Bosonic Dirty Paper Coding

TL;DR

This paper extends dirty paper coding techniques to single-mode bosonic quantum channels with classical interference, demonstrating interference cancellation and deriving bounds for different detection schemes, including joint detection.

Contribution

It introduces a quantum analog of Costa's dirty paper coding for bosonic channels and analyzes optimal coding strategies under various detection methods.

Findings

Interference can be canceled in bosonic channels using dirty paper coding.

Derived a lower bound for channels with joint detection.

Identified that the optimal coding coefficient differs from classical MMSE in pure-loss channels.

Abstract

The single-mode bosonic channel is addressed with classical interference in the modulation and with side information at the transmitter. This model can viewed as the quantum counterpart of the classical random-parameter Gaussian channel. Based on Costa's writing-on-dirty-paper result (1983), the effect of the channel parameter can be canceled even when the decoder has no side information, and regardless of the input power constraint. For both homodyne and heterodyne detection with a coherent-state protocol, the model reduces to a classical channel with either real or complex-valued Gaussian noise. Thereby, by applying Costa's dirty paper coding strategy, we observe that the effect of the classical interference can be canceled for those channels as well. Then, we consider the bosonic channel with joint detection, for which the classical results do not apply, and derive a dirty-paper coding lower bound. Furthermore, considering the special case of a pure-loss bosonic channel, we demonstrate that the optimal coefficient for dirty paper coding is not necessarily the MMSE estimator coefficient as in the classical setting.