On the Measurement attaining the Quantum Guesswork

TL;DR

This paper derives the optimal quantum measurement strategy to minimize guesswork when identifying quantum states, extending classical guessing strategies to the quantum domain for various ensembles and cost functions.

Contribution

It provides a solution for the optimal quantum measurement that attains the guesswork for a broad class of ensembles and cost functions, advancing quantum state discrimination methods.

Findings

Derived the quantum measurement attaining the guesswork

Extended classical guessing strategies to quantum ensembles

Applicable to a broad class of ensembles and cost functions

Abstract

The guesswork quantifies the minimum cost incurred in guessing the state of an ensemble, when only one state can be queried at a time. In the classical case, it is well known that the optimal strategy trivially consists of querying the states in their non-increasing order of posterior probability. In the quantum case, on the other hand, the most general strategy to obtain the optimal ordering in which to perform the queries consist of a quantum measurement. Here, we solve such an optimization problem by deriving the quantum measurement attaining the guesswork for a broad class of ensembles and cost functions.