Optimizing Quantum Models of Classical Channels:
The reverse Holevo problem

S. Loomis, John R. Mahoney, Cina Aghamohammdi, and James P. Crutchfield

Complexity Sciences Center
Physics Department
University of California at Davis
Davis, CA 95616

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.


Samuel P. Loomis, John R. Mahoney, Cina Aghamohammdi, and James P. Crutchfield, “Optimizing Quantum Models of Classical Channels: The reverse Holevo problem”, Journal of Statistical Physics 181 (2020) 1966-1985.
doi:10.1007/s10955-020-02649-2.
[pdf]

arxiv.org:1709.08101 [quant-ph].