Unextendible product operator basis

Journal of Mathematical Physics, vol. 63

Abstract

Quantum nonlocality is associated with the local indistinguishability of orthogonal states. Unextendible product basis (UPB), a widely used tool in quantum information, exhibits nonlocality, which is the powerful resource for quantum information processing. In this work, we extend the definitions of nonlocality and genuine nonlocality from states to operators. We also extend UPB to the notions of unextendible product operator basis, unextendible product unitary operator basis (UPUOB), and strongly UPUOB. We construct their examples and show the nonlocality of some strongly UPUOBs under local operations and classical communications. We study the phenomenon of these operators acting on quantum states. As an application, we distinguish the two-dimensional strongly UPUOB, which only consumes three ebits of entanglement. Our results imply that such UPUOBs exhibit nonlocality as UPBs, and the distinguishability of them requires entanglement resources.

Authors 5

1. Mengyao Hu Aachen Instituut-Lorentz

   Leiden University · Beihang University

   Affiliation as printed

   Instituut-Lorentz, Universiteit Leiden 2 , P.O. Box 9506, 2300 RA Leiden, The Netherlands

   School of Mathematical Sciences, Beihang University 1 , Beijing 100191, China

2. Lin Chen

   Beihang University

   Affiliation as printed

   International Research Institute for Multidisciplinary Science, Beihang University 4 , Beijing 100191, China

   LMIB (Beihang University), Ministry of Education 3 , Beijing, China

   School of Mathematical Sciences, Beihang University 1 , Beijing 100191, China

3. Fei Shi

   University of Science and Technology of China · University of Hong Kong

   Affiliation as printed

   Department of Computer Science, The University of Hong Kong 5 , Pokfulam Road, Hong Kong, China

   School of Cyber Security, University of Science and Technology of China 6 , Hefei 230026, China

4. Xiande Zhang

   University of Science and Technology of China

   Affiliation as printed

   Hefei National Laboratory, University of Science and Technology of China 8 , Hefei 230088, China

   School of Mathematical Sciences, University of Science and Technology of China 7 , Hefei 230026, China

5. Jordi Tura Aachen Instituut-Lorentz

   Leiden University

   Affiliation as printed

   Instituut-Lorentz, Universiteit Leiden 2 , P.O. Box 9506, 2300 RA Leiden, The Netherlands