Capacity Approaching Coding for Low Noise Interactive Quantum Communication Part I: Large Alphabets

We consider the problem of implementing two-party interactive quantum communication over noisy channels, a necessary endeavor if we wish to fully reap advantages for communication. For an arbitrary protocol with n messages, designed noiseless qudit channel poly (n ) size alphabet, our main result is simulation method that fails probability less than 2 -Θ(nϵ) and uses same alphabet n(1 + Θ(√{ϵ} )) times, which ϵ fraction can be corrupted adversarially. The thus capacity achieving leading order, conjecture it optimal up constant factor in √{ϵ} term. Furthermore, model does not require pre-shared resources such as randomness or entanglement between communicating parties. Our work improves best previously known where overhead non-explicit large [Brassard et al., SICOMP'19] low ϵ.