# Capacity Approaching Codes for Low Noise Interactive Quantum Communication

 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 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 $\epsilon$. URL http://acm-stoc.org/stoc2018/STOC-2018-Accepted.html