# Certified answers for ordered quantum discrimination problems

## TL;DR

This paper introduces a new quantum state discrimination scheme for ordered pure states that provides certified error bounds, enabling controlled and reliable quantum measurement outcomes.

## Contribution

It develops an efficient semidefinite program and a general lower bound for ordered quantum discrimination, enhancing error control in quantum state identification.

## Key findings

- Efficient semidefinite program for ordered quantum discrimination
- General lower bound for error distance in quantum discrimination
- Application to quantum change point and anomaly detection

## Abstract

We investigate the quantum state discrimination task for sets of linear independent pure states with an intrinsic ordering. This structured discrimination problems allow for a novel scheme that provides a certified level of error, that is, answers that never deviate from the true value more than a specified distance and hence a control of the desired quality of the results. We obtain an efficient semidefinite program and also find a general lower bound valid for any error distance that only requires the knowledge of optimal minimum error scheme. We apply our results to the quantum change point and quantum state anomaly detection cases.