Nonlocality of orthogonal product-basis quantum states

2015/09/10 by Yan-Ling Wang, Mao-Sheng Li, Zhu-Jun Zheng +2 · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Basis (linear algebra) #Bipartite graph #Combinatorics #Discrete mathematics #Geometry #LOCC #Mathematical analysis #Mathematics #Orthogonal basis #Physics #Product (mathematics) #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum entanglement #Quantum mechanics #Quantum nonlocality #Quantum state #Separable space #quant-ph

paper · pdf · doi:10.1103/physreva.92.032313

published as Phys. Rev. A 92 (2015) 032313 · 5 pages

openalex publication_date 2015/09/10 · arxiv created 2015/09/23 · arxiv updated 2015/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the local indistinguishability of mutually orthogonal product basis quantum states in the high-dimensional quantum system. In the quantum system of ℂ^d\ensuremath\bigotimesℂ^d, where d is odd, Zhang et al. [Z.-C. Zhang et al., Phys. Rev. A 90, 022313 (2014)] have constructed d² orthogonal product basis quantum states that are locally indistinguishable. We find a subset that contains 6d\ensuremath-9 orthogonal product states that are still locally indistinguishable. We generalize our method to an arbitrary bipartite quantum system ℂ^m\ensuremath\bigotimesℂⁿ. We present a small set with only 3(m+n)\ensuremath-9 orthogonal product states and prove that these states are local operations and classical communication (LOCC) indistinguishable. Even though these 3(m+n)\ensuremath-9 product states are LOCC indistinguishable, they can be distinguished by separable measurements. This shows that separable operations are strictly stronger than the local operations and classical communication.

Citations

• Any2⊗nsubspace is locally distinguishable
• Four Locally Indistinguishable Ququad-Ququad Orthogonal Maximally Entangled States
• Quantum cryptography using any two nonorthogonal states
• Distinguishability and Indistinguishability by Local Operations and Classical Communication
• Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement

Cited by

• Nonlocal sets of orthogonal product states in an arbitrary multipartite quantum system
• Novel methods to construct nonlocal sets of orthogonal product states in arbitrary bipartite high-dimensional system
• Alternative method for deriving nonlocal multipartite product states
• Locally distinguishing unextendible product bases by using entanglement efficiently