Zero-Error Classical Capacity of Noisy Quantum Channels
Friday, March 21 at 10:50am
Abstract: In 1956 Shannon introduced the notion of zero-error capacity to characterize the ability of noisy channels to transmit classical information with zero probability of error. The study of this notion and the related topics has since then grown into a vast field called zero-error information theory. In this talk we shall study the quantum counterpart of this notion in multipartite communication scenario, where $m$ senders want to transmit classical information to $n$ receivers with zero probability of error using a noisy multipartite communication channel. The senders are allowed to exchange classical, but not quantum, messages among themselves, and the same holds for the receivers. It is well known that if the channel is classical, a single use can transmit information if and only if multiple uses can. In sharp contrast, we exhibit, for each $m$ and $n$ with $m>1$ or $n>1$, a quantum channel of which a single use is not able to transmit information yet two uses can. This latter property requires and is enabled by quantum entanglement. The existence of such quantum channel in the case of $m=1$ and $n=1$ remains an intriguing open problem.
Reference: Runyao Duan and Yaoyun Shi, Entanglement between two uses of a noisy multipartite quantum channel enables perfect transmission of classical information, 2007. Available online: arXiv 0712.3700.
Runyao Duan received the B.S./M.S./Ph.D. degrees from the Department of Computer Science and Technology, Tsinghua University, Beijing, China in the year of 2002/2004/
2006 respectively. He is now an assistant professor at the Department of Computer Science and Technology, Tsinghua University. His current research interests include theoretical computer science, quantum computation and quantum information theory.