CIF: Small: CQIS: Recoverability and Markovianity in Quantum Information

该NSF奖旨在解决量子信息中有关熵不等的基本问题，如量子相对熵的单调性和强次可加性。这些熵不等是量子信息的核心，更广泛地说是物理学的核心，在量子通信通道的各种容量、熵不确定原理和热力学第二定律的某些公式的基础上。自20世纪70年代Lieb、Ruskai和Lindblad证明它们以来的40年里，以及自Petz在80年代表征它们的相等条件以来的30年里，Pi Wilde和他的合作者最近建立了这些熵不等式的最强精化。这些改进在最初的熵不等式所适用的某些设置下有关于可恢复性和马尔可夫性的解释。PI，配备了这些新的定理和其他工具，将解决关于量子系统中的可恢复性和马尔可夫性的基本问题。这些问题一直在等待答案，然后才能得到改进后的熵不等。由于量子相对熵的使用在整个量子信息中都是如此广泛，在可恢复性和马尔可夫性方面有一个广阔的领域需要探索，这可能会导致对量子信息本质的基本洞察。鉴于马尔可夫性和可恢复性是渗透到所有科学中的基本概念，与NSF奖一起开展的工作也可能影响到物理学的其他领域。这项提议的更广泛影响与NSF的使命是一致的，即促进科学进步；促进国家健康、繁荣和福利；保障国防安全；以及其他目的。事实上，物理学、计算机科学和数学的交叉研究以非凡的方式推动了科学的发展，在原则上和实践中都突破了可能的极限。这项提议的一个主要目标是加强路易斯安那州立大学研究生的培训。

This NSF award aims to address foundational questions in quantum information regarding entropy inequalities such as the monotonicity of quantum relative entropy and strong subadditivity. These entropy inequalities are at the core of quantum information and more generally physics, underlying various capacities of quantum communication channels, entropic uncertainty principles, and certain formulations of the second law of thermodynamics. PI Wilde and collaborators have recently established the strongest refinements of these entropy inequalities in the 40 years since Lieb, Ruskai, and Lindblad proved them in the 1970s and in the 30 years since Petz characterized their equality conditions in the 1980s. These refinements have interpretations in terms of recoverability and Markovianity in certain setups to which the original entropy inequalities apply.The PI, armed with these new theorems and other tools, will address fundamental questions regarding recoverability and Markovianity in quantum systems. These questions have been awaiting answers before the refined entropy inequalities were available. Since the use of quantum relative entropy is so widespread all throughout quantum information, there is a vast territory to explore in terms of recoverability and Markovianity, which may lead to fundamental insights into the nature of quantum information. The work developed with this NSF award may also influence other areas of physics, given that Markovianity and recoverability are such fundamental notions permeating all of science.The broader impact of this proposal is in line with the NSF Mission "to promote the progress of science; to advance the national health, prosperity, and welfare; to secure the national defense; and for other purposes." Indeed, research at the intersection of physics, computer science, and mathematics has advanced science in remarkable ways, pushing the limits of what is possible in principle and in practice. A major goal of this proposal is to enhance the training of graduate students at LSU.