2005/08/19 by R Garcia Diaz, R. Garcia Diaz, J. L. Romero +4
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Complementarity (molecular biology) #Dimension (graph theory) #Hilbert space #Mathematics #Observable #Physics #Property (philosophy) #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Qubit #Statistical physics #Theoretical physics #quant-ph
paper · pdf · doi:10.1088/1367-2630/7/1/256
published as New J. Opt., vol. 7, pp. 256, 2005 · 4 pages, no figures
arxiv created 2005/08/19 · openalex publication_date 2005/12/29 · arxiv updated 2011/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We point out that for an arbitrary number of identical particles, each defined on a Hilbert space of arbitrary dimension, there exists a whole ladder of relations of complementarity between certain local and nonlocal measurements corresponding to every conceivable grouping of the particles, e.g., the more accurately we can know (by a measurement) some joint property of three qubits (projecting the state onto a tripartite-entangled state), the less accurate some other property, local to the three qubits, becomes. We investigate the relation between these complementarity relations and a similar relation based on interference visibilities. We also show that the complementarity relations are particularly tight for particles defined on prime dimensional Hilbert spaces.