Extension of the Alberti-Uhlmann criterion beyond qubit dichotomies

TL;DR

This paper generalizes the Alberti-Uhlmann criterion from qubit dichotomies to multiple states and measurements, enabling broader applications in quantum state and measurement transformations with semi-device independence.

Contribution

The authors extend the Alberti-Uhlmann criterion to multiple qubit and qutrit states and measurements, providing a more versatile tool for quantum transformations.

Findings

Generalized criterion for multiple states and measurements

Applicable in semi-device independent scenarios

Enables new quantum transformation tests

Abstract

The Alberti-Uhlmann criterion states that any given qubit dichotomy can be transformed into any other given qubit dichotomy by a quantum channel if and only if the testing region of the former dichotomy includes the testing region of the latter dichotomy. Here, we generalize the Alberti-Uhlmann criterion to the case of arbitrary number of qubit or qutrit states. We also derive an analogous result for the case of qubit or qutrit measurements with arbitrary number of elements. We demonstrate the possibility of applying our criterion in a semi-device independent way.