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

• URL: http://arxiv.org/abs/2001.02818v1
• Date: Thu, 9 Jan 2020 02:48:43 GMT
• Title: Capacity Approaching Coding for Low Noise Interactive Quantum Communication, Part I: Large Alphabets
• Authors: Debbie Leung, Ashwin Nayak, Ala Shayeghi, Dave Touchette, Penghui Yao, Nengkun Yu
• Abstract summary: We consider the problem of implementing two-party interactive quantum communication over noisy channels. For a noiseless qudit channel over a $mathrmpoly(n)$ size alphabet, our main result is a simulation method that fails with probability less than $2-Theta(nepsilon)$ We conjecture that it is optimal up to a constant factor in the $sqrtepsilon$ term.
• Score: 15.078027648304115
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 a noiseless qudit channel over a $\mathrm{poly}(n)$ size alphabet, our main result is a simulation method that fails with probability less than $2^{-\Theta(n\epsilon)}$ and uses a qudit channel over the same alphabet $n\left(1+\Theta \left(\sqrt{\epsilon}\right)\right)$ 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. 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 $\epsilon$.

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