Capacity Approaching Codes for Low Noise Interactive Quantum Communication

TitleCapacity Approaching Codes for Low Noise Interactive Quantum Communication
Publication TypeConference Paper
Year of Publication2018
AuthorsLeung, D, Nayak, A, Shayeghi, A, Touchette, D, Yao, P, Yu, N
Conference NameAnnual ACM Symposium on the Theory of Computing STOC 2018
Date Published2018/01/01
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 $\epsilon$.