The capacity of the quantum depolarizing channel

TL;DR

This paper calculates the capacity of the quantum depolarizing channel, showing that simple product states and measurements suffice for optimal information transmission, and proves related additivity conjectures.

Contribution

It demonstrates that entanglement is unnecessary for maximizing capacity and proves the Amosov-Holevo-Werner p-norm conjecture for the depolarizing channel.

Findings

Capacity achieved by product states and measurements

Additivity of the channel's capacity and minimal entropy

Proof of the Amosov-Holevo-Werner p-norm conjecture for all p >= 1

Abstract

The information carrying capacity of the d-dimensional depolarizing channel is computed. It is shown that this capacity can be achieved by encoding messages as products of pure states belonging to an orthonormal basis of the state space, and using measurements which are products of projections onto this same orthonormal basis. In other words, neither entangled signal states nor entangled measurements give any advantage for information capacity. The result follows from an additivity theorem for the capacity of the product of the depolarizing channel with an arbitrary channel. We establish the Amosov-Holevo-Werner p-norm conjecture for this product channel for all p >= 1, and deduce from this the additivity of the minimal entropy and of the Holevo quantity.