2017/02/06 by Jacques Distler, Distler, Jacques, Sònia Paban +1
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1702.01724
openalex publication_date 2017/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We previously remarked that when an observable A has a continuous spectrum, then von Neumann's formula for the post-measurement state needs to be extended and the correct formula ineluctably involves the resolution of the detector used in the measurement. We generalize previous results to compute the uncertainties in successive measurements of more general pairs of observables. We also show that this extended von Neumann's formula for the post-measurement state is a completely positive map and, moreover, that there is a completely-positive interpolation between the pre- and post-measurement states. Weinberg has advocated that the time-evolution during the measurement process should be modeled as an open quantum system and governed by a Lindblad equation. We verify that this is indeed the case for an arbitrary observable, A, and a fairly general class of interpolations.