# Generalizations of $2$-dimensional diagonal quantum channels with constant Frobenius norm

## TL;DR

This paper studies quantum channels with constant Frobenius norm, showing equivalence in 2D and non-equivalence in higher dimensions, and generalizes certain families to arbitrary dimensions.

## Contribution

It introduces the concept of constant Frobenius norm channels, proves equivalence in 2D, and generalizes families to higher dimensions with non-equivalence results.

## Key findings

- All 2D diagonal channels with constant Frobenius norm are equivalent.
- Generalizations of 2D families to higher dimensions are not equivalent.
- The paper extends the understanding of quantum channel structures across dimensions.

## Abstract

We introduce the set of quantum channels with constant Frobenius norm, the set of diagonal channels and the notion of equivalence of one-parameter families of channels. First, we show that all diagonal $2$-dimensional channels with constant Frobenius norm are equivalent. Next, we generalize four one-parameter families of $2$-dimensional diagonal channels with constant Frobenius norm to an arbitrary dimension $n$. Finally, we prove that the generalizations are not equivalent in any dimension $n \ge 3$.