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

该 NSF 奖项旨在解决量子信息中有关熵不等式的基本问题，例如量子相对熵的单调性和强次可加性。这些熵不等式是量子信息和更普遍的物理学的核心，是量子通信通道的各种能力、熵不确定性原理和热力学第二定律的某些表述的基础。自 Lieb、Ruskai 和 Lindblad 在 20 世纪 70 年代证明这些熵不等式以来的 40 年来以及自 Petz 在 1980 年代描述其等式条件以来的 30 年来，PI Wilde 及其合作者最近对这些熵不等式进行了最严格的改进。这些改进对原始熵不等式适用的某些设置中的可恢复性和马尔可夫性进行了解释。PI 配备了这些新定理和其他工具，将解决有关量子系统中可恢复性和马尔可夫性的基本问题。在细化的熵不等式出现之前，这些问题一直在等待答案。由于量子相对熵的使用在整个量子信息中如此广泛，因此在可恢复性和马尔可夫性方面有广阔的领域需要探索，这可能会带来对量子信息本质的基本见解。鉴于马尔可夫性和可恢复性是渗透到所有科学领域的基本概念，利用该 NSF 奖项开展的工作也可能会影响物理学的其他领域。该提案的更广泛影响符合 NSF 的使命“促进科学进步；促进国民健康、繁荣和福利；确保国防；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显着的方式推动了科学的发展，突破了原则和实践中可能的极限。该提案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.