2012/10/11 by Elena R. Loubenets, Loubenets, Elena R.
Computer Science · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1210.3270
openalex publication_date 2012/10/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We prove that the Hilbert space description of all joint von Neumann measurements on a quantum state can be reproduced in terms of a single measure space (Ω, F, μ) with a normalized real-valued measure μ, that is, in terms of a new general probability model, the quasi-classical probability model, developed in [Loubenets: J. Math. Phys. 53 (2012), 022201; J. Phys. A: Math. Theor. 45 (2012), 185306]. In a quasi-classical probability model for all von Neumann measurements, a random variable models the corresponding quantum observable in all joint measurements and depends only on this quantum observable. This mathematical result sheds a new light on some important issues of quantum randomness discussed in the literature since the seminal article (1935) of Einstein, Podolsky and Rosen.