Quantum information measures of the Aharonov-Bohm ring in uniform magnetic fields

Shannon quantum information entropies S_ρ,γ, Fisher informations I_ρ,γ and Onicescu energies O_ρ,γ are calculated in the position (subscript ρ) and momentum (subscript γ) spaces for the azimuthally symmetric 2D nanoring that is placed into the combintaion of the transverse uniform magnetic field B and Aharonov-Bohm (AB) flux Φ. Position (momentum) Shannon entropy depends on the field as negative (positive) logarithm of ω_eff=(ω₀²+ω_c²/4)^1/2, with ω_c being cylcotron frequency, what makes the sum S_ρ+S_γ a field-independent quantity that increases with the principal n and aizmuthal m quantum numbers and satisfies entropic uncertainty relation. Position Fisher information does not depend on m, linearly increases with n and varies as ω_eff whereas its Onicescu counterpart changes as 1/ω_eff. The products I_ρI_{γ and} O_ρO_γ are both B-independent quantities. Dependence of the measures on the thickness of the ring is discussed. It is shown that position Shannon entropy has the same dependence on the AB flux Φ as the energy spectrum. Other analytic and numerical results for all measures are discussed too and their physical meaning is highlighted.