The depolarising channel and Horns problem

TL;DR

This paper studies how the depolarising qubit channel affects permutation invariant states, identifying the subspaces where the output resides, using Horn's problem and inequalities as key tools.

Contribution

It provides a novel analysis of the depolarising channel's action on symmetric Werner states using Horn's problem, linking quantum channels with algebraic inequalities.

Findings

Identifies the invariant subspaces supported by the depolarising channel output.

Establishes a connection between quantum channel action and Horn's inequalities.

Provides a mathematical framework for understanding depolarising effects on symmetric states.

Abstract

We investigate the action of the depolarising (qubit) channel on permutation invariant input states. More specifically, we raise the question on which invariant subspaces the output of the depolarising channel, given such special input, is supported. An answer is given for equidistributed states on isotypical subspaces, also called symmetric Werner states. Horns problem and two of the corresponding inequalities are invoked as a method of proof.