Classical capacity of bosonic broadcast communication and a new minimum output entropy conjecture

TL;DR

This paper investigates the capacity region of bosonic broadcast channels, proposing a new minimum output entropy conjecture that, if proven, would establish optimal communication strategies for quantum optical systems.

Contribution

It introduces a new minimum output entropy conjecture for bosonic channels and discusses its implications for the capacity region of bosonic broadcast communication.

Findings

Proposes a new minimum output entropy conjecture for bosonic channels.

Provides supporting evidence for the conjecture, though not a full proof.

Suggests that the capacity region equals the inner bound with coherent-state encoding.

Abstract

Previous work on the classical information capacities of bosonic channels has established the capacity of the single-user pure-loss channel, bounded the capacity of the single-user thermal-noise channel, and bounded the capacity region of the multiple-access channel. The latter is a multi-user scenario in which several transmitters seek to simultaneously and independently communicate to a single receiver. We study the capacity region of the bosonic broadcast channel, in which a single transmitter seeks to simultaneously and independently communicate to two different receivers. It is known that the tightest available lower bound on the capacity of the single-user thermal-noise channel is that channel's capacity if, as conjectured, the minimum von Neumann entropy at the output of a bosonic channel with additive thermal noise occurs for coherent-state inputs. Evidence in support of this minimum output entropy conjecture has been accumulated, but a rigorous proof has not been obtained. In this paper, we propose a new minimum output entropy conjecture that, if proved to be correct, will establish that the capacity region of the bosonic broadcast channel equals the inner bound achieved using a coherent-state encoding and optimum detection. We provide some evidence that supports this new conjecture, but again a full proof is not available.