Optimizing Quantum Models of Classical Channels: The reverse Holevo problem

TL;DR

This paper investigates how quantum states can optimize the simulation of classical channels, potentially reducing transmission rates and providing insights into quantum versus classical communication efficiencies.

Contribution

It introduces a framework for quantum simulation of classical channels, addressing when quantum resources outperform classical methods and connecting to entanglement-based distribution generation.

Findings

Quantum simulations can sometimes reduce classical channel simulation rates.

The problem relates to the local generation of distributions from entanglement.

Provides conditions under which quantum advantages are achievable.

Abstract

Given a classical channel---a stochastic map from inputs to outputs---the input can often be transformed to an intermediate variable that is informationally smaller than the input. The new channel accurately simulates the original but at a smaller transmission rate. Here, we examine this procedure when the intermediate variable is a quantum state. We determine when and how well quantum simulations of classical channels may improve upon the minimal rates of classical simulation. This inverts Holevo's original question of quantifying the capacity of quantum channels with classical resources. We also show that this problem is equivalent to another, involving the local generation of a distribution from common entanglement.