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Simultaneous measurement of non-commuting observables in entangled systems

The European Physical Journal Special
Erik F.G. van HeusdenTheodorus M. Nieuwenhuizen Institute for Theoretical Physics,
University of Amsterdam,
The Netherlands
2019 Physics

In an EPR setup, simultaneous measurement of two non- commuting observables is considered at station A and, possibly after a time delay, at station B. At each station one apparatus measures the z-component of a spin, while a second one measures the x-component of the same spin simultaneously. The dynamics of the measurements is solved explicitly. It is shown that no violations of Bell inequalities occur in Bell-like correlation experiments, and that, in fact, experiments of this type are subject to even stronger constraints. This is caused by the mutual influence of the two apparatuses coupled to the same spin, an effect which occurs at both stations.