Abstract
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.
Highlights
Spontaneous collapse models of state vector reduction represent a possible solution to the quantum measurement problem
Various extensions of quantum mechanics have been developed that lead to dynamical models for the collapse of the wave function
Continuous models have been been devised, in which the spontaneous collapse of the quantum state is realized in the form of a continuous stochastic process in Hilbert space
Summary
Let the set of compatible quantities characterizing the discontinuous stochastic process be. The parameter rules the accuracy of the sharpening and ai is the centre of the i-th hitting. It is assumed that the hittings occur randomly in time, distributed according to a Poisson law with frequency. The sharpening operator for the i-th hitting Si acts on the normalized state vector t⟩ giving the state vector.
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