Effects of the free evolution in the Arthurs–Kelly model of simultaneous measurement and in the retrodictive predictions of the Heisenberg uncertainty relations
| Autor: | J. A. Mendoza-Fierro, V. M. Velázquez Aguilar, L. M. Arévalo Aguilar |
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| Rok vydání: | 2021 |
| Předmět: |
Quantum Physics
Uncertainty principle Gaussian FOS: Physical sciences General Physics and Astronomy Probability density function Observable Momentum symbols.namesake Position (vector) symbols Statistical physics Quantum Physics (quant-ph) Reduction (mathematics) Hamiltonian (control theory) Mathematics |
| Zdroj: | The European Physical Journal Plus. 136 |
| ISSN: | 2190-5444 |
| DOI: | 10.1140/epjp/s13360-021-01943-6 |
| Popis: | 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. Comment: 24 pages, 3 figures, sent for publication |
| Databáze: | OpenAIRE |
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