Hadamard quantum broadcast channels

TL;DR

This paper determines the capacity regions for various communication tasks over Hadamard quantum broadcast channels, a quantum analog of classical degraded broadcast channels, by leveraging their structural properties.

Contribution

It provides the first complete capacity region characterizations for multiple communication tasks on Hadamard quantum broadcast channels, exploiting their unique measurement-preparation structure.

Findings

Capacity region for classical communication to both receivers

Capacity region for quantum communication to the stronger receiver

Capacity region for entanglement-assisted classical communication

Abstract

We consider three different communication tasks for quantum broadcast channels, and we determine the capacity region of a Hadamard broadcast channel for these various tasks. We define a Hadamard broadcast channel to be such that the channel from the sender to one of the receivers is entanglement-breaking and the channel from the sender to the other receiver is complementary to this one. As such, this channel is a quantum generalization of a degraded broadcast channel, which is well known in classical information theory. The first communication task we consider is classical communication to both receivers, the second is quantum communication to the stronger receiver and classical communication to other, and the third is entanglement-assisted classical communication to the stronger receiver and unassisted classical communication to the other. The structure of a Hadamard broadcast channel plays a critical role in our analysis: the channel to the weaker receiver can be simulated by performing a measurement channel on the stronger receiver's system, followed by a preparation channel. As such, we can incorporate the classical output of the measurement channel as an auxiliary variable and solve all three of the above capacities for Hadamard broadcast channels, in this way avoiding known difficulties associated with quantum auxiliary variables.