2007/05/31 by Andrzej Grudka, Paweł Kurzyński, Pawel Kurzynski · 1 citation
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum optics and atomic interactions #quant-ph
paper · pdf · doi:10.1103/physrevlett.100.160401
published as Phys. Rev. Lett. 100, 160401 (2008) · 4 pages, 1 figure, comments welcome
openalex publication_date 2008/04/21 · arxiv created 2008/07/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Cabello and Nakamura have shown [A. Cabello, Phys. Rev. Lett. 90, 190401 (2003)10.1103/PhysRevLett.90.190401] that the Kochen-Specker theorem can be applied to two-dimensional systems if one uses positive operator-valued measures (POVM). We show that the contextuality in their models is not of the Kochen-Specker type, but it is rather a result of not keeping track of the whole system on which the measurement is performed. This is connected to the fact that there is no one-to-one correspondence between the POVM elements and projectors on the extended Hilbert space, and the same POVM element has to originate from two different projectors when used in Cabello-Nakamura models. Moreover, we propose a hidden-variable formulation of the above models.