Regular Article

Robustness of purity: an operational approach to resource theory of purity

¹ College of Computer Science, Shaanxi Normal University, Xi’an, 710062, P.R. China
² Centre for Quantum Software and Information, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, Australia

^a e-mail: liyongm@snnu.edu.cn

Received: 20 December 2018
Received in final form: 8 March 2019
Published online: 7 May 2019

Abstract

Quantifying purity is a basic problem for quantum information theory. In this paper, we introduce the robustness of purity which has an operational interpretation. We find that robustness of purity satisfies all requirements for a valid purity measure, even for the stronger monotonicity which has not discussed before in the resource theory of purity. The upper and lower bounds of robustness of purity are obtained. The robustness of purity has an efficient numberical computability via semidefinite programming. We also prove the robustness of purity has operational significance as the best advantage one can obtain in mixture of unitary channel discrimination games. A trade-off relation between robustness of purity and mixedness is obtained. Finally, we discuss whether all the conditions holds for Rényi α-entropy purity and linear entropy purity respectively.