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

CIF：小：CQIS：量子信息中的可恢复性和马尔可夫性

基本信息

批准号：
1714215
负责人：
Mark Wilde
金额：
$ 40.05万
依托单位：
Louisiana State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-09-01 至 2021-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1714215&HistoricalAwards=false
关键词：
CIF Small CQIS Recoverability Markovianity

项目摘要

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.

该NSF奖的目的是解决有关熵不平等的量子信息中的基本问题，例如量子相对熵的单调性和强大的亚热性。这些熵不平等是量子信息和更普遍的物理学的核心，其基础是量子通信渠道的各种能力，熵不确定性原理以及第二种热力学定律的某些表述。自从Lieb，Ruskai和Lindblad的40年中，Pi Wilde和合作者最近确立了这些熵不平等的最强改进，并在1970年代以及Petz以来的30年中证明了它们在1980年代的平等状况。这些改进在适用原始熵不平等的某些设置中具有可恢复性和马尔可道的解释。使用这些新定理和其他工具，PI将解决有关量子系统中有关可恢复性和马克维亚语的基本问题。这些问题一直在等待答案，然后才能获得精致的熵不平等。由于量子相对熵的使用在整个量子信息中都如此普遍，因此可以从可恢复性和马尔可维亚性方面进行广泛的领域，这可能会导致对量子信息本质的基本见解。鉴于马克维亚语和可恢复性是渗透到所有科学的基本观念，该提案的基本观念与NSF的更大影响相符，这与NSF的任务相符，以促进科学的进步；以促进国民健康，繁荣和福利；为了获得国防；为了获得国防；为了获得国防；确实，物理，计算机科学和数学交集的研究以非凡的方式提高了科学，从而推动了原则上和实践中可能的限制。该建议的主要目标是增强LSU研究生的培训。