A Stern-Gerlach setup for the measurement on a quantum system (spin-$$ $\frac{1}{2}$ ) with a macroscopic quantum apparatus (the particle trajectory) produces a Schr\"odinger-cat-like superposition in which the spin states correlate with wave packets centered around macroscopically distinguishable positions and momenta. When an interaction with an environment is included, the pure density matrix of the system-apparatus combination reduces to a statistical mixture in the spin space, and exact solutions show that the decoherence time for this reduction goes inversly as the macroscopic separation between the two parts of the superposition correlating with up- and down-spin states. This is consistent with Zurek's approximate result for the decoherence time, and the persistence of system-meter correlations at large times makes it an interesting candidate to look at experimentally.A Stern-Gerlach setup for the measurement on a quantum system (spin-$$$\frac{1}{2}$) with a macroscopic quantum apparatus (the particle trajectory) produces a Schr\"odinger-cat-like superposition in which the spin states correlate with wave packets centered around macroscopically distinguishable positions and momenta. When an interaction with an environment is included, the pure density matrix of the system-apparatus combination reduces to a statistical mixture in the spin space, and exact solutions show that the decoherence time for this reduction goes inversly as the macroscopic separation between the two parts of the superposition correlating with up- and down-spin states. This is consistent with Zurek's approximate result for the decoherence time, and the persistence of system-meter correlations at large times makes it an interesting candidate to look at experimentally.

Physical Review ANov 1, 199719 citations

Theory of Quantum Measurement in Terms of Quantum Chaos

Nobuhiko Saitô

Quantum non-integrable systems have pseudochaos in the phase of the eigenfunctions. In particular, correlation function of wave functions at two different points disappears, when observation process, which requires space and/or time average over a small range, is taken into account. This gives rise to the realization of decoherence in measuring processes. By virtue of this property of quantum chaos, various problems and paradoxes are explained in the framework of conventional quantum mechanics. The subjects treated here are the duality of wave and particle, the wave function collapse in measurement, Stern–Gerlach experiments, Schrödinger's cat paradox, the Einstein–Podolsky–Rosen paradox and quantum Zeno effect.Quantum non-integrable systems have pseudochaos in the phase of the eigenfunctions. In particular, correlation function of wave functions at two different points disappears, when observation process, which requires space and/or time average over a small range, is taken into account. This gives rise to the realization of decoherence in measuring processes. By virtue of this property of quantum chaos, various problems and paradoxes are explained in the framework of conventional quantum mechanics. The subjects treated here are the duality of wave and particle, the wave function collapse in measurement, Stern–Gerlach experiments, Schrödinger's cat paradox, the Einstein–Podolsky–Rosen paradox and quantum Zeno effect.

Journal of the Physical Society of JapanJun 15, 20041 citation

A Logical Encounter of the Schrödinger’s Cat Paradox

R Azhagu Raj

AxiomathesAug 26, 20211 citation

A Simple Approach To Measurement in Quantum Mechanics

Anthony Rizzi

A simple way, accessible to undergraduates, is given to understand measurements in quantum mechanics. The ensemble interpretation of quantum mechanics is natural and provides this simple access to the measurement problem. This paper explains measurement in terms of this relatively young interpretation, first made rigorous by L. Ballentine starting in the 1970's. Its facility is demonstrated through a detailed explication of the Wigner Friend argument using the Stern Gerlach experiment. Following a recent textbook, this approach is developed further through analysis of free particle states as well as the Schrodinger cat paradox. Some pitfalls of the Copenhagen interpretation are drawn out.A simple way, accessible to undergraduates, is given to understand measurements in quantum mechanics. The ensemble interpretation of quantum mechanics is natural and provides this simple access to the measurement problem. This paper explains measurement in terms of this relatively young interpretation, first made rigorous by L. Ballentine starting in the 1970's. Its facility is demonstrated through a detailed explication of the Wigner Friend argument using the Stern Gerlach experiment. Following a recent textbook, this approach is developed further through analysis of free particle states as well as the Schrodinger cat paradox. Some pitfalls of the Copenhagen interpretation are drawn out.

arXiv:2003.03413Mar 4, 20201 citation

A Stern-Gerlach setup for the measurement on a quantum system (spin-$$

\frac{1}{2}

) with a macroscopic quantum apparatus (the particle trajectory) produces a Schr\"odinger-cat-like superposition in which the spin states correlate with wave packets centered around macroscopically distinguishable positions and momenta. When an interaction with an environment is included, the pure density matrix of the system-apparatus combination reduces to a statistical mixture in the spin space, and exact solutions show that the decoherence time for this reduction goes inversly as the macroscopic separation between the two parts of the superposition correlating with up- and down-spin states. This is consistent with Zurek's approximate result for the decoherence time, and the persistence of system-meter correlations at large times makes it an interesting candidate to look at experimentally.