# Communication of partial ignorance with qubits

**Authors:** Teiko Heinosaari, Oskari Kerppo  
**arXiv:** [1903.04899](https://arxiv.org/abs/1903.04899)  
**Date:** 2019-03-12  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1903.04899v1/

## Key points

- Communication tests introduced for communicating partial ignorance using a physical system
- Comprehensive characterization of implementations for qubits and partial results for qudits
- Difference in ability to implement communication tasks between qubits and rebits
- Introduction of ultraweak matrix majorization as a preordering for comparing communication tests
- Importance of considering operational dimensions in designing and implementing communication tasks
- Ultraweak matrix majorization provides a valuable tool for comparing and evaluating communication tests in a theory-independent manner.

## Summary

In the paper "Communication of partial ignorance with qubits" by Teiko Heinosaari and Oskari Kerppo, a class of communication tests is introduced where the objective is to communicate partial ignorance using a physical system. The authors provide a comprehensive characterization of the implementations of these tests in the case of qubits and present partial results for qudits. One interesting observation made in this study is that two physical systems with the same operational dimensions can differ in terms of their ability to implement these communication tasks. Specifically, the authors demonstrate that this difference exists between qubits and rebits. Furthermore, the paper addresses the question of whether some communication tests are more difficult than others. To answer this question in a theory-independent manner, the authors propose a new preordering called ultraweak matrix majorization. Overall, this research contributes to our understanding of how partial ignorance can be effectively communicated through physical systems. The findings highlight the importance of considering specific operational dimensions when designing and implementing such communication tasks. Additionally, the introduction of ultraweak matrix majorization provides a valuable tool for comparing and evaluating different communication tests in a theory-independent manner.