caa a22 4500 467906688 CHVBK 20180406152836.0 cr unu---uuuuu 170328e20061101xx s 000 0 eng 10.1007/s10701-006-9077-5 doi (NATIONALLICENCE)springer-10.1007/s10701-006-9077-5 Anastopoulos Charis Department of Physics, University of Paras, 26500, Patras, Greece aut Classical Versus Quantum Probability in Sequential Measurements [Elektronische Daten] [Charis Anastopoulos] We demonstrate in this paper that the probabilities for sequential measurements have features very different from those of single-time measurements. First, they cannot be modelled by a classical stochastic process. Second, they are contextual, namely they depend strongly on the specific measurement scheme through which they are determined. We construct Positive-Operator-Valued measures (POVM) that provide such probabilities. For observables with continuous spectrum, the constructed POVMs depend strongly on the resolution of the measurement device, a conclusion that persists even if we consider a quantum mechanical measurement device or the presence of an environment. We then examine the same issues in alternative interpretations of quantum theory. We first show that multi-time probabilities cannot be naturally defined in terms of a frequency operator. We next prove that local hidden variable theories cannot reproduce the predictions of quantum theory for sequential measurements, even when the degrees of freedom of the measuring apparatus are taken into account. Bohmian mechanics, however, does not fall in this category. We finally examine an alternative proposal that sequential measurements can be modeled by a process that does not satisfy the Kolmogorov axioms of probability. This removes contextuality without introducing non-locality, but implies that the empirical probabilities cannot be always defined (the event frequencies do not converge). We argue that the predictions of this hypothesis are not ruled out by existing experimental results (examining in particular the "which way” experiments); they are, however, distinguishable in principle. Springer Science+Business Media, LLC, 2006 sequential measurements nationallicence quantum probability nationallicence stochastic processes nationallicence decoherent histories nationallicence quantum measurements nationallicence contextuality nationallicence Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/11(2006-11-01), 1601-1661 0015-9018 36:11<1601 2006 36 10701 https://doi.org/10.1007/s10701-006-9077-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10701-006-9077-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Anastopoulos Charis Department of Physics, University of Paras, 26500, Patras, Greece aut NATIONALLICENCE 773 0- Foundations of Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 36/11(2006-11-01), 1601-1661 0015-9018 36:11<1601 2006 36 10701 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer