# Communication of partial ignorance with qubits

## TL;DR

This paper explores how to communicate partial ignorance using qubits and other quantum systems, providing a full characterization for qubits and insights into the complexity of different systems.

## Contribution

It introduces a new class of communication tests for partial ignorance, characterizes their implementation in qubits, and proposes a theory-independent ordering of test difficulty.

## Key findings

- Complete characterization of qubit-based communication tests
- Differences between qubit and rebit implementations
- Introduction of ultraweak matrix majorization for comparing test complexity

## Abstract

We introduce a class of communication tests where the task is to communicate partial ignorance by means of a physical system. We present a full characterization of the implementations of these tests in the qubit case and partial results for qudits. A peculiar observation is that two physical systems with the same operational dimensions may differ with respect to implementations of these tasks, as is shown to be the case for the qubit and rebit. Finally, we consider the natural question whether some of the communication tests are more difficult than others. A new preordering that we call the ultraweak matrix majorization is presented to answer this question in a theory-independent way.