Partial ignorance communication tasks in quantum theory

TL;DR

This paper introduces a generalized quantum communication task involving partial ignorance, analyzing its bounds and revealing a contextual advantage of quantum theory through operational equivalences.

Contribution

It generalizes partial ignorance communication tasks, employs various methods to bound success metrics, and demonstrates a quantum contextual advantage in this new framework.

Findings

Quantum advantage observed in specific communication tasks.

Bounds on success metrics derived using SDPs and frame theory.

Exhaustive analysis of bits and qudits scenarios.

Abstract

We introduce a generalization of communication of partial ignorance where both parties of a prepare-and-measure setup receive inputs from a third party before a success metric is maximized over the measurements and preparations. Various methods are used to obtain bounds on the success metrics, including SDPs, ultraweak monotones for communication matrices and frame theory for quantum states. Simplest scenarios in the new generalized prepare-and-measure setting, simply called partial ignorance communication tasks, are analysed exhaustively for bits and qudits. Finally, the new generalized setting allows the introduction of operational equivalences to the preparations and measurements, allowing us to analyse and observe a contextual advantage for quantum theory in one of the communication tasks.