Adversarial guesswork with quantum side information

TL;DR

This paper investigates the guesswork involved in quantum state discrimination with side information, establishing invariance properties for optimal strategies and computing explicit solutions for specific symmetric channels.

Contribution

It proves invariance of optimal pre-processing and covariance of optimal post-processing for covariant channels, and explicitly calculates guesswork for symmetric qubit channels.

Findings

Optimal pre-processing is invariant for covariant channels.

Optimal post-processing is covariant for covariant channels.

Explicit guesswork values are derived for symmetric qubit channels.

Abstract

The guesswork of a classical-quantum channel quantifies the cost incurred in guessing the state transmitted by the channel when only one state can be queried at a time, maximized over any classical pre-processing and minimized over any quantum post-processing. For arbitrary-dimensional covariant classical-quantum channels, we prove the invariance of the optimal pre-processing and the covariance of the optimal post-processing. In the qubit case, we compute the optimal guesswork for the class of so-called highly symmetric informationally complete classical-quantum channels.