The capacity of the quantum depolarizing channel

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 product channel ∆⊗Ψ, where ∆ is the depolarizing channel and Ψ is a completely arbitrary channel. We establish the Amosov-HolevoWerner 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 χ.