Capacities of the covariant Pauli channel

TL;DR

This paper analyzes the capacities of a specific family of qubit Pauli channels, providing exact formulas for some capacities, identifying regions where quantum capacity vanishes, and establishing bounds for others.

Contribution

It offers the first exact expressions for classical and entanglement-assisted capacities of covariant Pauli channels and bounds for quantum and private capacities.

Findings

Exact expressions for classical and entanglement-assisted capacities.

Identification of regions where quantum capacity is zero.

Upper and lower bounds for quantum and private capacities.

Abstract

We study the four well-known capacities of a two-parameter family of qubit Pauli channels. These are the channels which are covariant under the SO(2) group and contain the depolarizing channel as a special case. We find exact expressions for the classical capacity and entanglement assisted capacities, and analytically determine the regions where the quantum capacity of the channel vanishes. We then use a flag extension to find upper bound for the quantum capacity and private capacity of these channels in the entire region of parameter space and also obtain the lower bound for the quantum capacity by calculating the single shot quantum capacity numerically. In conjunction with previous results on depolarizing channels, our result is one step forward for determining the capacities of the full Pauli channel.