Capacity approaching coding for low noise interactive quantum communication

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 (where d is arbitrary), our main result is a simulation method that fails with probability less than 2 −Θ ( n є) and uses a qudit channel n (1 + Θ (√є)) times, of which an є 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 √є term. Furthermore, the simulation is in a model that does not require pre-shared resources such as randomness or entanglement between the communicating parties. Perhaps surprisingly, this outperforms the best known overhead of 1 + O (√є loglog1/є) in the corresponding 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 et al. , FOCS’14] for low є.

Authors

• Debbie W. Leung
• Ashwin Nayak 0001
• Ala Shayeghi
• Dave Touchette
• Penghui Yao
• Nengkun Yu

Keywords

• Capacity
• Coding Theory
• Interactive Coding
• Quantum Communication Complexity
• Quantum Information Theory