Dynamical Systems in Quantum Information Theory

University Of Houston, Houston TX

Investigators

Abstract

The subject of this project is quantum information theory, which is a crucial ingredient for the development of meaningful quantum technologies. Quantum devices use quantum systems, such as electrons, atoms, photons, to encode and process information. They make it possible to harness the effects of purely quantum phenomena such as superposition (the ability of being in "two places" at once) and entanglement (extremely strong connections between two, often quite remote, parts of the system) in order to drastically increase the security and speed of computational devices such as quantum computer. While entanglement became one of the most valuable resources in quantum theory, many of its attributes remain unknown. At present, one of the main technological challenges in quantum information arises from the destructive effects of environment, the effect known as decoherence. Decoherence is a partial loss of quantum information through a channel, in other words, the introduction of noise into the communication. This project will contribute to understanding how these losses may be theoretically predicted and minimized. Students at different levels will be trained through participation in this project. Another educational objective of the project is to promote STEM subjects and improve educational opportunities for students in Houston, TX, middle and high schools, with?main focus on economically disadvantaged neighborhoods. Two, often overlapping, research directions will be pursued in this project: quantum information theoretic inequalities and dynamics of quantum systems. Quantum information theoretic inequalities, such as monotonicity of quantum relative entropy and strong subadditivity of entropy, are at the core of providing a framework for what is theoretically possible to achieve in quantum information. Dynamics of open quantum systems describing the effects of the environment is notoriously challenging and vital problem. The principal goals of the project are: (i) to improve understanding of the role of entropy in the quantum setting through a sharpening of the monotonicity of different relative entropies as well as the formulation/derivation of quantum versions of classical information-theoretic inequalities; and (ii) to rigorously describe attributes of quantum entanglement by seeking upper bounds for the speed of generation of entanglement. This investigation is largely motivated by the need to understand and control the decoherence in quantum channels. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.