Capacity Approaching Coding for Low Noise Interactive Quantum Communication, Part I: Large Alphabets
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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 a noiseless qudit channel over a poly(n) size alphabet, our main result is a simulation method that fails with probability less than 2^-Θ(nϵ) and uses a qudit channel over the same alphabet n(1+Θ(√(ϵ))) times, of which an ϵ 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 √(ϵ) term. Furthermore, the simulation is in a model that does not require pre-shared resources such as randomness or entanglement between the communicating parties. Our work improves over the best previously known quantum result where the overhead is a non-explicit large constant [Brassard et al., FOCS'14] for low ϵ.
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