Title  Capacity Approaching Codes for Low Noise Interactive Quantum Communication 
Publication Type  Conference Paper 
Year of Publication  2018 
Authors  Leung, D, Nayak, A, Shayeghi, A, Touchette, D, Yao, P, Yu, N 
Conference Name  Annual ACM Symposium on the Theory of Computing STOC 2018 
Date Published  2018/01/01 
Abstract  We consider the problem of implementing twoparty 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
preshared resources such as randomness or entanglement between the
communicating parties.
Surprisingly, this outperforms the bestknown 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'14].
Our work also improves over the best previously known quantum result
where the overhead is a nonexplicit large constant [Brassard \emph{et
al.}, FOCS'14] for low $\epsilon$.

URL  http://acmstoc.org/stoc2018/STOC2018Accepted.html 