%0 Conference Paper %B Annual ACM Symposium on the Theory of Computing STOC 2018 %D 2018 %T Capacity Approaching Codes for Low Noise Interactive Quantum Communication %A Debbie Leung %A Ashwin Nayak %A Ala Shayeghi %A Dave Touchette %A Penghui Yao %A Nengkun Yu %X
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'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'14] for low $\epsilon$.
%B Annual ACM Symposium on the Theory of Computing STOC 2018 %8 2018/01/01 %G eng %U http://acm-stoc.org/stoc2018/STOC-2018-Accepted.html