Quantum guessing games with posterior information

TL;DR

This paper develops a comprehensive framework for quantum guessing games with posterior information, analyzing their structure, symmetries, and optimal strategies, with applications to incompatibility detection.

Contribution

It introduces a general formalism for quantum guessing games with posterior information, including structure and reduction theorems, and characterizes optimal measurements under symmetry conditions.

Findings

Framework enables analysis of any quantum guessing game with posterior info

Characterization of optimal measurements using symmetry and irreducible representations

Application to detecting incompatibility in quantum systems

Abstract

Quantum guessing games form a versatile framework for studying different tasks of information processing. A quantum guessing game with posterior information uses quantum systems to encode messages and classical communication to give partial information after a quantum measurement has been performed. We present a general framework for quantum guessing games with posterior information and derive structure and reduction theorems that enable to analyze any such game. We formalize symmetry of guessing games and characterize the optimal measurements in cases where the symmetry is related to an irreducible representation. The application of guessing games to incompatibility detection is reviewed and clarified. All the presented main concepts and results are demonstrated with examples.