# Solutions to the mean king's problem: higher-dimensional quantum error-correcting codes

## TL;DR

This paper introduces higher-dimensional quantum error-correcting codes to solve the mean king's problem, enabling accurate discrimination of eigenstates using classical delayed information.

## Contribution

The paper constructs novel quantum error-correcting codes specifically designed for the mean king's problem in higher dimensions, advancing quantum state discrimination techniques.

## Key findings

- Codes enable correct eigenstate discrimination with delayed classical info
- Construction of higher-dimensional quantum error-correcting codes
- Improved understanding of quantum error correction in noncommutative observables

## Abstract

Mean king's problem is a kind of quantum state discrimination problems. In the problem, we try to discriminate eigenstates of noncommutative observables with the help of classical delayed information. The problem has been investigated from the viewpoint of error detection and correction. We construct higher-dimensional quantum error-correcting codes against error corresponding to the noncommutative observables. Any code state of the codes provides a way to discriminate the eigenstates correctly with the classical delayed information.