@conference {2129, title = {Capacity Approaching Codes for Low Noise Interactive Quantum Communication}, booktitle = {Annual ACM Symposium on the Theory of Computing STOC 2018}, year = {2018}, month = {2018/01/01}, abstract = {
We consider the problem of implementing two-party interactive quantum
communication over noisy channels, a necessary endeavor if we wish to
fully reap quantum advantages for communication.\ \ 
For an arbitrary protocol with n messages, designed for
noiseless qudit channels, our main result is a simulation method that fails with probability less than
$2^{-\Theta(n\epsilon)}$ and uses a qudit channel $n(1 + \Theta
(\sqrt{\epsilon}))$ times, of which an $\epsilon$ fraction can be
corrupted adversarially.
The simulation is thus capacity achieving to leading order, and
we conjecture that it is optimal up to a constant factor in\ 
the $\sqrt{\epsilon}$ term.\ \ 
Furthermore, the simulation is in a model that does not require
pre-shared resources such as randomness or entanglement between the
communicating parties.
Surprisingly, this outperforms the best-known overhead of $1 +
O(\sqrt{\epsilon \log \log 1/\epsilon})$ in the corresponding
\emph{classical} model, which is also conjectured to be optimal
\  \  \ [Haeupler, FOCS\&$\#$39;14].
Our work also improves over the best previously known quantum result
where the overhead is a non-explicit large constant [Brassard \emph{et
\  \  al.}, FOCS\&$\#$39;14] for low $\epsilon$.
}, url = {http://acm-stoc.org/stoc2018/STOC-2018-Accepted.html}, author = {Debbie Leung and Ashwin Nayak and Ala Shayeghi and Dave Touchette and Penghui Yao and Nengkun Yu} }