播而迅速“丢失”。一个新的数学工具的工具包将被设计成定量测量的字符，速度和强度的这种扰乱过程。一旦实现了这一点，这些工具将被部署，以确定最佳的划分感兴趣的许多身体系统的部分的基础上最小的混乱标准。后者在概念上是一种“最小熵产生”原则，告诉我们“涌现”的子系统是那些对环境噪音更有弹性的子系统，然后可以最长时间地保持它们的信息身份。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The ability of dividing a physical system into its smaller parts is a key aspect of the scientific reductionist method. It allows one to understand the behavior of complex systems in terms of fundamental, simpler components and their interrelations and dynamical interactions. For quantum systems this division can be performed in a multitude of ways depending on the experimental resources available, the operational constraints and on the pursued objectives. The aim of this project is the development of a unified, conceptual and mathematical, framework for the optimal selection of quantum "subsystems”. This will help the progress of Quantum Sciences and possibly the deployment of transformative novel quantum technologies. The project has also important educational and training components as it will involve, in an essential fashion, graduate students. This will facilitate their future enrollment into the national, academic as well industrial, quantum workforces.The technical approach will be based on the notion of "information scrambling” which is the way in which information, initially encoded on a definite and localized set of degrees of freedoms, gets quickly "lost” by its uncontrollable spreading over an increasingly large and delocalized set of degrees of freedom. A toolkit of novel mathematical tools will be designed to quantitatively measure the character, the speed and strength of this scrambling processes. Once this is achieved, the tools will be deployed to determine the optimal division of interesting many body systems into parts based on a minimal scrambling criterion. The latter is conceptually a sort of “minimal entropy production” principle telling us that the "emergent” subsystems are those more resilient to environmental noise and can then preserve their informational identity for the longest times.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.