Quantum Solutions to Stern-Gerlach Experiments

Tilman Sauer

Michel Gondran, Alexandre Gondran

The Stern-Gerlach experiment is the fundamental experiment in order to exhibit the quantization of spin and understand the measurement problem in quantum mechanics. However, although the Stern-Gerlach experiment plays an essential role in the teaching of quantum mechanics, no complete analysis of this experiment using Pauli spinors is presented in the pedagogical literature. This paper presents such an analysis and develops implications for the theory of quantum measurement. We first propose an analytic expression of both the wave function and the probability density in the Stern-Gerlach experiment. Our explicit solution is obtained via a complete integration of the Pauli equation over time and space. The probability density evolution describes a slipping of the wave packet into two separate packets due to the measurement device, but it cannot account for impacts. We therefore calculate the de Broglie-Bohm trajectories, which not only explain impacts naturally, but also accounts for the spin quantization following the magnetic field gradient. It is then possible to propose a clear explanation of measurement effects in the Stern-Gerlach experiment.

Mengjun Hu, Haixing Miao, Yongsheng Zhang

The historical significance of the Stern-Gerlach experiment lies in its provision of the initial evidence for space quantization. Over time, its sequential form has evolved into an elegant paradigm that effectively illustrates the fundamental principles of quantum theory. To date, the practical implementation of the sequential Stern-Gerlach experiment has not been fully achieved. In this study, we demonstrate the capability of programmable quantum processors to simulate the sequential Stern-Gerlach experiment. The specific parametric shallow quantum circuits, which are suitable for the limitations of current noisy quantum hardware, are given to replicate the functionality of Stern-Gerlach devices with the ability to perform measurements in different directions. Surprisingly, it has been demonstrated that Wigner's Stern-Gerlach interferometer can be readily implemented in our sequential quantum circuit. With the utilization of the identical circuits, it is also feasible to implement Wheeler's delayed-choice experiment. We propose the utilization of cross-shaped programmable quantum processors to showcase sequential experiments, and the simulation results demonstrate a strong alignment with theoretical predictions. With the rapid advancement of cloud-based quantum computing, such as BAQIS Quafu, it is our belief that the proposed solution is well-suited for deployment on the cloud, allowing for public accessibility. Our findings not only expand the potential applications of quantum computers, but also contribute to a deeper comprehension of the fundamental principles underlying quantum theory.

H. Schmidt‐Böcking, Lothar Ph. H. Schmidt, Hans Jürgen Lüdde +3 more

Meng-Jun 孟军 Hu 胡, Haixing Miao, Yong-Sheng 永生 Zhang 张

The historical significance of the Stern–Gerlach (SG) experiment lies in its provision of the initial evidence for space quantization. Over time, its sequential form has evolved into an elegant paradigm that effectively illustrates the fundamental principles of quantum theory. To date, the practical implementation of the sequential SG experiment has not been fully achieved. In this study, we demonstrate the capability of programmable quantum processors to simulate the sequential SG experiment. The specific parametric shallow quantum circuits, which are suitable for the limitations of current noisy quantum hardware, are given to replicate the functionality of SG devices with the ability to perform measurements in different directions. Surprisingly, it has been demonstrated that Wigner’s SG interferometer can be readily implemented in our sequential quantum circuit. With the utilization of the identical circuits, it is also feasible to implement Wheeler’s delayed-choice experiment. We propose the utilization of cross-shaped programmable quantum processors to showcase sequential experiments, and the simulation results demonstrate a strong alignment with theoretical predictions. With the rapid advancement of cloud-based quantum computing, such as BAQIS Quafu, it is our belief that the proposed solution is well-suited for deployment on the cloud, allowing for public accessibility. Our findings not only expand the potential applications of quantum computers, but also contribute to a deeper comprehension of the fundamental principles underlying quantum theory.

Jonah Maxwell Miller