Zero-error classical capacity of noisy quantum channels
Runyao Duan
Tsinghua University
Friday, March 21 at 10:50am
CSE 3941
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 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.
Short bio:
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.