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arXiv · 2109.00581

Effects of the free evolution in the Arthurs-Kelly model of simultaneous measurement and in the retrodictive predictions of the Heisenberg uncertainty relations

J A Mendoza-Fierro·L M Arévalo Aguilar·V M Velázquez Aguilar
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Abstract

The simultaneous measurement approach of Arthurs and Kelly has been a significant tool for the better understanding of the measurement process in quantum mechanics. This model considers a strong interaction Hamiltonian by discarding the free evolution part. In this work, we study the effect of the full dynamics -- taking into account the free Hamiltonian -- on the optimal limits of retrodictive and predictive accuracy of the simultaneous measurement process of position and momentum observables. To do that, we consider a minimum uncertainty Gaussian state as the system under inspection, which allows to carry out an optimal simultaneous measurement. We show that the inclusion of the free Hamiltonian induces a spreading on the probability density of the measurement setting, which increases the value of the product of the variances of the so-called retrodictive and predictive error operators, this is equivalent to a reduction in the accuracy of the measurement.

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J A Mendoza-Fierro, L M Arévalo Aguilar, V M Velázquez Aguilar. 2021-09-01. Effects of the free evolution in the Arthurs-Kelly model of simultaneous measurement and in the retrodictive predictions of the Heisenberg uncertainty relations. https://doi.org/10.1140/epjp/s13360-021-01943-6

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