Simultaneous measurement of non-commuting observables in entangled systems

• Published in: The European physical journal. ST, Special topics Vol. 227; no. 15-16; pp. 2209 - 2219
• Main Authors: van Heusden, Erik F. G., Nieuwenhuizen, Theodorus M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2019; Springer Nature B.V
• Subjects: Atomic; Bell's inequality; Classical and Continuum Physics; Condensed Matter Physics; Materials Science; Measurement Science and Instrumentation; Molecular; Non-equilibrium Dynamics: Quantum Systems and Foundations of Quantum Mechanics; Optical and Plasma Physics; Physics; Physics and Astronomy; Regular Article; Spin dynamics; Time lag
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjst/e2019-800216-2

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.