Locally distinguishing unextendible product bases by using entanglement efficiently

2019/06/28 by Zhichao Zhang, Zhi-Chao Zhang, Xia Wu +1
Computer Science · Mathematics · Physics and Astronomy · #Class (philosophy) #Combinatorics #Computer network #Computer science #Discrete mathematics #LOCC #Mathematics #Multipartite entanglement #Physics #Product (mathematics) #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum channel #Quantum entanglement #Quantum mechanics #Quantum nonlocality #Quantum teleportation #Resource (disambiguation) #Set (abstract data type) #Squashed entanglement #Teleportation #quant-ph

paper · pdf · doi:10.1103/physreva.101.022306

published as Phys. Rev. A 101, 022306 (2020)

arxiv created 2019/06/28 · openalex created_date 2019/07/12 · openalex publication_date 2020/02/07 · arxiv updated 2020/02/12 · openalex updated_date 2026/08/05

Abstract

Any set of states which cannot be perfectly distinguished by local operations and classical communication (LOCC) alone can always be locally distinguished using quantum teleportation with a maximally entangled state as resource. However, in quantum information theory, entanglement is a very valuable resource, so it leaves the following problem: How to accomplish this task more efficiently than teleportation, that is, design the local discrimination protocol using less entanglement. In this paper, we first present two protocols to locally distinguish a particular unextendible product bases (UPB) in 5\ensuremath\bigotimes5 by using different entanglement resource. Then, we generalize the distinguishing methods for a class of UPB in d\ensuremath\bigotimesd, where d is odd and d\ensuremath\geqslant3. Furthermore, for a class of UPB in d\ensuremath\bigotimesd, where d is even and d\ensuremath\geqslant4, we prove that these states can also be distinguished by LOCC with multiple copies of low-dimensional entanglement resource. These results offer rather general insight into how to use entanglement resource more efficiently and also reveal the phenomenon of less nonlocality with more entanglement.

Citations

• Distinguishability of Bell States
• Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels
• Distinguishing the elements of a full product basis set needs only projective measurements and classical communication
• Four Locally Indistinguishable Ququad-Ququad Orthogonal Maximally Entangled States
• Distinguishability and Indistinguishability by Local Operations and Classical Communication
• Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
• Bound Entanglement Can Be Activated
• Nonlocality of orthogonal product-basis quantum states
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer