Partial-ignorance communication tasks in quantum theory

: Kerppo Oskari

Publisher: AMER PHYSICAL SOC

: 2022

: Physical Review A

: PHYS REV A

: 062607

: 105

: 6

: 13

: 2469-9926

: 2469-9934

DOI: https://doi.org/10.1103/PhysRevA.105.062607

: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.105.062607

: http://arxiv.org/pdf/2202.08581

We introduce a generalization of the communication of partial ignorance where both parties of a prepare-andmeasure setup receive inputs from a third party before a success metric is maximized over the measurements and preparations. We call these communication scenarios partial ignorance communication tasks of type Tn,m, where n indicates the number of possible correct answers in the communication task and m loosely represents the information about the correct answer that is revealed to the party preparing states. Various methods are used to obtain bounds on the success metrics, including semidefinite programs, ultraweak monotones for communication matrices, and frame theory for quantum states. The simplest scenarios in this alternative generalized prepare-andmeasure setting, partial-ignorance communication tasks of types T3,1, T4,1, and T4,2, are analyzed exhaustively for bits and qudits. Finally, this generalized setting allows the introduction of operational equivalences to the preparations and measurements, allowing us to analyze and observe a contextual advantage for quantum theory in the partial ignorance communication task of type T4,1.