For a Landau electron, position-shift estimation with mechanical momenta gives a lower quantum Cramér-Rao bound than with canonical momenta, and thermal noise makes the canonical bound a piecewise envelope of SLD and RLD bounds.
We can show that this holds for Model 1 and Model 2
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Uncertainty relation for the position of an electron in a uniform magnetic field from quantum estimation theory
For a Landau electron, position-shift estimation with mechanical momenta gives a lower quantum Cramér-Rao bound than with canonical momenta, and thermal noise makes the canonical bound a piecewise envelope of SLD and RLD bounds.