![Schematic representation of a single detector setup for generating and measuring superposition state. A single photon is emitted from the source and hits a beam splitter (BS), generating a superposition of |γ⟩R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$| {\gamma } \rangle _R$$\end{document} and |γ⟩L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$| {\gamma } \rangle _L$$\end{document}, namely |ψ⟩=cL|γ⟩L+cR|γ⟩R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$| {\psi } \rangle = c_L| {\gamma } \rangle _L+c_R| {\gamma } \rangle _R$$\end{document}. A single photon detector (SPD) is placed in R position.](https://www.researchgate.net/publication/356165249/figure/fig4/AS:1089557843976260@1636782241771/Schematic-representation-of-a-single-detector-setup-for-generating-and-measuring_Q320.jpg)
![N=1000\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N=1000$$\end{document} paths of the probability of having the single photon state in the R sector (|cR|2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|c_R|^2$$\end{document}) as function of t in case of a single photon detector with γ=γ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma = \gamma _1$$\end{document} (see also Fig. 1). The time scale in ns =10-9\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$=10^{-9}$$\end{document} s. For all the figures, in blue are the paths for the case without the von Neumann activation delay for the detector, in red are the paths with von Neumann activation for T=10-4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T=10^{-4}$$\end{document} ns.](https://www.researchgate.net/publication/356165249/figure/fig5/AS:1089557843976290@1636782241952/N1000documentclass12ptminimal-usepackageamsmath-usepackagewasysym_Q320.jpg)
November 2021
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Spontaneous collapse models of state vector reduction represent a possible solution to the quantum measurement problem. In the present paper we focus our attention on the Ghirardi–Rimini–Weber (GRW) theory and the corresponding continuous localisation models in the form of a Brownian-driven motion in Hilbert space. We consider experimental setups in which a single photon hits a beam splitter and is subsequently detected by photon detector(s), generating a superposition of photon-detector quantum states. Through a numerical approach we study the dependence of collapse times on the physical features of the superposition generated, including also the effect of a finite reaction time of the measuring apparatus. We find that collapse dynamics is sensitive to the number of detectors and the physical properties of the photon-detector quantum states superposition.
