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

该奖项旨在解决量子信息中关于熵不等式的基础问题，如量子相对熵的单调性和强次可加性。这些熵不平等是量子信息和更普遍的物理学的核心，是量子通信信道的各种能力、熵不确定性原理和热力学第二定律的某些公式的基础。自从Lieb、Ruskai和Lindblad在20世纪70年代证明了这些熵不等式以来的40年里，以及自从Petz在20世纪80年代描述了它们的相等条件以来的30年里，PI Wilde和合作者最近建立了这些熵不等式的最强大的改进。在原始熵不等式适用的某些设置中，这些改进在可恢复性和马尔可夫性方面有解释。拥有这些新定理和其他工具的PI将解决量子系统中有关可恢复性和马尔可夫性的基本问题。在精确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，这可能会导致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贯穿于所有科学领域的基本概念，这项与NSF奖相关的工作也可能影响物理学的其他领域。该提案的广泛影响符合NSF的使命“促进科学进步；促进国家的健康、繁荣和福利；巩固国防；还有其他目的。”事实上，物理学、计算机科学和数学交叉领域的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。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.