Calculating a maximizer for quantum mutual information

TL;DR

This paper determines the optimal input states for maximizing quantum mutual information over a specific quantum channel, revealing that a simple two-state ensemble suffices for capacity calculation.

Contribution

It introduces a method to find the maximizer for quantum mutual information using antipodal states, simplifying the capacity analysis for the amplitude damping channel.

Findings

Maximizer for quantum mutual information is achieved with two non-orthogonal antipodal states.

Product-state capacity of a convex combination of channels can differ from individual capacities.

The optimal ensemble for the channel involves only two specific states.

Abstract

We obtain a maximizer for the quantum mutual information for classical information sent over the quantum qubit amplitude damping channel. This is achieved by limiting the ensemble of input states to antipodal states, in the calculation of the product-state capacity for the channel, the resulting maximizing ensemble consisting of just two non-orthogonal states. We also consider the product-state capacity of a convex combination of two memoryless channels and demonstrate in particular that it is in general not given by the minimum of the capacities of the respective memoryless channels.