Metainformation in Quantum Guessing Games

TL;DR

This paper introduces the concept of metainformation in quantum guessing games, revealing how knowledge about future side information can influence success probabilities and strategy effectiveness in quantum information processing.

Contribution

It formally distinguishes metainformation from side information, uncovering new operational effects and strategic nuances in quantum guessing scenarios.

Findings

Metainformation can enhance success probabilities in certain scenarios.

Timing and type of information significantly affect quantum guessing strategies.

Metainformation can make post-measurement information as useful as prior information.

Abstract

Quantum guessing games offer a structured approach to analyzing quantum information processing, where information is encoded in quantum states and extracted through measurement. An additional aspect of this framework is the influence of partial knowledge about the input on the optimal measurement strategies. This kind of side information can significantly influence the guessing strategy and earlier work has shown that the timing of such side information, whether revealed before or after the measurement, can affect the success probabilities. In this work, we go beyond this established distinction by introducing the concept of metainformation. Metainformation is information about information, and in our context it is knowledge that additional side information of certain type will become later available, even if it is not yet provided. We show that this seemingly subtle difference between having no expectation of further information versus knowing it will arrive can have operational consequences for the guessing task. Our results demonstrate that metainformation can, in certain scenarios, enhance the achievable success probability up to the point that post-measurement side information becomes as useful as prior-measurement side information, while in others it offers no benefit. By formally distinguishing metainformation from actual side information, we uncover a finer structure in the interplay between timing, information, and strategy, offering new insights into the capabilities of quantum systems in information processing tasks.