FET: Small: Frontiers of Quantum Shannon Theory

Cornell University, Ithaca NY

Investigators

Abstract

The goal of the award "Frontiers of Quantum Shannon Theory" is to pursue theoretical research in several domains of quantum information science. The main idea underlying all projects is to understand how much quantum information can be transmitted over a physical communication link. Quantum information refers to information that is useful for a quantum computer to process and store, and which can be helpful in realizing faster calculations than is possible with traditional computers. In reality, physical communication links introduce disturbances into the information that is transmitted over them, and it is necessary to perform correction procedures to recover that information. The benefit of this research to society is that it will lead to a greater understanding of how to process quantum information, which can ultimately be beneficial for tasks like distributed quantum computing or the exchange of secret information. Distributed quantum computation has the potential of performing calculations at a much faster pace than is possible with traditional computers. At the same time, the award will involve the training of several graduate students not only in the classroom but also in the research process, to be mentored by the investigator. More broadly, the investigator is a lead organizer of Cornell Quantum Day, a triannual event in which Cornell students and postdocs, and the surrounding research community, gather to present research results and engage in scientific discussions. During the summers, the investigator also takes on high school and undergraduate students into his research group to learn basic research skills and contribute to research projects in the form of programming and computer simulations of quantum information protocols and algorithms. In more detail, the project consists of several tasks to be pursued by the investigator. First, the investigator will research a phenomenon known as the superactivation effect, in which two quantum communication links can have an ability to send quantum information at a non-zero rate even if the two links have no ability to send quantum information on their own. Specifically, the investigator will consider this phenomenon in the non-asymptotic regime of a limited number of channel uses. Second, the investigator will research limitations of quantum communication over any physical link by means of a concept called joinability of quantum states. This concept of joinability is not meaningful in classical information theory, but it takes on a distinct meaning in quantum information theory due to the phenomenon of entanglement. The investigator will also research methods for calculating how much entanglement a given quantum state contains, by means of a method called k-extendibility. Specifically, the investigator will produce algorithms that exploit symmetry and representation theory to provide significant reductions in runtime for calculating measure of entanglement based on k-extendibility. Finally, the investigator will research a notion of communication capacity called probabilistic approximate capacity and obtain bounds on this quantity, as this concept aligns more naturally with the unideal states produced in experiments. 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.