Distinguishing the elements of a full product basis set needs only projective measurements and classical communication

2003/11/30 by Ping-Xing Chen, Ping Xing Chen, Cheng-Zu Li +1 · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Basis (linear algebra) #Character (mathematics) #Computer science #Generalization #Geometry #Mathematical analysis #Mathematics #Multipartite #Multipartite entanglement #Physics #Product (mathematics) #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Quantum nonlocality #Set (abstract data type) #Squashed entanglement #Tensor product #quant-ph

paper · pdf · doi:10.1103/physreva.70.022306

arxiv created 2003/12/05 · openalex publication_date 2004/08/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Nonlocality without entanglement is an interesting field. A manifestation of quantum nonlocality without entanglement is the possible local indistinguishability of orthogonal product states. In this paper we analyze the character of operators to distinguish the elements of a full product basis set in a multipartite system, and show that distinguishing perfectly these product bases needs only local projective measurements and classical communication, and these measurements cannot damage each product basis. Employing these conclusions one can discuss local distinguishability of the elements of any full product basis set easily. Finally we discuss the generalization of these results to the locally distinguishability of the elements of incomplete product basis set.

Citations

• Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels
• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
• Mixed-State Entanglement and Distillation: Is there a “Bound” Entanglement in Nature?
• Quantum cryptography using any two nonorthogonal states
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Quantum cryptography based on Bell’s theorem
• Quantum Computation and Quantum Information

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
• Locally distinguishing unextendible product bases by using entanglement efficiently
• Asymptotically perfect discrimination in the local-operation-and-classical-communication paradigm