Optimizing Quantum Models of Classical Channels: The reverse Holevo problem
This addresses a theoretical problem in quantum information theory by inverting Holevo's capacity question, offering insights into quantum advantages in communication, though it appears incremental as it builds on established concepts.
The paper tackles the problem of simulating classical channels using quantum states to potentially reduce transmission rates, showing that quantum simulations can improve upon minimal classical rates and linking this to generating distributions from shared entanglement.
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.