Partial ignorance communication tasks in quantum theory

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.

References in corpus (9)

• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Bounding the set of quantum correlations
• Is the quantum state real? An extended review of $\psi$-ontology theorems
• Preparation contextuality powers parity-oblivious multiplexing
• Bounding the set of finite dimensional quantum correlations
• Bounds on Quantum Correlations in Bell Inequality Experiments
• Better Bell Inequality Violation by Collective Measurements
• Characterising and bounding the set of quantum behaviours in contextuality scenarios
• Bounding and simulating contextual correlations in quantum theory