New Research on the Resource Theory of Quantum Channels

The research achievement has been reported in the official website of SIQSE.

Recent research by a team at Southern University of Science and Technology (SUSTech) introduced a new resource theory of quantum channels and applied it to study communication over quantum channels.

Shenzhen Institute for Quantum Science and Engineering (SIQSE) Chief Research Scientist and Institute of Electrical and Electronic Engineers (IEEE) Fellow Masahito Hayashi worked with his collaborators to introduce a new resource theory of quantum channels relevant to communication scenarios. The research was published in the high-impact academic journal Physical Review Letters (PRL) under the title, “Application of the Resource Theory of Channels to Communication Scenarios”.

Quantum resource theories offer a highly versatile and powerful framework for studying different phenomena in quantum physics. However, a common criticism is that the framework often ends up with a formalistic level not solving existing problems. In particular, it has been elusive whether the resource theory of quantum channels would be helpful for answering concrete problems at all.

On the other hand, entanglement-assisted information transmission via quantum channel has been a major field of research in quantum information theory at all times. Its central goal is to understand how much of the resources are required to accomplish the desired information transmission by utilizing quantum entanglement.

Quantum entanglement is known as a resource of magical power of quantum system. The aim clarifies how entanglement enhances information transmission, while analyzing this improvement is notoriously difficult due to their complex structures. This motivates the question of whether we can adopt the quantum resource theory framework to investigate the improvement of information transmission by using entanglement, consolidating it as effective tools to solve concrete problems.

Masahito Hayashi and his collaborators took the first step in this direction. They introduced the resource theory of communication, a resource theory of channels relevant to communication via quantum channels. With this formalism, they successfully characterized fundamental properties of a quantum channel as a communication mean: how much information the channel can reliably send (channel capacity) under the efficient use of entanglement and how hard it is to effectively implement the channel (channel simulation cost).

The introduced framework allowed them to employ several novel ideas and techniques that have recently been developed in the study of resource theories to address the “classic” problems in quantum information theory. In particular, they extended the results on the operational characterization of resource theories and obtained an important property known as the strong converse property, which shows the ultimate limitation of the amount of information transmission under the efficient use of entanglement, as well as characterized its channel simulation cost by formulating it as a resource transformation task in the proposed resource theory.

They further showed that their resource theory has an intimate connection to the communication with help of ultimate correlation allowed by causal theories respecting the theory of relativity, suggesting that their framework may serve as an effective theoretical platform to investigate fundamental limitation of communication over quantum channels.

This research shed new perspective to fundamental problems in quantum Shannon theory while lifting the resource theory of channels to effective tools in addressing concrete problems. The technique formalized is extendable to more generic settings thanks to the systematic nature of the resource theory framework.

Ryuji Takagi, a Ph.D. student at Massachusetts Institute of Technology (MIT), was the first author of the paper. Ryuji Takagi, Kun Wang (SIQSE), and Masahito Hayashi were the corresponding authors. SUSTech was the second affiliation.

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