Quantum trade-off coding for bosonic communication

TL;DR

This paper analyzes the capacity trade-offs in bosonic quantum channels, extending previous results to thermal and amplifying channels, and provides practical guidelines for photon allocation in high-photon regimes.

Contribution

It offers detailed derivations of quantum trade-off capacities for bosonic channels and extends these results to thermal and amplifying types, including a photon allocation rule of thumb.

Findings

Trade-off capacity regions for thermal and amplifying bosonic channels derived.

Performance gains of trade-off coding over time-sharing demonstrated.

Photon allocation strategy for high mean photon numbers established.

Abstract

The trade-off capacity region of a quantum channel characterizes the optimal net rates at which a sender can communicate classical, quantum, and entangled bits to a receiver by exploiting many independent uses of the channel, along with the help of the same resources. Similarly, one can consider a trade-off capacity region when the noiseless resources are public, private, and secret key bits. In [Phys. Rev. Lett. 108, 140501 (2012)], we identified these trade-off rate regions for the pure-loss bosonic channel and proved that they are optimal provided that a longstanding minimum output entropy conjecture is true. Additionally, we showed that the performance gains of a trade-off coding strategy when compared to a time-sharing strategy can be quite significant. In the present paper, we provide detailed derivations of the results announced there, and we extend the application of these ideas to thermalizing and amplifying bosonic channels. We also derive a "rule of thumb" for trade-off coding, which determines how to allocate photons in a coding strategy if a large mean photon number is available at the channel input. Our results on the amplifying bosonic channel also apply to the "Unruh channel" considered in the context of relativistic quantum information theory.