Certified answers for ordered quantum discrimination problems

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.

9 pages, 10 figures

References in corpus (6)

• Quantum state discrimination and its applications
• Maximum Confidence Quantum Measurements
• Unambiguous discrimination of mixed states
• On the Optimality of Square Root Measurements in Quantum State Discrimination
• Exact Identification of a Quantum Change Point
• A Structure of Minimum Error Discrimination for Linearly Independent States

Cited by in corpus (2)

• Quantumness of pure-state ensembles via coherence of Gram matrix based on generalized $\alpha$-$z$-relative Rényi entropy
• Online identification of symmetric pure states