Guesswork of a quantum ensemble

TL;DR

This paper introduces analytical solutions for the quantum guesswork problem, including for qubit ensembles with uniform distributions and specific geometric configurations, advancing understanding of quantum state discrimination.

Contribution

It provides the first analytical solutions for quantum guesswork in finite ensembles, especially for qubit ensembles with uniform probability and geometric structures.

Findings

Analytical solutions for quantum guesswork in finite ensembles.

Explicit guesswork calculations for qubit regular polygons and polyhedra.

Enhanced understanding of quantum state discrimination complexity.

Abstract

The guesswork of a quantum ensemble quantifies the minimum number of guesses needed in average to correctly guess the state of the ensemble, when only one state can be queried at a time. Here, we derive analytical solutions of the guesswork problem subject to a finite set of conditions, including the analytical solution for any qubit ensemble with uniform probability distribution. As explicit examples, we compute the guesswork for any qubit regular polygonal and polyhedral ensemble.