A universal set of qubit quantum channels

TL;DR

This paper characterizes the geometric forms of qubit channels, introduces a universal set for all unital and extremal qubit channels, and provides a minimal, concatenation-based framework for understanding single-qubit quantum operations.

Contribution

It offers a new, compact generalization of the Fujiwara-Algoet conditions and constructs universal, minimal sets of quantum channels for all unital and extremal qubit channels.

Findings

Provided a generalized condition for complete positivity of qubit channels.

Constructed universal sets capable of generating all unital and extremal qubit channels.

Demonstrated the minimality of these universal sets.

Abstract

We investigate the set of quantum channels acting on a single qubit. We provide an alternative, compact generalization of the Fujiwara-Algoet conditions for complete positivity to non-unital qubit channels, which we then use to characterize the possible geometric forms of the pure output of the channel. We provide universal sets of quantum channels for all unital qubit channels as well as for all extremal (not necessarily unital) qubit channels, in the sense that all qubit channels in these sets can be obtained by concatenation of channels in the corresponding universal set. We also show that our universal sets are essentially minimal.