#### Theory Seminar

# CSPL/Theory Seminar: Zero-error classical capacity of noisy quantum channels

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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 will study the quantum counterpart of this notion within the following communication framework: m senders want to transmit classical information to n receivers with zero probability of error using a noisy 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 perfectly 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.

For the case of m=1 and n=1, we propose a weaker notion of error-free classical capacity to describe the ability of a quantum channel to transmit classical information unambiguously. Then we construct explicitly a quantum channel that has positive error-free classical capacity but only when entangled input states are allowed.

We further examine the effect of additional resources such as shared entanglement between the sender and the receiver, classical feedback, and quantum feedback. We find these resources are extremely useful as they not only can dramatically increase both the zero-error and error-free capacities, but also can greatly simplify the calculation of these capacities in many cases.

This talk is based on some recent joint works with Yaoyun Shi (University of Michigan).

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: http://arxiv.org/abs/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.