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

Louisiana State University, Baton Rouge LA

Investigators

Abstract

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.