Bounds on entanglement distillation and secret key agreement for quantum broadcast channels

TL;DR

This paper extends bounds on entanglement distillation and secret key agreement from single-sender channels to quantum broadcast channels with multiple receivers, using multipartite squashed entanglement.

Contribution

It introduces multipartite squashed entanglement measures to bound secret key and entanglement rates in broadcast channels, generalizing previous single-sender results.

Findings

Derived bounds for secret key rates in broadcast channels

Developed new properties of multipartite squashed entanglement

Applied bounds to pure-loss broadcast channels with two receivers

Abstract

The squashed entanglement of a quantum channel is an additive function of quantum channels, which finds application as an upper bound on the rate at which secret key and entanglement can be generated when using a quantum channel a large number of times in addition to unlimited classical communication. This quantity has led to an upper bound of $\log((1+\eta)/(1-\eta))$ on the capacity of a pure-loss bosonic channel for such a task, where $\eta$ is the average fraction of photons that make it from the input to the output of the channel. The purpose of the present paper is to extend these results beyond the single-sender single-receiver setting to the more general case of a single sender and multiple receivers (a quantum broadcast channel). We employ multipartite generalizations of the squashed entanglement to constrain the rates at which secret key and entanglement can be generated between any subset of the users of such a channel, along the way developing several new properties of these measures. We apply our results to the case of a pure-loss broadcast channel with one sender and two receivers.