Capacity of multimode quantum Gaussian channels

TL;DR

This paper derives explicit formulas for the capacity of multimode quantum Gaussian channels, demonstrating that increasing the number of modes is always optimal under fixed power constraints.

Contribution

It provides analytical formulas for channel capacities, including ensemble-averaged Holevo capacity, for multimode quantum Gaussian channels with passive and active transformations.

Findings

Increasing the number of modes is always optimal under fixed power.

Explicit formulas for Holevo capacity and capacities under detection methods are derived.

Results extend to channels with weak active transformations.

Abstract

We derive explicit formulas for the capacity of multimode quantum Gaussian channels which serve as a fundamental model for optical version of multiple-input multiple-output channels. We show that it is always optimal to increase the number of modes under fixed power constraint. We derive an analytical formula for the ensemble-averaged Holevo capacity in the case of random passive transformations. The analogous results are also obtained for capacities achievable under homodyne and heterodyne detection. We further discuss the generalization of the model to include weak active transformations.