Conditional channel simulation

TL;DR

This paper introduces a novel quantum channel simulation tool using a control system, enabling the simulation of complex channels and deriving bounds for quantum communication capacities, including for non-Gaussian channels.

Contribution

It presents a new simulation method for quantum channels based on control systems, extending to asymptotic and memory channels, and applies it to derive capacity bounds.

Findings

Derived upper bounds for private communication over various channels.

Established the two-way quantum and private capacity of the dephrasure channel.

Extended simulation techniques to asymptotic and memory channels.

Abstract

In this work we design a specific simulation tool for quantum channels which is based on the use of a control system. This allows us to simulate an average quantum channel which is expressed in terms of an ensemble of channels, even when these channel-components are not jointly teleportation-covariant. This design is also extended to asymptotic simulations, continuous ensembles, and memory channels. As an application, we derive relative-entropy-of-entanglement upper bounds for private communication over various channels, including non-Gaussian mixtures of bosonic lossy channels. Among other results, we also establish the two-way quantum and private capacity of the so-called `dephrasure' channel.