Gaussian benchmark for optical communication aiming towards ultimate capacity

TL;DR

This paper establishes the fundamental limits of Gaussian-based optical communication capacity, demonstrating that Gaussian schemes are insufficient to reach the ultimate Holevo bound, and explores non-Gaussian methods to surpass these limits.

Contribution

The paper rigorously proves the additivity of Gaussian capacity and introduces a benchmark for assessing non-Gaussian protocols in optical communication.

Findings

Gaussian capacity is additive and achieved with separable encoding and decoding.

Gaussian schemes cannot reach the Holevo capacity in low-photon regimes.

Non-Gaussian receivers can surpass Gaussian capacity with proper encoding.

Abstract

We establish the fundamental limit of communication capacity within Gaussian schemes under phase-insensitive Gaussian channels, which employ multimode Gaussian states for encoding and collective Gaussian operations and measurements for decoding. We prove that this Gaussian capacity is additive, i.e., its upper bound occurs with separable encoding and separable receivers so that a single-mode communication suffices to achieve the largest capacity under Gaussian schemes. This rigorously characterizes the gap between the ultimate Holevo capacity and the capacity within Gaussian communication, showing that Gaussian regime is not sufficient to achieve the Holevo bound particularly in the low-photon regime. Furthermore the Gaussian benchmark established here can be used to critically assess the performance of non-Gaussian protocols for optical communication. We move on to identify non-Gaussian schemes to beat the Gaussian capacity and show that a non-Gaussian receiver recently implemented by Becerra et al. [Nat. Photon. 7, 147 (2013)] can achieve this aim with an appropriately chosen encoding strategy.